 probably is. These are already flowing in. How are you, Nikola? I mean, I'm well how are you? Yeah, nice to see you. Likewise. Last time was in Uppsala where we were eating chocolate cake in the sunshine, like with other real humans. Tanishi were almost live, so be a bit cautious. Hi, Ralph. Oh, it's so nice to see everyone. Isn't it? Nikola, the title of your talk is really inspiring. Well, I didn't give an abstract deliberately because I thought maybe the abstract won't sound as good as the title. Very nice. But I'll try. I'll try. I once gave a talk about world peace through DFT, so. Okay. Okay. Yeah. It didn't work, did it? I'm working on it. Okay, I trust you, Shobana. I think you're about our last hope. Time, I guess. Yeah. Do we start? How do I know when to start? You will tell me, Nikola? Just start. Yes, I think you can start. Yes. Okay. Hello, everybody. Welcome to the second day of the Total Energy Workshop. I am Shobana Narasimhan from the Jawaharlal Nehru Center for Advanced Scientific Research in Bangalore, and I will be chairing the talks today. So first, we have a plenary talk by Nikola Spauldan from Ipihar Zurich, and she has, as you can see on the screen, a rather interesting and provocative title of finding happiness and saving the world through electronic structure calculations. Nikola, it's all yours, and I will remind you when you have five minutes left. Okay. Thanks a lot, Shobana, and thank you to the organizers, Nikola Silke, Francesco and Tanushri for their hard work in putting this workshop together. When Nikola first asked me to speak, he emphasized the importance of keeping our community together, even though we can't meet in person, and I very much appreciate that sentiment, particularly for our junior colleagues who you're missing out not only on the usual exchange of information in a conference, but also on this opportunity to develop your professional identities as part of this very rich electronic structure community. So I hope that we can help a little bit with that sense of identity today with this virtual workshop, and even if I can't help you with that, I hope to at least convince you that you have the computational and physics tools both to find happiness and to save the world. So I thought we should start by congratulating ourselves a little bit and reflecting on the really important technical developments that our community has made. So I made a list here of some of my favorite papers in electronic structure theory over the kind of lifetime of my generation, and I thought we could have a people's choice vote on what are our favorites. So the first two, I think everybody is very familiar with the Hohenberg-Kohn and Kohn-Sham papers really introducing the density functional theory formalism. The second two, any of you who ever did an LDA calculation will have used these. The separately older paper is the quantum Monte Carlo calculation of the exchange and correlation in the interacting electron gas and the Purdue-Zunger parameterization of that, and of course we had the wonderful opportunity yesterday to hear from Alex Zunger about his recent work. The third one, of course, car-paranello molecular dynamics, and tomorrow you'll hear from Michaela Paranello about his recent work. And then the last two have a little bit of a triester connection since we can't actually be there today. Raphael Arrester and David Vanderbilt's development of what we now call the modern theory of polarization. So let me start a poll and give you 30 seconds. You should now see a poll and you have the option to vote for one of these options. If you want to vote for a different paper, then you can enter it in the chat and then maybe Shobana can track and see if you see anything interesting that we should share with everybody. Oh, this is really interesting. I can see the results coming in. And it says, host and panelist cannot vote. Oh, okay. But we have already, we have 160 votes already, so it's enough. Okay. Pretty much what I was expecting. Some votes are still pouring in. I can't show you it until I end the poll, I think. So, okay, we're slowing down. Quick, anybody, if you want to enter. Is there anything in the chat, Shobana? Any others? No, there isn't. Okay. So let me end the poll and you can see. I guess that's pretty much what I expected, that by far the favorite is the Honeburg cone sham papers. But the others all got, yeah, they're kind of share of the votes between them. Very good. Sorry, Alex. I think the youngsters don't appreciate the importance of the, your parameterization of the LDA functional. Do you all see it now? Yeah. Oh, sorry. Yeah. Now you see it probably. Yeah. So the original DFT papers are clear favorites with the others kind of sharing between them. So what I want to talk about today though is one that actually didn't win the people's choice, which in my opinion is one of the great breakthroughs of the last decades in electronic structure theory and density functional theory. And that's the work by Raphaela Restor and David Vanderbilt and many other contributors on the theory of polarization. And because this is the, these are the papers that are really going to lead us to happiness and saving the world. So let me quickly, for the sake of all of the students, remind you of the problem that was solved in the early 90s. So back then in kind of prehistoric times for some of you, what we didn't know was whether the polarization of a bulk periodic solid, a periodically repeating solid was actually a bulk quantity or a surface quantity. And we didn't know how to define it. And so of course the polarization in a molecule, the dipole of a molecule, there's no difficulty associated with that. But if we have an isolated molecule with a negative ionic charge and a positive ionic charge, the electronic charge E, then the dipole is just E times D pointing from negative to positive. There's no ambiguity, there's no issue there. In a periodic solid, the intuitive way to define the polarization is this the dipole per unit volume. And so if we put our molecule in a unit cell and periodically repeat it, then we could just say it's the dipole per unit cell divided by the volume per unit cell. And so we'd get the same polarization E times D divided by the volume of the unit cell. But of course, because our system is periodic, we have many possibilities of how we can choose the unit cell. And so let me, as an example, take this for our unit cell, unit cell of size A. And now you see if we take the dipole per unit cell and divide it by the unit cell volume, we have two problems. We get that the polarization is pointing in a different direction, right? It's going from negative to positive. So now it's going to the left. And it has a different size. It's this distance now A minus D over V. I'm going to rewrite that as E times D over V minus E times A over V. This was the polarization we got last time, and it's changed by this amount. And this thing is going to reappear. It has a special name. It's called the polarization quantum. Okay, so this was a problem. This was a problem in the late 80s, early 90s. The problem got even worse if you think about a one-dimensional chain of ions that's centrosymmetric. So here's an example. My negative and positive ions are all spaced by the same distance D. And clearly this is a non-polar chain, right? If I sit on this positive ion, I have negative ions equally spaced to either side of me. There's no dipole moment associated with this chain. But if I do the same procedure and calculate the dipole moment per unit cell, I don't get zero. I get minus E the charge times D over V for this unit cell or plus E times D over V for this unit cell. And if I keep going and choose other unit cells, let's say I took a really strange looking unit cell with this cation and this anion in it, I find that I got always E times D over V plus some integer number of this thing we labeled before the polarization quantum, E times A over V. So this is very, very weird, right? I have a centrosymmetric chain and it's non-polar, but its polarization can never be zero with this recipe. In fact, the polarizations, the allowed polarizations that I can make by taking different unit cells are equally spaced. I've sketched, I've just drawn as a cartoon, some of them, some of them here. There's no zero, but what you can see is that they're centrosymmetric, right, around zero. So, oops, so I have a centrosymmetric chain. It never has zero for its polarization, but it has this series of polarization values, which makes a centrosymmetric set of values. And they're separated by this thing, E times the lattice constant divided by V, which we call the polarization quantum. Okay, so this was the problem that needed solving in the late 80s. And this modern theory of polarization solved these problems. And here, I'm not going to derive this theory today, but I just want to write down the key results that are in those papers we looked at right at the start and which I'm going to be needing to use today. So the first thing is that the polarization of a periodic insulating solid really is a bulk property. It's not a property of the surface, it's a bulk property, and it's, but it's multi-valued. It doesn't have a single value. It's unique, but it's multi-valued. And so it's given by some amount plus N times this polarization quantum. And the polarization quantum, what it corresponds to is taking an electronic charge and displacing it by a lattice vector. And of course, in a periodic solid, that doesn't change the physics of the system because always an electronic charge comes to fill in the one that's moving because if it's moved because of the periodicity, but it does change the polarization by E times R divided by the volume. So this is the origin of this ambiguity. It was also a key result of this modern theory of polarization that centrosymmetric insulating periodic solids have centrosymmetric, what we call these values of polarization, the polarization lattice as a centrosymmetric series of values allowed for the polarization. And it's possible for this to contain zero or it has to contain half a quantum, otherwise that's the only two ways you could make centrosymmetric series of numbers. And this all seemed a bit weird except what was also noted was the differences between polarizations. So for example, the spontaneous polarization between a para-electric centrosymmetric structure and its ferroelectric state, the measurable part of the ferroelectric polarization, these are single-valued. So there was actually no ambiguity between theory and experimental reality. So I very much recommend that you go read that last set of papers on our poll at the end. And if you want a kind of easy introduction, I also have a kind of beginner's guide to the modern theory of polarization that avoids a lot of the tricky mathematics and a YouTube series. So if you prefer to watch the movie rather than read the book, you can also work through it very at a gentle pace on YouTube. Okay, so that's the kind of little introduction for the newcomers to this area for some of the students who might not have been familiar with this topic. Now I want to apply it to some real material. And the material that I'm going to discuss today, I'm going to talk about just one particular polarization in one particular specific material is a perovskite structure oxide, bismuth ferrite, bismuth ion oxide. So bismuth oxide, bismuth ferrite is multi-feroic. So it has the combined property of being ferroelectric. It has a spontaneous ferroelectric polarization, a spontaneous electric dipole, and it's also magnetic. It's actually anti-ferromagnetic. And so its crystal structure is the perovskite structure. So it has an ion ion at the center of an octahedron of oxygens. And these ion ions are magnetic, of course, they have five 3D electrons. So they have a very large magnetic moment. And they're anti-ferromagnetically coupled to each other by the usual super exchange through the oxygen. They have a little small magnetic moment because the moments count a little bit to give a small net magnetic moment. The bismuth ions, it's bismuth, it's 3 plus trivalent bismuth, which has a very strong stereochemically active lone pair of electrons. So the bismuth shifts by a large amount, large fraction of the unit cell along the 111 direction relative to the rest of the ions. And that gives it a rather large spontaneous polarization along the 111 direction. So bismuth ferrite is very popular because of this multi-feroic property, this combination of the magnetic ordering and the ferroelectric ordering, both at rather high temperature, which allows it to be used for exotic behaviors, for example, controlling the magnetism with an electric field. Bismuth ferrite is not a new material. Here's a actually rather beautiful crystal from Hans Schmidt's collection of, you see it's rather large, two centimeters across crystal of bismuth ferrite. It's very attractive. These kind of fern-shaped textures are because of twinning in the crystal. So it's a really beautiful piece of crystal, but it's of course not very good for doing ferroelectric measurements and so on. So with this crystal, it was not established that bismuth ferrite was a good multi-feroic. And it was really only in the early 90s, sorry, in the early 2000s when largely the group of Ramesh succeeded in growing bismuth ferrite thin film. So this is a high-resolution transmission electron micrograph from Marta Russell. It's now at Impa. And you see here the very bright white dots are the bismuth atoms. The faint white dots are the iron. You don't see the oxygens in this image. And you see that this is a thin film and it's very, very perfect. So one could, with such films, really do physics, do very detailed characterization. And so it was measured that there is indeed a very large, spontaneous ferroelectric polarization associated with these