 I will keep looking for Elisa. She's not answering right now. Do you want me to wait, Stefano, or to just start? Not necessarily. The important thing is that she's available by the end of the talk. So I wish she will join as soon as possible, but I think you can start wherever you feel like that. Asimo, can I start? Yes, please. Thank you. Okay, great. All right, so I think we can start this last session of the school. It's really a pleasure to welcome today Nicola Spalding. Nicola, she's a professor of materials theory in the department of materials at the ETH Zurich. She studied in Cambridge. She got a PhD in Berkeley. She's been a member of the faculty at UC Santa Barbara for quite some time. I think this is what actually we met for the first time. She was actually directing at the time this beautiful international center for materials research. And then she moved to Zurich in 2011. She got several prizes. I'm not going to the list of prizes. I mean, quite successful, Nicola. But just to mention one, I mean, one that's quite important, which is the L'Oreal UNESCO Award for Women in Science. This is the top award for women scientists. But this also allows me to mention that Nicola has been strongly advocating for gender balance in basic sciences. And I'm really thankful to Nicola for her support here at the ICDP. So the title is quite interesting. It's finding happiness and saving the world through electronic structure calculations. And I guess I'll stop here and let you go ahead, Nicola. Thank you very much again. Thank you, Sandra, for the kind introduction and it's a pleasure to be joining the school. It would of course be much more of a pleasure to be getting to meet you all in Trieste, but this is the best that we can do at the moment. So yeah, the title of my talk is how we can use what you've been learning the last couple of weeks to save the world and also hopefully find happiness. And I'm going to start by flashing up a slide that probably most of you are very familiar with, the United Nations Sustainable Development Goals. And I'd like to make the case that none of these goals are reachable without advances in science and technology, in particular material science. And the kinds of electronic structure calculations that you've been learning how to do in the next couple of weeks are really essential in contributing to meeting many of these goals. So if you get a little bit tired and it's been a long couple of weeks for you in the next, in the next hour, have a think about what you're doing in your research or your research direction, your research goals, and how you see that contributing to helping meet some of these sustainable development goals. I'm going to give you a couple of examples of my research, some of which we kind of aimed to achieve and others which were really quite by accident to give you some ideas. Okay, but first we have to learn some stuff because of course saving the world is not easy. And so I want to, I want us to learn a little bit more electronic structure theory if you didn't feel like you had enough in the last two weeks. I'm going to focus on a breakthrough which happened actually partially in Trieste in the 1990s, and that was the development of what we know as the modern theory of polarization, which I understand correct you haven't really touched on some of you probably a little bit familiar with it but you didn't really study it in detail in the school. So I'll give you a little bit of background and then we'll go and see how we can use this to try and find happiness and save the world. The papers I'm referring to by Raphael Arresta and King Smith and Vanderbilt really introduce the formalism for calculating electric polarization in crystalline solids. And let's take some time to think about why that was a really difficult thing that they did and why it was such a huge breakthrough is such a huge achievement that they were able to do it. The question that they answered was, is the polarization of a periodic solid a bulk quantity at the time it was still believed that it was perhaps a surface quantity it wasn't so clear whether it was a bulk or surface quantity. And if so, how should it be defined. It's not a problem if you have a finite system if you think about just just a molecule say with the negative charge of minus one electron and a positively charged ion plus one electron. Then we can trivially write down the dipole by just summing up the sizes of the charges times the position, and we get a dipole of E if it's the size of the electronic charge times D the spacing between the ions and the dipole is pointing from negative to positive. So there's no ambiguity if we're interested in molecules or, or your finite size systems, we can write down the dipole. The problem is it when we have a bulk periodic solid, and you can think well okay that can't be so hard. Why don't I just write down the dipole moment for unit volume that could be a good description of the polarization. So let's try that let's imagine we have a bulk periodic solid just a one dimensional chain made up of polar molecules, and we write down the dipole moment of this unit cell in the middle and divided by the volume of the unit cell. And we get a polarization which makes sense it's the size of the dipole that we had previously divided by the volume. So if we have a bulk periodic solid though, we can choose anything we like for the unit cell right we don't have to choose the light gray lines that I've drawn here, we could make say this choice for the unit cell. And we now work out the dipole per unit volume, we work out the dipole by something over the charges times the position again, then we get a different answer we get e times d over v, like we did before, minus e times a over v where a is the size of the unit cell you can give you a better go yourselves just make you were this this your unit cell, and some over the charges times that position times their distance from the origin, and you'll find you get a different answer. So there's two problems here one is that we have a different number for the polarization if we define it as dipole per unit value. And it's also pointing in the other