bismuth ferrite thin films. It's 90 microcoulombs per square centimeter along the 1, 1, 1 direction, or perpendicular to the film direction along the 0, 0, 1 direction perpendicular to the film. It's around 50 microcoulombs per square centimeter. Okay. So now with the thin films, one can really do science and engineering with the bismuth ferrite. But there's a problem when one starts working with ferroelectrics in thin films. And that's that when one has a ferroelectric polarization, when one has a polarization, then there's a charge associated with the surface perpendicular to that polarization. And one can see that rather intuitively, if you think about just the units of polarization, it's dipole per unit volume, which is charge per unit area. Usually it's reported in microcoulombs per square centimeter. And so if there's a polarization of a certain 50 microcoulombs per square centimeter, that means that one end of the thin film, there's a charge on the surface of the magnitude of the same size as the polarization. And of course, it's negative on the bottom end and positive on the top end of the polarization. And this is a problem. Of course, if you have a very charged surface, it's electrostatically unstable, and it's very unhappy. It doesn't want to remain in this configuration. And so this is bad news. If you want to make ferroelectric devices, usually it leads to suppression of the polarization. For example, the polarization might decide to lie in the plane of the film. It might form domains. It might screen by making electron-hole excitations across the gap to make the surface metallic and screen the surface charge that way. Or it could even adopt a different phase, which is non-polar. It could go into the para-electric state. So I want to show you where this surface charge in bismuth ferrite actually allowed us to do something positive, which was to stabilize a rather interesting phase that has this property of having zero polarization. And it's a phase that's not the ground state if one doesn't have this special electrostatics, but it becomes the lowest energy phase as a result of the need to screen the surface charge. And so this is work done by Julian Mundi who is now at Harvard and Bastien Grocer, who's a student in my group and our collaborators. And let me show you first the high-resolution transmission electron micrograph. This is very beautiful. So this is a heterostructure of lanthanum ferrite, which is a non-ferroelectric insulator. Then bismuth ferrite, the material of ferroelectric multi-ferroc that we've been discussing. And then lanthanum ferrite again. And I'll return to this point later. It's very important that it's lanthanum ferrite here. It's very important that lanthanum is a trivalent ion just like bismuth. I'll come back to that point later. And the micrograph has been artificially colored such that the blue color is showing bismuth atoms that have shifted upwards relative to the average. And the red color is showing bismuth atoms that have shifted downwards. So normally if this were the usual ground state, the ferroelectric ground state of bismuth ferrite, all the bismuths would have gone in the same direction. That would have given it the electric dipole. But here they're going up and down in pairs. And here's a blow-up of, I'm losing my mouse, sorry, the blow-up of this section here. We see that two of the bismuths have gone up and two of the bismuths have gone down. And so this structure, if you just kind of count the dipoles, this structure is antipolar. It has dipoles. It has local dipoles. We can see that we have net displacement between the bismuths and the ions. But some of them are going in one direction and some of them are going in the other direction. So using density functional theory, Bastien Grosse was able to identify this phase. He was able to find a metastable phase, which from whichever angle we looked at it, when we compared it with the transmission electron micrographs, we saw the same patterns of the bismuths and ions. And he showed that this phase was rather low in energy relative to the ground state. It was higher in energy than the ground state, but not by very much. It was rather close in energy to the ground state phase. We're allowed to call it antifurroelectric, because at least in the computer, Bastien found a pathway by which he could take this phase with its opposite dipoles into a phase which was furroelectric with the dipoles lined up. And that's a requirement for a system to be antifurroelectric, not just antipolar. The other thing that Bastien was able to show with a simple electrostatic model was that when one applies an electric field to this antifurroelectric structure, which is stable only in the heterostructure because of the electrostatic boundary conditions, when one applies an electric field of about a thousand kilovolts per centimeter, then the furroelectric ground state becomes more stable. So this is Bastien's calculation of the energy as a function of applied electric field. Of course, the non-polar structure doesn't care about the electric field. It doesn't change its energy, but the R3C phase comes down in energy. And this is for a heterostructure, which is why the ground state, the polar state is initially higher in energy because of the electrostatic boundary condition. And so let me show you the measurements then. This is a measured polarization as a function of electric field. And sorry, I have to move all the thumbnails to be able to point. And you see that with no electric field, there's no polarization. When an electric field is applied, it switches and becomes a polar structure. So this is very exciting. This is our first example of saving the world with electronic structure calculations. Here's a schematic of all of the sustainable development goals that have been identified by the United Nations, and two of them are, of course, action on climate and affordable and clean energy. And usually when we think of materials for alternative energy, we think of photovoltaics, energy harvesting materials. But of course, energy storage materials, materials that we can store off the grid are very important, too. And antifurororelectrics are very promising in this direction. Okay, but for happiness, to find happiness, there's another aspect of bismuth ferrite that we need to understand. And that comes back to this weirdness of centrosymmetric materials having polarization lattices that don't contain zero. And bismuth ferrite is actually an example of one of these. In its centrosymmetric structure, in its high symmetry perovskite structure, where the bismuth ions are not displaced, this is the structure of this bismuth ferrite at very high temperature, the so-called para electric structure, the polarization lattice contains the half quantum. And let me just quickly demonstrate that. If I am calculating the polarization in the 001 direction, and if I take this to be my unit cell, and these atoms to be my basis, then the positive layer from the bismuth 3 plus oxygen 2 minus is at zero. And the negative layer, which has charged minus e, is halfway along the unit cell. So my polarization, the dipole per unit volume, is minus e times a over 2b. If instead I choose my unit cell like this, then my negative layer is at zero, and my positive layer is halfway up the unit cell, my polarization is plus e times a over 2b. Which is just, and if I took different unit cells, I'd get different numbers, they'd all be spaced by the polarization quantum, and this first number is half a quantum and so on. If I put in the actual numbers, I find that half the polarization quantum is 50 micro coulombs per square centimeter. So the polarization lattice of bismuth ferrite in its centrosymmetric form is contains half, contains 50 micro coulombs per square centimeter, this is the half quantum. And if you remember back to when we first discussed the polarization, the spontaneous polarization of bismuth ferrite, the magnitude in the 001 direction is also 50 micro coulombs per square centimeter. This is totally coincidence, it's just a consequence of how much the bismuth atom happens to displace, but by accident, the size of the half quantum, the size of the polarization in non-polar bismuth ferrite is equal to the size of the spontaneous polarization. And actually, this is something we knew already, although I guess I had personally not really kind of registered the implications of this in 2005 with Jeff Neaton, Claude Edderer, Umesh Wegmari, and Karen Rabe, when we calculated the polarization as a function of the distortion in bismuth ferrite. Here you see the different branches of the polarization lattice for the para-electric undistorted phase, here are the values we just looked at, 50 minus 50, 150, and so on. And as we distorted the bismuth ferrite to its ground state para-electric structure, it evolved from a value of say minus 50 to a value of zero. The spontaneous polarization, the switchable bit is this part here, and you see that's the same, whichever branch of the polarization lattice we go along. As I mentioned earlier, this was an important result of the modern theory of polarization. So now if I look at the polarization of ferroelectric bismuth ferrite, you see that one of the allowed values is zero. And likewise, if I switch into the other direction, one of the allowed values for the polarization of bismuth ferrite is zero. So we have this very strongly ferroelectric material, which actually can have a polarization of zero, which seems a little bit counterintuitive. The fact that the internal polarization cancels with the spontaneous polarization also has profound implications for the surface chemistry, though, because it means that the surface charge compensates. So if we look at the surface charge in the centrosymmetric phase, the FeO2 minus surface in the 001 direction turns out has a surface charge of minus 50 microcoulombs per square centimeter. And the bismuth oxygen plus surface has a charge of plus 50 microcoulombs per square centimeter. And I'm not going to go through the details of how one knows that this surface picks out this value from the centrosymmetric polarization lattice, but I strongly recommend this paper from Max Stengel, which details very clearly how one makes this connection. The important point I want to make is that the size of the surface charge from the half quantum in the centrosymmetric phase, by coincidence, is equal to the size of the surface charge from the spontaneous polarization. So we have a surface charge compensation in bismuth ferrite also. Nicola, you have five minutes. Perfect. I shall aim exactly for ending on time. Okay, so then we can see that we have two combinations of polarization orientation and surface termination for which the surface charge from the spontaneous polarization exactly compensates the surface charge from the half quantum polarization. And this is what's going to bring us happiness. So here is my bismuth ferrite thin film. I've chosen bismuth oxygen at the bottom and FeO2 at the top. And so the bottom has an internal positive charge and an internal negative charge at the top. The polarization is opposite. The polarization, the spontaneous polarization is negative at the bottom and positive at the top. So these cancel and we have completely happy electrostatically stable compensated surfaces. There is no driving force for this bismuth ferrite thin film to form domains or to reverse its polarization. Conversely, if I try to switch the polarization, my surfaces are doubly unhappy. They have the unhappiness from the spontaneous polarization, the surface charge from the spontaneous polarization combined with the surface charge from the internal polarization. And we can see this in the calculated density of states. This is the density of states as a function of energy layer by layer through my bismuth oxygen film, bismuth ferrite film. And you can see in the happy situation, there's no internal electric field, the valence band and conduction band, the foamy energies here are constant through the film. Whereas in the unhappy case, there's a very large internal electric field and even at the surfaces it becomes metallic to screen this electrostatic instability. Okay. So on happiness, we can now use this happiness and unhappiness of the bismuth ferrite surfaces to dissociate water. And this is work from Chiara Gattinoni and EPEC FA. And so what we find is on a happy surface, again with our density functional calculations, and this will also allow us to save the world of course, because we can generate hyperconductors. On the happy surface, which is charged neutral, then the molecular water tends to adsorb. Whereas on the unhappy surface, which is very highly charged, dissociative absorption of OH minus or H plus is strongly preferred. And so this gives us a cycle whereby if we start with happy bismuth ferrite, we absorb water, we switch the bismuth ferrite with an electric field and dissociative absorption is preferred. And of course, the ions that are disfavored, then there's a strong driving force for them to leave. So for example, the H plus ions stay on the FeO2 minus surface, the OH minus ions stay on the bismuth oxygen surface. So we've split our water and we've removed, even we have a mechanism even for removing the opposite ions. When we switch back, then we're back to the happy surfaces, the charged ions leave and we re-dissociate molecular water and we can repeat this cycle. The same chemistry can also allow water remediation. This is the work of Salvador Panay from the ETH. And this is some nasty dirodom in B, which is mixed with bismuth ferrite and it breaks down to small benign molecules. And because of the multi-feroic property, you can stimulate this with a magnetic field. So let me stop there. I'll skip over the analogy kind of extension to magnetic behaviors because I want to assign for the students a homework. I give you quite some time to do this homework until the summer of 2065 because I figured you're kind of in your 20s now and that's kind of your retirement time. But you should pick one of these sustainable development goals and with your skills and tools and capabilities work to all solving one of them. So I've shown you some a couple of examples of how electronic structure theory can help with clean water and our oceans and also help with climate action and affordable energy but you can pick whichever one you like and I think you'll find that whichever, wherever you look, electronic structure theory will be able to help. So thank you for listening and I'm happy to take any questions. I have to try and find you all on my screen. You all disappeared. Okay, I've got you back. Okay. Thank you, Nicola, for an excellent talk as always and also for keeping perfect time. You have 516 participants on Zoom as well as several on YouTube. Hopefully not 516 questions. No, there are only a couple. Is Marwan Alam wants to ask a question? Can you unmute yourself and ask your question? Yes. Hello. Hello. I don't see you. Are you there? Okay, I'll just listen. Yeah, I'm okay. I have a question. You can tell yourself, maybe you can introduce yourself briefly and tell us where you're from. Okay, I'm Marwan Alam. I am from Pakistan and I'm a student of physics. Okay, nice to meet you. Thank you for coming. I'm sorry, I'm not here. Are you asking your question? I don't hear you. Can you ask your question, please? Hello. Okay, let me ask his question for you. He asks, what breakthrough can multifarroic materials make if DFT calculations help the experimental researchers who then synthesize it? Okay, so I'd say, okay, that's a good question. What comes first, the DFT calculation or the experiment? And I think in multifarroics, we have many examples where it's really kind of going around, right? So we first started thinking, okay, how could one make a multifarroic? And we thought, okay, bismuth could be good and magnetic ions combining together. And actually, I remember our first DFT calculations, we proposed bismuth manganite for many good reasons, which turned out to be wrong, actually. And so then the experimentalists said, okay, that didn't work. They tried bismuth ferrite. And then we were able to, actually with the data I showed you, then explain why it had such a large polarization. And then so in terms of designing new materials, I think there are many examples. In terms of functionality, also thinking about, for example, how might one with an electric field reorient the magnetism? That's also not so obvious, but it's something that it's perhaps easier to play within the computer, or it's easier to characterize what's happened when you do it in the computer than it is to measure what's happened often. So also in terms of explaining and characterizing materials, I think there's very much been a back and forth between density functional calculations and experiment. I think the question... How the effective is the method of DFT to calculate the multi-properties, for example, the magnetic and the electric properties at the same time? How much effective the DFT is? Yeah, that's a very good question. So actually very standard density functional theory, it does rather good with multi-ferroics. They're not particularly exotic materials. We know that DFT is very good for electric polarization. There are magnetic insulators where... Bismuth ferrite is D5 ion. So even the gap is a huge exchange gap. And so they're not... It's ordered way above room temperature, so we don't even need to use the kind of advanced techniques that Alex Zung had talked about yesterday of trying to... The interesting physics is happening in the magnetically ordered phase. So they're actually quite simple. They're not really... They're not so strongly correlated in the exotic sense. You know, the great big classical spin, certainly for Bismuth ferrite. Yeah, that's a good question. Sorry, I misunderstood. Can Akshay Mahajan ask his question, please? Thank you. Thank you very much. Is Akshay Mahajan there? Can you unmute yourself and ask your question? Okay, I'll ask it again. He asks, what do you views on comparison of 2D intrinsic ferroelectric materials and pin-film ferroelectrics? One problem I know with 2D is out of plane ferroelectricity, ignoring experimental stuff for now. So I'm not sure I entirely understood the question. Yeah, now I can understand. Okay, okay, go ahead. Maybe I can stop going too, because we're just going to put it on the slide. One minute. Okay, yeah. So Professor So right now, there are many first principle calculations on 2D ferroelectrics, where you have just mono-rayers, which could be separated from your 3D structure, like you separate graphene from graphite due to ash material. So most of the people that I've seen tell now how they are first principle calculation only, where they formed intrinsic ferroelectricity within the monolayer itself. So mostly the problem is because there is a small region, so most of the time this ferroelectricity is in plane. So that is one problem, like you have the thin films as well. But there are some people have done some 2D ferroelectrics which have out of plane. So most of the time in those papers, the reason that is given is that the critical thickness problem with this thin films of the ferroelectricity. So that's why in most of the paper which promotes this two-dimensional ferroelectrics, they say that since there is this critical thickness problem for the ferroelectric system, this two-dimensional ferroelectric system will be much better. Yeah, so for bismuth ferrite, these monolays have also been made for bismuth ferrite. I don't think this characterization has been done, but from what we understand, bismuth ferrite should have an out of plane polarization with zero depolarizing field, right? Because of this cancellation between the surface charge from the centrosymmetric layering and the surface charge from the spontaneous polarization. So it should be stable and polar, but it should be really hard to switch because the opposite orientation is doubly unhappy than just a regular ferroelectric. So it's special in that case in that one can make a really stable polar very thin film with no, which is not electrostatically unstable, but it's much, much more difficult to switch. I think for something like a regular ferroelectric that doesn't have this special property, then the polarization is always going to go in the plane. Okay. I think we have time for just one last question. So Shashi Bhushan Mishra wants to ask you a question. Can you unmute yourself and ask the question, please? Is Shashi Bhushan Mishra there? It seems like I'm having to ask all the questions today. Why on happy surface water splits, but on other it didn't dissociate? Okay. So my naive understanding is that when you have a completely uncharged surface, then you're more likely to favor molecular adsorption. Whereas if your surface is strongly charged, you're more likely to favor adsorption of charged species that are opposite in charge to the charge of the surface. That's maybe a little naive. I could also just give you the trivial answer. We did the DFT calculations in both cases, adsorbing the molecule and the dissociated species. And we found that it was lower energy to adsorb molecular on the uncharged surface and to adsorb dissociated on the charged surface. So maybe my naive understanding is right. It's not correct. Okay. I think we're out of time. Yeah. Is it due to electric field? Hello? Yeah. So I think, I mean, I think my intuition is that it's the different electrostatic certainly surely contributes, whether it's the only effect that I don't. Okay. I think we will wind up this session now. If you have further questions, I'm sure Nikola would be happy to answer them offline. I'm volunteering your services, Nikola. So we have a short break for about eight minutes now and then we'll come back with the rest of the talk. So you can go have a quick coffee and come back. Thank you. Thanks a lot for your interest, everybody. Thanks, Jovanna. I couldn't see the chat. So I couldn't see what people were asking. So it's great that you read them. Yeah. I think there are a lot of them are from students starting out, I would guess. But that's maybe nicer because they're less reluctant if you read them than if they have to interrupt. Yeah. And then there's some questions on the YouTube also about why cone sham, etc. So Alex Tunger had raised hand, maybe he wanted to. Oh, I didn't see that. Well, you can chat now. I didn't see that. Is he there? I think he also left for coffee. Okay. Yeah. I didn't see the, I also couldn't see the raised hands. I tried to scroll through and see if there were any raised hands, but I couldn't see them and there too many to keep track of. So you think we would have sorted out this Zoom business by now? I'm still on my tiny laptop. I'm like holding out buying a big screen for home because I keep thinking we've got to get back to the office soon, you know, so it's tiny little laptop screen. Oh, hello, Max. You just popped up in a square. See you. Hi, Alex. Shall we try to share screen with the speakers? Yeah. So is Madil Mustafa there? Yes, I'm here. Am I saying your name right? Oh, it's Hadil. Yeah, it's Hadil Mustafa. Am I saying it correctly? Yes. So yeah, so that we're not seeing, we're seeing it in your presenter's view. So can you go to the full screen view? We're still seeing your, we're seeing it in the editing mode. I was sharing and do it again. Yeah, screen. What about? No, just make it full screen. Okay. You know, at the bottom, yeah, you click on, yeah, now it's fine. Yeah, it's fine. Okay. So maybe I'll check with the next person. Ibanez Asperon. Yeah. Can you hear me? Can you tell me how to say your name? It's Yulen. And the surname is Ibanez Asperon. But if it's too complicated, Yulen, it's enough. Oh, that isn't there on the program. So how is that spelled? The name, Yulen. Yulen. Exactly. Okay. All right. Yulen Ibanez Asperon. Can I try to share my screen? Yes, please. Hadil Mustafa, can you stop sharing please? Yes. So I will share the screen. Yeah, it looks fine. Perfect. Okay. Well, just in case before I start speaking, I will ask whether you hear me and I will Yeah, yeah, of course. Then I will start speaking. Yeah. And Ketano, are you there? Yes. Let me try to share my screen, Shobana. Yeah. You need to go full screen. Is it? Yeah, that's fine. Great. And Georgia Dungich? Hi. Yeah. Am I saying your name correctly? Yeah, it's perfect. Okay. I will try to share. Do you see it in full screen mode? Yes, I do. Thank you. Okay. So each of you have 18 minutes for your talk and three minutes for questions. How many minutes before the end would you like me to give you a warning? Three minutes or five minutes? So what would be good? Five minutes is good, but I think that I will finish before the 18 minutes. Okay. All right. So I'll tell you when you all have five minutes left. So we will start in another minute. So you can already start sharing your screen. Yeah. You still need to go full screen. Yeah, that's fine. No, now it's not okay. Okay. Yeah, this is okay. Do you want to just try changing your slides just to check that that works? Yeah, that's okay. So you can go back to your bed. Okay. So we'll start with the shorter talks now. So the first talk is by Havil Mustafa from the Technical University of Denmark. And she will talk about investigation of one-dimensional materials. And I just want to remind all of you that if you have questions for the talk, because it's a bit hard for me to keep track of our raised hands when there are so many participants, it would be good if you just type your questions into the chat box. Please go ahead. So thank you for the presentation. And thanks for Organizer. And finally, thank you for having me here. So I'm trying to make a database for my one-dimensional materials with their calculated properties. So if we take a look on one of the materials, it will look like that. So here I have the 1D component and some structure information. And here I have all the calculated properties, the thermodynamic stability, the phonons, the basic electronic properties, the band structure calculated using PBE, the effective masses, the band structure calculated using HSE. And finally an overview of all the items that have been calculated. So what is a one-dimensional material? A material is said to be one-dimensional if it's a periodic in one direction and has limited extension in other directions. So it's a chain of atoms. One-dimensional materials are interesting subset of materials with the promising application in different fields. And here I have three different examples. In the first one, the 1D component is titanium sulfur with the chains, which has been used as a transistor. And in the second one, the 1D component is the tantalum selenide, which has been used for application as a small nanowire and interconnect. And the final last example is a more complicated structure of the 1D component, which has a core in the center that are electrically conducted. So for the identification of one-dimensional materials, all the work has been done by Peter Lassen, where he made a screening that applied for the inorganic crystal structure database and the crystallographic own database, where the dimensionality of a material is determined based on the interatomic distances. And he defined a scoring parameter in order to identify all the low-dimensionality materials. So two materials, i and j, are bounded if the distance between them are less than the sum of the covalent radius, multiplied by a parameter called k. So k is considered as a continuous variable, and that's why they can define a scoring parameter. And the dimension of a component can be determined as the rank of the subspace of the of the atoms