direction right our polarization points from negative to positive, and now it's pointing to the left in the unit cell. So this was the problem that this breakthrough of restaurant case with inventive of soul. I want to point out just one thing that this difference here between the value we got for this unit cell and the value we get for the bottom unit cell. It's the electronic charge times the lattice sector times the size of the unit cell divided by the volume, and this is going to pop up again and again and repeatedly we call it the polarization quantum it's like a unit a kind of chunk of polarization Okay, so this isn't a new sense we don't have a simple way to define polarization for periodic solid, it gets worse actually the problem is even worse than it's it's it seems already. And we can see that if we look at a centrosymmetric lattice so now I've made this again the simplest possible periodic solid I could make of just alternating negative and positive charges. And this time they're all spaced a distance D so this system is not polar it doesn't have a dipole because I sit on the positive charge, the negative charges equally far apart to each side so there's no. It's centrosymmetric has a center of inversion it's not a polar lattice it doesn't have a net dipole. And let's do the same repeat the same same process and just work out the dipole moment the unit volume and I'll start by choosing this unit cell and if I sum over the charges times that position in this unit cell I get minus e times d over v. If I take this unit cell on the left here, I get plus e times d over v. And I could keep going at the construct all kinds of unit cells that might look a bit weird maybe say containing this cat iron together with this and iron and I'd get very many values which would all be e times d over v plus some integer times e times a over v this polarization quantum the electronic charge times the lattice vector divided by the unit cell volume. Or I could rewrite that I could write all of the numbers that I can generate for the dipole moment for unit volume of this centrosymmetric lattice, in terms of the polarization quantum. And what I see is I get pq over two three pq over two five pq over two and so on these numbers are all separated by the polarization quantum. But my numbers don't contain zero, even though it's very clear that this is a non polar lattice and by any sensible definition I'd want to say polarization is zero. What you can see is that this array of numbers that I have is a centrosymmetric array right we call this the polarization lattice and it is centrosymmetric but it doesn't contain zero. So these are the problems this was the status in the early 90s that that needed fixing and this modern theory of polarization that was introduced. Solve this problem and the key is the three key results let's look at two of them first. The first result was that the polarization of a periodic insulating solid is really a bulk property, but it's a multi valued property. The polarization is not a single number, it's an array, it's a lattice of numbers, and it's given by some p0 plus n times the polarization quantum. The polarization quantum is the charge times the lattice vector divided by the volume. Centrosymmetric solids those that are non polar have centrosymmetric polarization lattices. And if you make any array of numbers if you want the list of numbers to be centrosymmetric to be equal to the plus or minus. There are only two ways you can do that you can do that if they contain zero, or you can do it if they contain a half half a quantum. And so these I'd say are two really key results of the modern theory of polarization. So this might seem a little bit unsatisfactory though polarization we'd like to think okay it's just like should be a number to be a kind of thermodynamic quantity and how could it be this this list of numbers and let me show you how we connect this slightly abstract behavior to experimental reality. And to do that, we should compare our centrosymmetric or para electric or non polar lattice so this alternating plus and minus ions with the photoelectric polar case that we looked at first. And I've tried to line these up so that I've lined up the anions the negative charged irons above each other. In the ferroelectric polar case, I've just shifted the cation to the left. So the dipole is made by in each you in each cation is sorry to the right each cation is shifted to the right to make the polar case. And if we compare these two. If we look how the polarization how the dipole moment for you to follow you changes between the centrosymmetric para electric and the polar ferroelectric structure. If we choose this unit cell we see that the dipole has changed by a charge of plus one shifting to the right by delta. If we choose this unit cell which started off with a different value for its dipole moment. Again the change in polarization as we've gone from centrosymmetric to polar is a charge of plus one shifting to the right by a distance delta. The unit cell we choose whichever say whichever branch of the polarization lattice we're sitting on whichever value we're taking of this many valued quantity, we get the same answer for our changes in polarization. The change in polarization is plus the electronic charge times the distance it's the cation space divided by the. And of course when we make a measurement actually a thorough electric polarization, what we measure is always a change in polarization we for example switch the orientation of the electric polarization and see how much current flows through an external circle. So we have a exact connection between the theoretical situation and the experimental reality. So I'm bringing that to my list of key results of the modern theory of polarization polarization is multi valued centrosymmetric solids don't have to contain zero in there in their list of possible values, and this is all okay. It costs differences in polarization, for example the spontaneous polarization, which is the chain polarization between a para electric and a ferroelectric state are single that. Okay, I'm not going to go through too much of like the actual background