and its connected neighbors. So after that, we estimate the dimensionality by using different value of k. So at the low value of k, no bond exists between the atoms, and then we are only dealing with the atoms itself, and then it's zero-dimensional materials. And then when k increases, then the bond begins to sit up between the atoms, and then at a certain value of k, k1, then we have a 1d component that appear, and then when k increases to k2, then the 1d component disappears, and then we have a 2 or a 3d component. So if we take an example here and look at the boron nitride, then at low value of k, then we have a zero-dimensional materials. Then at k1, the covalent bond begins to sit up between the atoms, and then we are dealing with a 2d materials. And then at k2, then the red line appear between the layers, and then we are dealing with a 3d component. So here we see plot for all the structure in ICSD and COD, colored according to their dimensionalities, and here we have all the 1-dimensional materials. This plot is when we are looking at 1-dimensional materials, and it's characterized by a high value of k2 minus k1, and a value of k1 not much larger than 1. And the black line here is the scoring parameter at 0.5. The k2 minus k1 shows also our width of the range. And here we have examples of different dimensionality materials, both the low-dimensional materials, 1 and 2 and 3, and some mixed-dimensionality 1 and 2 and 1 and 3, with a high-squaring parameter for all of them. So from now, we will deal with the 1-dimensional materials. So all the materials that are from ICSD and COD can be found in the CMR database, which stands for Computational Material Repository, and this is our initial database that we will use to find our 1-dimensional materials. And for that we have some criteria. First of all, that the 1d scoring parameter is larger than all the other scoring parameters, both the low-dimensional is 2 and is 3, and also the mixed-dimensional scoring parameters. That the units all include up to 80 atoms and up to four different chemical elements. And the 1d component includes up to 20 atoms. And we remove by hand all the materials that has some issues, be missing atoms, or invalid structure like theoretical structure or partial structure. And then we end up having 287 materials, which is what we will call for our core materials. So for those core materials, we make geometry classification by calculating the 1-square distance between two 1-dimensional systems. And for that we take into account that we ignore the chemical identity of the atoms and only look at the coordinates. The two materials may include different numbers of atoms. And for that we multiply both of them with the lowest multiple of atoms. And finally, rotating and scaling the units along the materials. And here we have our illustration of the root-minus-square distance, where the cluster of similar materials are lying at the diagonal. After that we make a distribution of our distance matrix, where the y-axis is the number of the consider structure. And the peak at zero are represented the diagonal at the distance matrix. And as we also can see that we are dealing with two parts, the first part where the material are close to each other and where they are far away from each other. For that it makes sense to make a separation and we did that at 0.75 function. We make a further analysis by looking at the single linkage clustering, which is characterized as a function of the cutoff distance, which is 0.75. And from that we got 48 groups. 27 of them contain three materials or more. And 13 groups have five materials or more. And here we have the materials that have five or more. And as we can see some of the materials are characterized according to the grouping in the periodic table. As we can see here we have zirconium iodide, zirconium bromide, and zirconium chloride. As we also can see that we have in the first group two zirconium iodide, which is because that they are expanded from two different 3D materials. So now we want to extract our database by making some elements substitution. And in this paper they introduce a probability measure which shows the probability of getting a new stable material when we make a substitution from an element A to an element B, which are shown by the dark color here. And in our case we make an element substitution from A to B with a probability measure that is larger than 0.2. And here is all our substitution that we did. And we get the 565 new structures, which is our shell materials. So for both the core and the shell materials here is our computational workflow, which has two parts. The first part is the structure and the stability, and the second part is the properties. So the structure and the stability, we start by making a relaxation of the cell and the atoms in all the magnetic state. And here we see the magnetic state for the core materials. As we can see, almost all of them are non-magnetic, and some of them are ferromagnetic, and a few of them are anti-ferromagnetic. For the shell materials, almost all of them again are non-magnetic, but now more of the materials are anti-ferromagnetic compared to the ferromagnetic. We looked at the dynamical stability and the thermodynamic stability. For the properties, we calculate the balance structure using PBE and HSE. We calculate the density of state, the work function, and I think masses. The workflow is managed using atomic simulation environment and atomic simulation repository. So we also looked at how stable our one-dimensional materials are, comparing the energy between the 1D and its extracted 3D component. So for that, we make a new calculation where we use the same computational details as in the relaxation, but now instead of using PBE as the strange correlation function, we use PBE3. And as we can see, almost all of them are ranging a bit over zero, which shows that they are slightly unstable. And because of that, we can still extract the 1D from the 3D and calculate their properties. Some of the materials are having a negative value, which means that when we extract the 1D from the 3D, we gain some energy, which means that the 3D are unstable. And these three values are probably wrong, but our calculations are running automatically and something wrong might happen. For the materials that are lying here, that means that the the 1D are unstable and the 3D are more stable, that it's hard to extract the 1D from the 3D. We did the same for the shell materials, and as we can see, almost all of them are also lying a bit above zero, and we have some outliers here. You have five minutes left. Which shows that we have been lucky with our choices as almost all of them are good enough to be done. So for the dynamical stability, the first thing we do when we look at the material is the relaxation. We calculate the relaxation, but as the relaxation only shows that we are on a saddle point, we calculated the dynamical stability, which is the phonon in the cell. And for that, we calculated the forces, which represent the curvature of the potential energy surface. And if the principal curvature is negative, then the structure is unstable. And here I have two materials. This one is stable and this one is unstable. And here we have the three translation mode. For the thermodynamic stability, the convex hole is constructed in the enthalpy space. And as we can see, the blue line is the convex hole, and the blue point here are the bulk references structure, which are all from the open P. And the orange point here are our 1D component. So all the materials that are lying at the convex hole are stable, which means that this one is unstable. And we also looked at the energy difference between the 1D and 3D for the convex hole. And as we also can see, for both the core and the shell, almost all of them are good enough to be done. And we have some outliers again. So for the properties, we are currently investigating some properties. But here I have the band gap energy. As we can see, for the materials that are lying at zero, they are metallic. And the materials that are lying between one and two, they can be interesting for some light absorption. So the conclusion is that we have begun a systematic study of one-dimensional materials using DFT. The materials are classified based on the root mean square distance. We obtained the atomic geometry and other properties like the convex hole and the band structure. We are working on investigating some properties. And the other 1D database can be found in the work from Ivan Reed. And I also know that Nikolai Massari's group are also working with the 1D materials and Hennie. Yeah, that's it. Thank you. Thank you very much. Are there any questions? Let me look on the chat. Okay. So Singara Velan has a question. Can you unmute yourself and ask the question? Okay. Hello. Yeah. Please, can you ask your question? Just I want to know about that convex hole. Yeah. What do you want to know about it? Can you just make your question more specific? What do you want to know about it? Actually, you told about the formation energy, right? Yeah. Then what's the relation between this convex hole and the formation energy? Both are same. So the energy above the convex hole is our formation energy and the materials that are lying at the convex hole are the materials that are Is the question about why one plots a convex hole and what it is used for? Oh, yes. Is that your question? Yes. That is my question. So maybe you can explain to him about why you plot a convex hole to look for phase segregation, etc. Okay. So why I plot the convex hole? Just in order to be sure that our material are stable, so the thermodynamic stability shows how stable our material is and to be sure that our material is stable. So the relaxation only shows that we are on a subtle point and on a subtle point. And that's not enough to be sure that our material is stable or not. Okay. Okay. Thank you. I can explain to you more if you'll write to me, but basically, when you have something with many constituents, you can plot a picture like this and if it doesn't lie on a convex hull, it will phase segregate into other constituents. Okay. Okay. Who else? Said Bahid Hosseini says he has a question you want to ask. Hello. Can you hear me? Thank you very much for your last talk. This is Bahid from University of Tehran, Iran. I'm going to ask you about the machine learning technique. What features did you consider for learning these things? So I actually... You talked about the distance of the atoms, you know. Is it enough, you know, for this, for dimensionality analysis? Did you use any machine learning? Yes. I used a code that is done by one in the group in order to extract the new four materials. So I didn't do it by myself. Okay. Okay. Thank you very much. Okay. I have a question if I may. I was wondering why you chose to start from 3D materials. I mean, I naively would think that the structures of 1D materials would be quite different from that of the corresponding 3D material. And so is it useful to start from the 3D material or is it typically that it looks like a part of the 3D material that's been pulled out because you have chosen materials which have essentially 1D-like character in 3D also? We only chose the... We looked at the 1D materials that are extracted from 3D materials that look almost like 1D. So it's chains of atoms. So that's why we can extract the 1D from it. Okay. I think we are out of time. Thank you very much again. Can you stop sharing your screen, please? So the next talk is by Yulin Ibanez Asperol from the Materials Physics Centre in Spain. Can you share your screen, please? Yes. I will share now. So can you hear me fine and see if I'm fine? Yes. It's excellent. And he will talk about admonitory calculation of the shit photocurrent by one-year interpolation. Please go ahead. Thank you very much and hello everyone. So today I will talk about the shift current which is an effect that is a particular contribution to the bulk photovoltaic effect which is a more general effect although often both terms are used interchangeably. Now this consists of a non-linear light absorption process that takes place in non-centrosimeric crystals that is the material must break in version symmetry in order to show this effect. Very large photo voltages about bank up value can be attained in this effect and it was largely studied during the 70s and 80s but we find renewed interest today. Now one of the main characteristics of this effect is that it can conduct a photocurrent in an homogeneous material. If we think of usual photovoltaics one needs an interface like a PN junction in order to generate an internal electric field that will drive the photo excited electrons but in a bulk photovoltaic this is done automatically by the material. So the role of the interface in some sense is done now by the broken inversion symmetry of the material that allows to conduct electrons along certain directions. A simple or intuitive point of view or the physics to understand this is to think that every time the electron absorbs a photon it changes its energy but also it changes its position within the unit cell or to be more strict the real space center of the bands are displaced or shifted upon the photo excitation that's why it's called the shift current. So when the material absorbs light in average electrons end up moving in a certain direction and therefore they generate a photocurrent. Now as said this effect was measured some time ago here we have a typical example a typical spectrum we have the photovoltaic in the y-axis and the wavelength of light in the x-axis and besides well this was measured in a ferroelectric variant titanate which was is a prototypical bulk photovoltaic and besides the large value of the photovoltaic there is one important thing to notice here and it's that for different polarization of the light one can attain photovoltaics that have opposite sign that is current will flow in opposite directions depending on the polarization of light and even more if we restrict to a given polarization the sign can change as a function of frequency so in this sense it's an effect that has a large degree of freedom. Now the recent interest is motivated because the bulk photovoltaic effect and more generally non-linear optical effects seem to be closely related to some fundamental properties of materials like topology for instance in the work in the upper panel this is a density functional theory work that showed that the shift current experiences a sudden change of sign when the topological phase boundary is crossed so it's very sensitive to the topology of the of the system. Another line of recent research that has been pushed forward recently is that of two dimensional materials again the one the upper work is a density functional theory work where very large shift current photo conductivities were predicted in single light layer monocled coordinates so here we see that the photo conductivity reaches up to a hundred micro and per per volt square whereas the typical bulk values are of order 10 so there is an order of managed enhancement when the dimensionality is reduced to two dimensions and this was mainly ascribed to the strong banjo singularities of the density of states in 2d. Recently there have been a lot of interesting results in the field of bulk photovoltaics and non-linear optical effects this is a short survey of those for the interested audience and this was the introduction up to here of the shift current and from now on I will focus mainly on two points one will be the approach of theoretical formalism for the calculation of the shift photo current using banjo interpolation and then we show the applications of the of the method first in galleon arsenic which will serve as a benchmark system and then in a more interesting system graphically visited when which will serve to discuss dipole selection rules so as a warm up and before going to the non-linear response let's let's remind how the standard linear case looks like we will work in this in the particle case now in the standard response the current is proportional linearly to the electric field of light here a would be the direction along which the current flows and the relationship between the two quantities is given by the photoconductive the optical conductivity. Expression of these quantities written here n and m are band indexes the f's are occupation factors and the delta takes care of energy conservation now the important bit is in the transition matrix elements and in this case these matrix elements are those of the position operator why does position appear here well we can think that if we describe the light in length gauge then the electric field of light will couple to the position operator of the electron and that's why we need to take matrix elements of the position operator in order to describe the response so for practical calculations one has to calculate what's called the dipole term it's also known as the very connection and for this one needs to compute case-space derivatives of the rock function now if we go one step further and now analyze the shift current response this is a second order DC current response in this case the photoconductivity is different this one transforms like the piezoelectric tensor and it's an expression is shown here now we still have the dipole one hand in transition matrix elements but now we have a new term that is not present in the linear phase which is the generalized derivative written here and this generalized derivative contains among other terms a case-space derivative of the whole dipole term and this is a travel from quantity to calculate because of the case-space phase indeterminancy of block states so the main challenge resides in computing this term for an accurate description of the shift current in the literature there have been a number of proposals I am a popular one adopted by the group of Andrew Robb and among others it's it's been to use discretized expressions for the derivatives using finite difference formulas and this approach is very suitable for regular case-space reads that are commonly used in density function of theory calculations now this technique has been successfully applied to a number of materials here on the right we show barium titanate where the theory matches very well the experimental values and even the trends are well reproduced but on the other hand this this scheme can become computationally heavy as it needs many k-points for first principle each refunction needs to be calculated by ammunition methods at each k-point so if we want to study systems where we need a lot of k-points like 2D systems or even bias and e-metals then we need this would become computationally heavy so that's why we have considered an alternative strategy which is to consider veneer interpolation now broadly speaking in the veneer formalism one needs to consider a finite energy window where one wants to describe properties like the shift current spectrum so then why if one follows the veneer procedure one can end up interpolating veneer interpolating several quantities within within this window and this can be the band structure this is a well known example but not only one can also interpolate a transition matrix elements and that's that's that's our aim that's where we have worked we have tried to express the shift current transition matrix elements and more specifically the generalized derivative in terms of veneer functions in the veneer function language now as a quick reminder veneer functions which are denoted by lattice vector r they live in real space because they are given by a Fourier transform of the block functions from reciprocal to real space and here they use our unitary matrices that mix bands so in this sense because of this real space structure the veneer formalism it's very close to the thymine formalism actually now then it all consists on plotting this expression into the matrix elements and start collecting terms there are many terms that appear but at the end of the day in veneer formalism all of them can be calculated from just two matrix elements in veneer basis one is the the matrix elements of the hamiltonia in veneer basis for an analogy with thymine this would be the on-site and hoping terms and this fully describes the energetics of the of the problem for instance they are enough to to give the energy spectrum but we also have matrix elements of the position operator and this is perhaps a bit less familiar since again if we think of a tight binding in tight binding position is diagonal the position enters only it just marks where the orbitals will sit but in veneer formalism we have the full of diagonal structure of the position operator in real space in that sense it's a sort of exact tight binding model and as we will see this description will be important in capturing the shift undergone by the electron when it's photo excited but before that let me let me just point the main advantages of this of this method and mainly point that it allows an efficient calculation of the shift current of the shift photo conductivity thanks to veneer interpolation up to a million k points are easy to feasible which reduces the computational time heavily and let me also mention that this formalism is now implemented into the latest version of the veneer 90 program and work is on the way to have it implemented into the python veneer very called two so with this i will show now results for gallium arsenide which will then serve as a benchmark for the method now in this upper panel i'm showing the shift photo conductivity for the only component that is allowed by symmetry in this material and i'm comparing our results with results available in the literature now the comparison is good but for reference here i included also the calculation of the linear response and we see that the agreement between the two results is very similar in both cases which makes us be confident about the method and let me also note that the peak structure of both response functions is very similar and it's actually related to the underlying joint density of states and its peak structure so the test is passed but we can use now the veneer formalism to learn more about the about the problem of the physics that are underlying and how can we do that well we can because of the formalism we can switch manually off the diagonal matrix elements of the position operator we can refer to this as the diagonal type binding approximation because in in that binding those terms are not considered so the result of doing so is shown in blue so for the linear response we see that it doesn't do much so this means that those terms are not important for for the linear response so this approximation is good for the linear response but not excuse me you have five minutes left thank you very much so it does do uh sorry it does have a big impact on the shift current spectrum because it uses a relative error of approximately 50 percent so for the numerics this general position matrix elements are important for the shift current and even more they they are a quantitative proof of the strong wave function sensitivity of this of this particular response so and in the remaining of the talk I would like to now focus in another in the next material and more is the interesting system that is a second application of the method and this is a graphic visible so this material is a layer semiconductor that has a broken inversion symmetry because of its structure it contains weakly couple layers and we can expect a quasi 2d properties that will again we can expect a large shift current response now uh the most important physics happened close to the bandage here in the upper panel we show the band structure and in the lower panel the direct band gap so the bandage lies somewhere between the s and x points here pointed by the red dot and the direct minimum band gap is 1.2 eb not also that there is a subtle point at the x point at 1.3 eb approximately so we can say that the band bandage region lies between these two energies now we have applied our formalism for calculating the shift current and we show here the two conductivity components that are allowed by point group symmetry y y y and y x so the first one is fairly small yes the first one is fairly small uh while the other one starts to grow right at the uh from the bandage and reaches a maximum at 1.3 around 1.3 now this value is very large is actually this magnitude is among the largest bulk values reported in the literature and picks in a suitable energy range for some potential applications so in this sense this material can be interesting but that's about the the size but what about the direction of the current now these two components allowed by symmetry correspond to quite different setups in one of them current flows parallel to the electric field of light this is usually the most common setup but in the other one it flows perpendicular to the field and if we focus on the bandage region in the gray area we notice that only the perpendicular component is finite the parallel one is completely vanishes so why is this why does it vanish even though it's allowed by symmetry so this actually can be traced back to a quantum dipole selection tool associated with mirror eigenvalues as we will show next um the crystal structure has a mirror mirror reflection it is mirror symmetric in the x coordinate so now because the bandage lies lies actually at a mirror invariant point the s x line it's a mirror invariant line and the bandage lies there then this means that the bandage states have definite mirror quality and this parity can take on two possible values plus or minus means minus in the case of vc2n valence and conduction bands shown here have opposite parities so let's keep this in mind and consider now the expression for the shift current matrix element and more in particular the dipole term so one can distinguish two dipole selection rules depending on the relative parity of conduction and valence bands when states have the same parity the matrix elements containing the mean of mirror index is forced to vanish that is the dipole term rx is forced to vanish whereas if the states have opposite parity then the matrix elements without the mirror index in this case ry is the one that vanishes and what does this mean in practice well combining this with the shift current expression dipole selection rules imply that in one case the current can only flow parallel to the field while in the second case the current must flow perpendicular and this the first situation actually is what was what takes place in monolayer germanium sulfate and this is shown as in retrospective which was analyzed in these two works and the second situation that we have shown it's actually taking place in vc2n so the interested audience can look for more information here if interested and with this with acknowledgments to the people that has been involved in this work Ivo Sousa, Stefan Zirkin and Fernando De Juan and thank you for a very interesting talk we do have some online questions we may not have time for all of them Babu, Brejna, Prasad would you like to ask your question? Hello, am I audible? Yes, thank you Professor Julian for the nice talk I have a question which is that it is spin orbit coupling is necessary for doing the shift current calculations good question so it's not it's not a key player because well the the results I have shown are for semiconductors with a big band gap spin orbit coupling here wouldn't play much of a role it's not like it's not like some effect like anomalous holy feg where spin orbit coupling can be key but here the physics are not dictated by spin orbit coupling they can be in recently interested materials for