theory that the kind of proofs that underlie these statements, you should either go back to the original papers if you're really comfortable. Basically, if you want to kind of easy conceptual introduction before that I have a kind of a tutorial article I guess which is a little bit more gentle introduction. I also have a series of YouTube videos if you don't want to read if you just want to watch the movie, which will give you a little bit more background. Before we go on to use this though I should just tell you practically how if you want to calculate a polarization using quantum espresso or any other electronic structure code. How should you go about doing it so that you have that kind of in your toolbox you can go practice with the skills you've been learning last couple of weeks. The first thing if you have a bulk periodic solid and you want to calculate its polarization first is you have to calculate the structure of the solid you have to calculate the positions of the ions. And what's super important is you have to make sure your system is insulating if something is metallic. It can't sustain an electric polarization and so I'm sure you've been learning this week about for example magnetic insulators these could be rather challenging to achieve insulating behavior in a density functional so you have to be very careful and make sure that your system is insulating in order to have a sensible definition of polarization. Once you do once you have that and you have a few choices. The first option is you can do just what we've been doing with these cartoons, you can take all of the ionic positions and multiply the position of the ion by the formal charge and add them up. You can work out the dipole moment for unit volume just by simply saying okay calcium is plus two oxygen is minus two lithium plus one and so on some of those formal charges and multiply my positions. This is an approximation it doesn't give you the really the true answer but it actually is not that it's not a bad approach it's not going to be too far off from the true answer. Normally the correct answer. You can do one of two options the first option you would first sum over the ionic positions again and multiply by the pseudo charges the charges on the pseudo potentials. And that gives you the polarization the dipole moment for units are coming from the ions from the ions described by the pseudo potentials. So you have to add to this the contribution from your valence electrons, and you can calculate that by summing over the centers of the bannier functions the bannier centers, multiplied by how many however many electrons each family function takes usually to maybe one of the magnetic system. And this approach is is formally correct this gives you formally the the correct DFT value for the for the polarization I'm not sure if you learned how to construct bannier functions in the last couple of weeks but this is a very nice kind of capability or extension to quantum express the quantum express it's one of the codes that's most set up for calculating these bannier functions. The third option which is also formally correct and is formally identical to option to is to sum over the ionic positions, multiplied by their pseudo charges that gives you the ionic contribution and then to get the part coming from the electrons, you can make what's called a very face calculation of the electronic contribution. This is basically the same as the bannier function contribution but working in reciprocal space instead of real space, and some codes are more structured to make the very face calculation more convenient than the bannier construction. So you can take any of these methods but what you have to realize is whatever option you take, your answer will be multi valued, you will never get just one answer you'll always get the answer plus n times this polarization quantum, and that you can't get around it's not wrong, that's really the way bulk polarization in a period of solid. Okay, so that's the end of the difficult bit the difficult bit the stuff you have to learn if you want to save the world and now I'm going to talk about some examples. I suggested to send her at the start of anyone has questions that you really need clarifying just type them in the chat and you'll take a look and you know everybody types in I have no idea what she's talking about. I can go back and explain some stuff again or otherwise we can take questions at the end to prefer so just go ahead if you type in the chat if there's something you'd really like to ask right away. Okay, so let's look and see how this works in in in a real material and the material that I've chosen as a perovskite structure upside bismuth ferrite it's what's called a multi ferroic material. And that means that it's both thorough electric so it has a spontaneous polarization, which is along the diagonal of the perovskite unit cell. And it's also magnetic because of the presence of the iron. So the iron ions are very large magnetic dipole moment they're surrounded by an octahedron of oxygen ions in the perovskite unit cell, and the iron ions provide the magnetism. And then the bismuth ions that are the corners of the unit cell in purple here, they provide this very large electric electric dipole moment in the unit cell. Here's a picture of one of the earliest earliest known crystals of business ferrite this is a rather beautiful sample it's a single crystal. This kind of firm like structure. This these are twins these are different orientations of the polarization kind of meeting each other. And that gives it this rather rather beautiful texture so this is a sample from the 1980s from hands late hands from the University of Geneva. You can see, we mentioned already that thorough electrics have to be good insulators. This looks like a metal. It's actually not a metal it's an insulator but it has a rather a lot of defects in it and so this is why it has this kind of kind of black color so this is very pretty crystal but not a particularly good crystal for doing high quality characterization and it certainly can't be has a polar you couldn't switch the polarization electrically so it's not good for