non-linear phenomena like bi-semi-metals where the band gap is smaller and then the spin orbit coupling will have bigger effects oh okay thank you and how about the senior shifts because since we are dealing with semiconductors we might need to have a accurate gap to have a good spectrum of shift current totally true the good thing is that the shift current the matrix elements and the whole conductivity is invariant under the assistive shift so it will just shift the spectrum the calculated the spectrum to higher energies usually but the the profile of the spectrum would be the same it's invariant oh thank you thank you so much side by Hossini can you ask your question briefly because we are sort of running out yes sorry thank you very much for your non-stike I have a question about the slides 17 in the slide 17 yes there are some peaks on the diagram could you tell me the physical meaning of these peaks or not because I mean imaginary dielectric function we know that the peak shows the absorption but you know for current shift what is the meaning of these peaks thank you very much it could be a similar meaning so I said both the linear and the shift current response show the same peak structure and the origin is actually the joint density of the state so where bands show more or less parallel dispersion when you have two bands that are connected and that energy and have sort of parallel dispersion you will have a big peak in the joint density of states and this will also be shown in the shift current thank you thank you thank you very much for your nice talk I think we have to move on now to the next talk so can you stop sharing your screen please so the next talk is by Ketano Rodriguez Miranda can you make a full screen Ketano yeah so this is Ketano Rodriguez Miranda from the University of Sao Paulo in Brazil and he will talk about materials discovery for biomedical applications from machine learning and first principles calculations to finite elements thank you very much for your kind introduction I hope that has everyone well and you actually would like to be my beloved Trieste to have a medal in the city pick up here so I'd like to thank the organizers for this incredible opportunity to give this talk in the total energy online and it's very interesting to share this work that has been a combination of expertise like the materials engineering the chemistry mechanical engineering and a physicist towards the proof of concept to use material discovery for biomedical application now the seminar is actually all about the use of a combination of a metaphysics in a multi-scale approach we're going to try to figure out biomedical applications where you're going to use machine learning together with first principle calculations in order to check and verify just the properties of the systems and basically try to end the cycle to look for a real application so you're going to see how this electrical properties is really works on a bond for instance now the motivation is looking for the structural biomaterials and bio implants you are very much interested in that because of the use so you have this interface between the the bond and the implant and this requires several right the right combination of the density as well the electrical properties of that in order to avoid the bond stress shield the effect now in the case of the bond this is very complex material into this interface between the metallica implant with the bond you have several challenges here so one of them is that you have a very rigid part the external part of the bond but also have a low modulus region that is actually with the soft part and where you have the blood in the other bioactive sense happening so what you're trying to see is how can you look at for materials that have the right combination where you can use it for instance in bio implants and also to avoid fracture and particularly you have a huge pain in case of you have this disbalance between those machines so this has been motivated because in Brazil this is actually a huge market you were talking about something of the order of four billion US dollar a year that you lose because you are not able to to have those materials of those systems to use ourselves in this with the population aging is this supposed to have even more needs with this kind of system now of course you have already several options in place the most of them is related to titanium metallica titanium where the basic the current the best one is the so-called the gun metal where you have the t and t alloy here you have a very good combination between the the low elastic modulus the good bio compatibility high strengths but the problem is the high cost of it so you are looking for particularly here materials that have a low cost but you still have a good balance between the we'll just train in the model line particularly looking for the elastic self global strain respect to the cost of the cost so this family of uh uh systems is uh it's here and they're like try to look into something that is more uh at low cost but you still have the good profits from uh in the bio compatibility now one thing that you the first thing that you have to do is to look for the the periodic table for the bio implants uh and basically here you have the metallic systems this is the elements uh on it and looking for the biocompatibility of that and there are several other profits that you have to look for in the in this particular case you search only for the green ones this for us it'll be you could avoid any problem for the bio compatibility and then uh requires the titanium zirconia in niobium but of course you have the ruthenium but the ruthenium is better to use for catalysis and also the also you have a very high cost of that now uh in this way you are looking for uh alloys that have this combination uh titanium niobium zirconium and you hope that the elastic profits can reach those uh this this region in particularly uh low cost for the problems would be the composition of that now uh to do that one strategy is that people use a lot on the material discovery now is still a very trying error so but the problem here is that you have a multi-dimensional optimization problem that you have to look for which is the best composition for a given system however most of the time the parameters in the the profits are unknown so you have to look for that in the one way is to uh only uh search for the best candidate so in this way you can synthesize characterizing test it is in the way that you can save a lot of time in also cost so the approach that you're going to use is actually back in time in terms of the evolution of the methodologies from the scientific point of view you're going to use the machine learning methods in order to make a selection of potential candidates then you validate it with a dysfunctional theory then you're going to use the linear elasticity to see for real application before doing actually the the experiments on this system now the methodology that you have been using is a combination of uh multi-physics and multi-scale methodologies that you want to narrow down the possibilities uh in order to apply for a real system so in this way we start with our databases uh in particular here you have used the materials project uh and remember that one thing that has motivated us a lot on this work is that because in Brazil uh eight percent of the niob is here and uh could be something that could be used it for uh from the economical point of view now you have used machine learning methods in order to uh get uh information of the electrical properties based on the composition this was some of the packages and also libraries that you have used uh with that select some of the materials and you test it with the dysfunctional theory uh uh when here particularly you have a problem that you have to use the special quasi structures in order to approach the alloy problems now this information that comes from the dysfunctional theory then is used to feed the electrical properties where you perform some finite element simulations you could see if the alloys and systems that you search is in a good shape to be used in our real conditions and also for real application now uh how that has been done this uh several steps under the way to reach the uh the full alloy and the material itself so we start with the composition structure as has been seen several of the talks today so you narrow down the possibilities looking only for the transition post-transition methods this gives to you this amount of uh entries now you figure out even more you excluded any ionic or covalent character of those systems then uh you look also for electrical properties in the range of titanium alloys that is interesting for us and finally uh the information that comes from the heat formation in the entropy mixing so this gives us around the 12,000 entries now what you are looking for is uh to be able to predict the electrical properties based only on composition so we're using this machine learning process so in this way uh what one important step is to look for in the exploratory part of the machine learning process is to look for which features will be potentially the best in order to describe an even target property so to do that you do a feature selection so you could figure out what is the uh the best features that can somehow in let us have a model based on the only composition only based on composition and finally uh this is to be fitted uh some linear models or random uh partial regressors in order to be able to train a model uh towards the book models or the shear models again using only the composition uh information so this is was more or less the step regarding to the machine learning process now uh just to give you an idea about uh this has been done for the shear models here you have a uh you explore several options one is the linear regression or under florist as well the neural networks with the full descriptors and uh select a number of descriptors so based on that you could see that the the uh the database compares the predictor in our model uh in particular for the render floor is quite interesting and also have a very small error compared with the other uh system now you have been able with this model uh to propel a selective one uh here you're using the keras library in order to uh to have this information and then you are able to get what is the batch features that uh uh somehow can capture the last model i using base basically using the composition now in this particular case for the shear modulus you're in that with the person ratio to be uh the most representative one of course you have the other ones that i can comment uh later on but uh somehow uh with this information then you are able to get the phase diagram the titanium zirconia and niobium using this model i uh only using only the composition information to get the information from the elastic point of view so in this particular case i'm showing the postal ratio that is how related to is the uh mix entropy you know and uh you could make the correlation between what is the uh what is this machine learning methods melt models is given to us together with the physics behind those systems now uh this is very interesting so you could do uh then they calculated the elastic model line this is that what you see is the um machine learning prediction using two completely different methods the render forest and the neural networks in doing that view is a very interesting sweet stop uh sweet spot here on where you have a large concentration of titanium and titanium and then you also have the uh the combination of zirconia in niobium so this could could be seen in both methodology in both models in this uh with that this was the map for us to look for those compositions in order to see if you can end up with a material with a low uh model i that uh elastic model i that can be applied on bio uh in plants and bio uh applications now however uh i have to remind you that this is this machine learning predictions is only based on composition means that uh is acknowledged to the structure so this is where you have to use the first principle calculations for instance in order to uh understand and validate if those compositions are really uh stable stable and also can be used uh as a good material for uh bio implants and bio uh structures so this is more or less what you have done for this uh under the sweet spot on this composition then you look based on first principle calculation about the phase diagram diagram and here i show to you the phase diagram of titanium with pressure and temperature uh because you have to look for if the structure uh that you are looking for is really the one that can be uh stable for a given uh situation in this particular case since the titanium is the uh largest amount uh you know alloy you are looking for the beta phase that is the the low modulus ones that is the bcc phase in the in particular here you have to avoid two points one is the transition between the low temperature phase the alpha to beta and also if you uh if you cool it uh it's low enough then then you you can reach those uh this region that they're the one that you would like to go and finally if you do a fast cooling then uh you may end up on the uh omega phase so this is a problem you have five minutes left great yeah so and then you you'll figure out here you'll uh uh you'll get a phase that uh uh have a higher uh moduli so you have to understand uh from the thermodynamic point of view from the elastic point of view what is going on so then you have you've done a series of calculations based on this functional theory to see how is this stability of both phases the omega and uh the beta and also the better respect to the alpha one now uh then uh because of the time let me just uh quickly uh show to you what uh you have uh end up so you look for the influence of that uh the conyon then you keep it fixed this uh this content then you change the uh uh the amount of niobium because the niobium is stabilize the beta phase in titanium so look for uh this degree of collapse between the omega in the the beta phase where you have the perfect omega phase and here will be uh the uh the beta phase and also the competition in energy between those you could see that uh uh if you change the amount of a niobium in the system then at regions above uh 11 percent then you stabilize this uh beta phase this that is the one that you would like to go now uh you also look for the one for uh the competition between the beta and the alpha phases this is calculated gives free energy and you see as well that you will increase the amount of niobium then uh uh you have a higher niobium composition goes to lower better uh uh transition phase between uh the alpha and the beta phase now with that you could see that uh uh this amount of niobium will be interesting in order to stabilize this system as well you have to see if uh how is the elastics proper so this here I'm going to show show you a two-dimensional information for the elastic model line with increasing niobium content and uh uh in summary what uh uh I can give more details later but in summary you could get a best composition uh uh and uh based on the elastic property so basically the information that uh for uh the contents with a niobium above 11 you have a good candidates for the bonding implants you figure out the special compositions and uh uh you calculated the full elastic property of that and finally of course you have some uh differences between the machine learning the uh dysfunctional the expected but the issue in a good shape compared with the experimental part so this means that this compositions could be a potential for uh alternative for t and z t uh as standard material now this is very interesting because in the end you could figure out a nice composition that gives to you uh gives to us uh good elastic problems now for to the end then you have applied that for our implant model so you have usually actually a bone and try to uh see if uh you have a fixing a plate on this bone how is the effect of that as well uh you have this model for the joint plant model where you look at how is the response of uh those systems regarding to the elastic properties of the bones as well as the alloy properties that you have figured out together with the reference one that is uh usually commercially nowadays so just to give to you an idea about how is the effect of that so here's the stress distribution for the implants so you are talking about this region of the bone and you have this uh plate that fix these two parts of the bones if you have a fracture now uh if you compare the stress response of the alloys that you figure out together with the reference one basically you have a very similar mechanical behavior so uh and also it's uh well i mean the the performance you compare with the titanium alloys is uh much better now uh you also uh this is the example for the other model you have a similar result so basically uh compares the reference one the stress here is the bone misses the stress uh is more or less uh you have a very similar uh uh response from the mechanical point of view and this implant usually is keep it is put it here no and then you have this very uh complex combination that you have the interface between the bone and the implant in the uh those materials that figure out have a good uh uh response now just as I conclude the remarks so the machine learning was able to capture the features and define a composition so it spots uh figure out uh uh low models alloy the initial calculation allow us to explore the composition rates so then uh here in particularly you see the importance of niobium to the structural and electric properties and you could get uh optimal ternary composition for those applications and finally the finite element simulations uh could allow us to explore real case systems and you have a very good combination of the ternary alloys that you discover together uh compare with the standard t-n-z-t alloy that you have it done and basically you didn't see any significant uh difference between the stress response between those uh those a lot so as I take message home so the multi-scale this multi-scale approach allows to predict and also to propose a compatible material with the standard t-n-z-t one and uh now you are trying to see if you could uh synthesize those and real uh and make a real application so with that this has been uh uh shown on this paper and finally uh I would like to thank my team uh in brazil in particularly uh daniella bruno and camilo for those in the brazilia fund the agencies that support this work and finally thank you very much for our ctp for everything that has done uh myself and my career thank you very much shabana this is it and I'm open for questions thank you katana there are actually several questions I don't think we'll have time to take them all uh john marco rena nase has a question john marco can you ask your question yes I was wondering how you perform feature selection and in particular I was wondering if that's so important when you do a random forest so the one that uh you have in this particular case you have done uh you have used it uh a set of around 500 features that it was available for those materials in the uh in this particular case you have used this uh keras library to make this selection now uh regarding to the uh for the run of forest and the other uh uh methodologies that you have used it so uh what would you like to see here is actually how robust was this particular region that you're looking for and uh in this way you you have you have done uh first with the run of forest and see uh I mean the amount of the air or that you have there was uh good enough but you try a completely different uh uh our way that was the uh neural network and this this part that there was the one that was robust for us now for the uh it was interesting to see that for the different cases several of the properties that come out as uh good descriptors was more or less the same okay maybe uh you partially answer this question but Nathan Daleman has a question can you ask it please hello yes yes so so it's it's uh actually on the same slide so I was wondering where where the what causes these differences between the random forest and the neural network on slide nine where you were showing the comparison so in the region that you are interested in they they give quite similar prediction but then outside of these regions is this due to the feature selection or due to something else so we imagine that yeah yeah you imagine I mean uh that this may definitely do to the feature selection that was not exactly the same uh uh that you have obtained both however uh for the uh particularly uh the general response was more or less the uh a similar one and you are you will have been very much interested on this particular region here because the one that call us the attention it's supposed to be the ones that could you have a better uh uh applicability for our application but the final details yeah okay okay yes okay where I can't write behind yeah no just comment that I can write in the chat the final details about why okay we're running behind time but maybe I'll just love one last question Hannah Rubin can you ask your question please Hannah Rubin I saw it yeah I'm there can you hear me yes ma'am can you hear me yeah yes yes thank you sir for the nice presentation uh sir I just want to know when your slides that you've shown you have calculated the role of the PL valence electron but for the transition elements the d valence electrons play a vital role in uh because of their hybridization and the elastic properties so I just want to know what is the role played by the d valence electron in this case so the d valence was part of it but as you can see here it does not come out uh as uh uh they really compare with the other features that remember one thing that you are much you are very much interested here is to have a model based on composition only for the elastic properties so even uh it may be a uh important feature uh for the electronic point of view for instance but this in this particular case where you're looking for the elastic properties it does not come out as the one that is relevant compared with the other one yeah yeah okay I think we are out of time there are many more questions many more raised hands so I'm sure Ketano would be willing to answer if you were to approach it definitely yes okay thank you for a very interesting talk and we'll move on to the last talk in the session this is by George Dunge from the Tindall National Institute in Ireland and the title of this talk is lattice thermal conductivity highly and harmonic materials beyond the Boltzmann transport approach uh hello yeah my name is George Dunge and as you said I'm going from Tindall National Institute in core Ireland and I'm going to present a well fairly new method of calculating lattice thermal conductivity of highly and harmonic materials which goes beyond the standard Boltzmann transport equation approach this work was done in collaboration with Tula Helman from Linkupi University under supervision of Ivana Savic and Steven Faye a quick overview of the talk first I'm going to introduce some relevant quantities that will facilitate the discussion in the rest of the talk then I'm going to outline the derivation of this new approach for calculating lattice thermal conductivity which we which I will call green kubo approach then I'm going to present results for germanium telluride and explain them using vibrational properties calculated from this green kubo approach in the end I'm going to conclude by summarizing summarizing results presented in this talk there are many reasons why one should be interested in modeling lattice thermal conductivity for our group in particular we are interested in uh improving the thermoelectric efficiency of the material of the materials and one of the most promising ways of achieving that is to reduce lattice thermal conductivity uh four six materials are one of the most promising thermoelectric materials mostly because of their low lattice thermal conductivity which is a consequence of them being close to the structural phase transition this proximity to the structural phase transition makes these materials extremely unharmonic which limits their phonon lifetimes uh additionally this unharmonicity causes phonospectral functions in these materials to exhibit exotic behavior for example in lead telluride uh experimental results showed that the phonospectral function exhibits double peak structures rather than expected one peak structure in this talk I'm going to focus on germanium telluride another example of the four six materials and promising thermoelectric material that undergoes a structural phase transition from rhombohedral to cubic phase at 600 to 700 kelvin there are many ways of calculating lattice thermal conductivity from first principles for example one might run molecular dynamic simulations and then use green kubo relations to uh connect fluctuating heat currents and lattice thermal conductivity coefficient alternatively one might use phonon dynamics or some some people call it lattice dynamics approach to extract the relevant phonon properties then use those phonon properties in boltzmann transport equation usually in relaxation time approximation to extract lattice thermal conductivity boltzmann transport equation sees phonons as a gas of vehicle interacting particles that carry heat between scattering events that happen every phonon lifetime how do we use boltzmann transport equation in practice well we first calculate vibrational properties of the materials from the density functional theory and then using for example the temperature dependent effective potential method as we did in our case of course this method boltzmann transport equation and also the method that i'm going to show later on are not um only viable with using uh this method of extracting vibrational properties you could practically use whatever you want uh so what we do is we expand the material Hamiltonian in the Taylor series with respect to the atomic displacement uh the coefficients in this expansion are called atomic force constants for example the second order interatomic force constants give us harmonic phonon properties such are phonon frequencies and group velocities third and higher order interatomic force constants give us phonon self-energy which measures the interaction between phonons this phonon self-energy is a complex function of frequency for each phonon mode the imaginary part of phonon self-energy gives us a phonon lifetimes as shown here then we use these properties calculated from first principles in the boltzmann transport equation expression that i showed in the last line here to actually calculate the lattice thermal conductivity here just to note this n uh denotes the phonon population at certain temperature which is calculated as a was a Einstein occupation factor uh another property of interest is the scattering cross section or the probability of uh phonon to interact with the probe which can be uh neutron or light incoming in the material this scattering cross section will be um proportional to the spectral function which is a Fourier transform of the uh displacement autocorrelation function the boltzmann transport equation assumes that the spectral function takes a form of a lorenzian function which means the imaginary part of the self-energy is a constant with respect to frequency and the real part of the self-energy is zero however we can calculate the spectral function directly from first from the perturbation theory and we get a bit more complicated expression but the most important part to note here is that the uh self-energy in this case imaginary and the real part are the function of frequency so how does how do these two expressions compare for highly unharmonic materials uh i'm showing that on the graph here so i calculated phonon spectral function fully from first principles and the perturbation theory and i'm showing that in the red line here while the blue line shows what boltzmann transport equation thinks uh the phonon spectral function looks like and we can obviously immediately note that the stuck difference between these two lines this difference led us to question the applicability of the boltzmann transport equation in modeling lattice thermal conductivity in highly unharmonic materials so what we want to do is to include the entire information from this phonon spectral function in our calculation of the lattice thermal conductivity how do we do that so while we start from the green cubo expression for the lattice thermal conductivity here uh kappa is the lattice thermal conductivity and we is the volume of the simulation cell t is the temperature kb is the boltzmann constant yot is the heat current and the brackets here uh mean the heat current gets autocorrelated first what we have to do is to define a heat current yot we use the definition of the heat current shown here people who are calculating lattice thermal conductivity from first principles will notice that this definition is different from more commonly used pyroless one which defines heat current through the phonon population operator but one can show that the pyroless definition of the heat current is an approximation of this expression another point i want to uh another detail i want to point here is this quantity v q s s prime which is the generalization of the phonon group velocities um the s and s prime are the phonon branches so this goes beyond the standard definition of the phonon group velocity to include the off diagonal terms in the group velocity matrix uh in the phonon eigenvector space the a and b operators can be defined in terms of the phonon creation and inhalation operator as shown in the last line here once you go through whole derivation of this expression you end up to uh expression like this one shown in the first line uh important thing to note here is that we have an integral over the frequency range and under the integral we have what we can see what we can recognize as the phonon spectral function so we did include the entire information of the phonon spectral function in our calculation of the lattice thermal conductivity another important point to note here is that the summation here goes uh through two branches two branch index s and s prime so we can split this expression in two parts the first part is diagonal in phonon branches which is the traditional uh definition of the heat current and the second term is non-diagonal in the phonon phonon branches one can show that the diagonal part so when s is equal s prime in the limit of the low unharmonicity that means that imaginary part of the self-energy is much smaller than the phonon harmonic frequency and the real part of the self energy is zero that this expression reduces to the Boltzmann transport equation in the relaxation time approximation the non-diagonal part uh has been already described in these two recent publications as the primary transport mechanism in amorphous materials in our uh in the previous formula it has a slightly different um expression and we can note that the non-diagonal part gives contribution only if there is a substantial overlap between two spectral functions of phonons with the same q vector but different branches and here i'm showing the overlap of the spectrum functions of two soft modes in germany and telluride close to the phase transition and we can see that the overlap is only for the low frequency region so that only the low frequency region will give contribution to the non-diagonal part of the lattice thermal conductivity now i would like to show the the results for germany and telluride first i'm showing the relative difference between uh results obtained with green kubo method and uh results obtained with the boltzmann transport equation uh we notice that the boltzmann transport equation consistently underestimates the results from the green kubo method we can also notice that the this underestimation is not large at most it's around 14 percent uh we also notice that the difference scales roughly linearly with temperature which we might expect because phonosulfan energy scales roughly linearly with temperature uh also the difference peaks at the phase transition which is also understandable because we expect germany and telluride to be mostly most unharmonic at the phase transition if we split this difference coming to parts that come from diagonal and non-diagonal part of the lattice thermal conductivity we can we can see that they are roughly equal in germany and telluride one has to keep in mind that germany and telluride is fairly simple material with only two atoms per unit cell we expect in more complex crystals that the non-diagonal part will be much more prominent so why is there increase in lattice thermal conductivity you have five minutes left okay why is there increase in lattice thermal conductivity going from a boltzmann transport equation to the green kubo approach one can look at it by mapping the green kubo expression to the boltzmann transport equation expression to extract the phonon lifetimes if we do that we uh calculate the phonon lifetimes in boltzmann transport equation and the phonon lifetimes in green kubo method as defined here and we find that the phonon lifetimes in the green kubo method increase substantially especially in the for the region of the soft modes well does that make sense intuitively does not and um and if we look at this phonon spectral function we can see that the boltzmann transport equation spectral function has a smaller line width than the green kubo spectral function this means that one should expect higher phonon lifetimes from the boltzmann transport equation than the from the green kubo which is not in accordance with the previous picture to analyze this more deeply we Fourier transform our spectral function into time domain to get a time dependent display atomic displacement of the correlation function and we showed this for two temperatures at 300 and 631 kelvin at 300 kelvin we get expected behavior for weekly and harmonic material relatively weekly and harmonic material where we have oscillations and overall decay of the correlation however at 631 kelvin the unharmonicity so strong that we do not observe any oscillation at all and only have the phonon the decay of the autocorrelation function we can fit these two behaviors to the damped oscillator function to extract what we usually associate with phonon lifetimes and frequencies if we do that and we plot the fitted lifetimes as the red points here and the boltzmann transport equation lifetime as the blue points we can see that the fitted lifetimes are indeed smaller than the boltzmann transport equation lifetimes which is in accordance in our with the spectral function graph so why is there an increase in the lattice thermal conductivity then in the green kubo approach we explain that by extracting the unharmonic phonon populations from the displacement autocorrelation functions and we can see that unharmonic phonon populations mostly increase in the entire frequency range and most prominently for the phonon soft modes so we can say that the increase in the lattice thermal conductivity that we observe in green kubo approach is actually due to the increased phonon populations why do phonon populations increase we understand that from the plot of the frequency shifts between fitted frequency and the assumed harmonic frequency in the boltzmann transport equation approach and we can see that the phonon softening due to the phonon phonon interaction causes unharmonic phonon populations to increase which increases the overall lattice thermal conductivity we started this investigation because we wanted to make sure that our results or germanium teller right close to the phase transition make sense and we already proved that because the difference between green kubo approach and the boltzmann transport equation approach are not very big around 10 which is way less than what you would expect from the than the variance in experimental results which are shown in this figure here as the green as the gray region but it is hard to gauge the predictive power of this green kubo approach due to other effects that influence lattice thermal conductivity in germanium teller right much more such as for example vacancy scattering the predictive power of this method might be better tested in more complex materials with more atoms per unit cell that exhibit the amorphous like lattice thermal conductivity in the end i'm concluding by saying that we presented a method for calculating the lattice thermal conductivity of highly unharmonic materials based on green kubo approach this method incorporates information from the entire spectral function of phonon modes in the case of germanium teller right boltzmann transport equation underestimates the lattice thermal conductivity compared to the green kubo approach the reason for the increase of the lattice thermal conductivity in green kubo approach with respect to the boltzmann transport equation is due to the increase of the phonon populations due to phonon-phonon interaction the more details about this approach and in general the lattice thermal conductivity in germanium teller right can be found in this archive link here thank you for your attention thank you for a very nice talk there are several questions i think we have time for maybe one or two uh you hit gupta do you want to ask your question you hit gupta are you there okay let me ask the question the question seems to be our calculations lattice thermal conductivity by using slacks equation not accurate enough to give exact results accurate results um i didn't i didn't hear the question at all okay sorry uh can can you hear me now yes yes so the question was our uh calculating lattice thermal conductivity by using slacks equation not accurate slacks equation yeah uh i i'm not familiar with okay i'm not either so i can't help you uh you hit gupta are you there can you elaborate on your question okay uh punk punk somehow all the questions seem to be from india uh punkage kumar gajar do you want to ask your question punkage kumar gajar are you there yeah yeah can you ask your question can you ask your question yeah yeah my question is okay while calculating the lattice thermal conductivity why in most of the cases we ignore the electronic contribution uh well there is two good answers to that question the first answer is that uh well in the modeling of the thermoelectric properties the lattice thermal conductivity is somewhat decoupled from the uh electronic properties of the material so you want to reduce lattice thermal conductivity without actually um reducing the electronic properties of the material uh specifically in the case of the germanium telluride one would expect for very low doping that the lattice thermal conductivity will be the uh the dominant factor in the total uh total thermal thermal conductivity so that's the reason why we not considering the electronic part of the of the thermal conductivity in this in this work and is the same as true can we move on to the next question please because we're running out of time uh natalia asked do you want to ask your question hello do you hear me yes yeah thank you very much for the nice talk my question was about the fact that in your lattice thermal conductivity the new expression you neglect probably the force order and harmonicity in the frequency shift and i was wondering whether you believe that this could be an explanation for the high value of the lattice thermal conductivity and in particular could you do you expect that it could explain the big difference you find in the cubic structure if i yeah yeah i understand the question so if i if i go back here uh well in this method it doesn't really you don't have to stop at the third order and harmonicity you can go in the expansion of the hamiltonia to whichever order you want your expression for the phonon self-energy is going to get a bit more complicated but this method is not constrained on using only third order and harmonicity so that part of the question i i think is answered the other part of the question is the fourth order and harmonicity the reason why our results are so different from the experimental one in the cubic phase i'm not sure if that's true we calculated the fourth order and harmonic force constants but we found that they in the lowest approximation do not have a large influence on the phonon spectral functions so it's either the the lowest approximation is not sufficient in this material or the fourth order and harmonicity is not relevant so it's it's inconclusive we don't have a conclusive answer to that question but it is a very good question and worth exploring for the run okay thank you unfortunately we have to cut the discussion short because we have to wind up i thank all the speakers and i thank all the participants we have continued to have a very large number of participants online i thank everyone for their interest lots and lots of questions and i can see that a lot of the questions are from students and i congratulate them on their curiosity and their enthusiasm i thank the organizers for inviting me to chair this session and i hand over now to Nikola in case he has any announcements thank you no i don't have any announcement i think we can go to the coffee break and then in 10 minutes we can meet again in the in the poster rooms so see you later and see you tomorrow at the same time thank you