making thorough electric devices for example. Here's another sample and this is a sample from the early 2000s from the group of Ramesh and this is a high resolution electron micrograph of the same same material, which you can see is very perfect at least over the length scale of a few nanometers. So this is on this high resolution electron microscopy method is looking down columns of atoms in the structure so it would be kind of looking down this direction in the cartoon here. And the white dots are columns of bismuth atoms. So you can see it's forming the kind of cubic perovskite structure. And maybe you can see if you have a good screen these very slightly lighter dots in the middle. These are the iron ions one doesn't see the oxygens with this technique. And if you have very good eyesight, you'll see that the iron ions are not exactly in the middle of the bismuth ions and that's because there's structural distortion in the material that makes the dipole. Of course, it would be easier to see the dipole if we saw also the oxygen anions. So this was a real breakthrough for the for the field of understanding thorough electricity and these magnetic thorough electrics when such beautiful high quality films could be made. Yeah. And so the polarization is along the 111 direction. This film is grown so that 111 would be in the diagonal. And so the polarization, this is a kind of thin film, a layer, the polarization that's pointing out of the plane of the film, which is the part that can be measured, has a has a value of about 50 microcoulons per square centimeter. And we'll come back to this number later. You don't have to remember it. Okay, so I want to show you then the first calculation of the polarization in bismuth ferrite a density functional calculation of the polarization to illustrate some of these concepts that we introduced at the start of the talk. And so this is work done in 2005 by Jeff Neaton, Claude Edderer, Umesh Bangmari, myself and Karen Rae. And what's being plotted here is the polarization. I converted it to the polarization in that zero zero one direction perpendicular to the plane of the film because that's what I want to discuss later. And the x axis here is the percentage of distortion, where zero represents the centrosymmetric para electric structure so with no polarization. And plus R3C R3C is just the space group of the ground state plus 100 means the system is completely relaxed to its ground state with the polarization in one direction, and minus 100 is with the polarization reversed in the opposite direction so that the Okay, so let's I want to point out a couple of things and first I want us to look at the undistorted centrosymmetric non polar structure and look at the values that one calculates for the polarization. I think this I have to confess I think this was done using the best code and sorry it was a long time ago I don't remember. Let's look at the values and for the unpolar non distorted structure, we see that we don't have zero as a polarization, we have 50 minus 50, 150 minus 150, and so on so this is exactly or analogous to the simple one dimensional chain that we looked at the undistorted centrosymmetric structure has a polarization lattice that doesn't contain zero. It contains instead the half polarization point which turns out to be 50 micro clones per square centimeter. Okay. Then when we gradually allow the structure to distort to its for electric structure you see that the polarization involves from its value in the undistorted structure and whichever branch on this polarization lattice we choose to evolve from whichever unit cell if you like we pick to evaluate the polarization. We have exactly the same evolution and the measurable bit that we measure if we do a switching experiment what we call the spontaneous for electric polarization. That's the difference between the thorough electric and power electric values that's the same in every case right and so whichever of these branches we measure or we calculate along we get the same value for the spontaneous polarization. Here's the polarization quantum, this is the charge times the lattice vector divided by the unit cell volume, and in this case it's about 100 units micro clones per square centimeter. Okay, so that's how it looks when you go and make a dysfunctional calculation of polarization for a both periodic song. Okay, a couple of things I want you to notice. The first is this zero here. And also over here. And this is an allowed value for the polarization of the fully thorough electric structure if it's in one orientation or another the loud values of the polarization or 100 200 and so on. The spontaneous polarization is 100 minus 50 it's about 50 micro clones per square centimeter, but one of the allowed values is zero and this is not something we noticed at the time but it's going to be significant for some new results I want to show you. Okay, so we have this zero in our allowed values polarization for the actual thorough electric polar structure. The other thing I want to point out and this may be totally familiar to many of you is what the units are polarization is this is going to lead us into into the next point. So the unit so think remember polarization again is dipole the unit volume dipole is charged time distance of a volume which is distance cubed. So the units of polarization come out as charged divided by area right so charge times distance of a distance cube is just charged over area. And in the thorough electrics community, for some reason which I don't know why that usually that charge is given in microcoulombs attended the minus six columns, and the area is given in centimeters way I guess because then you get kind of nice numbers coming out for your for your values so microcoulombs per square centimeter. Okay, so that leads us immediately to see that associated with thorough electricity associated with the thorough electric polarization is a surface charge just by looking at the units that we can see that immediately. And this is really the case here's a kind of bulk solid again it could be a thin film it could continue and in the in the direction in the plane. And the bulk polarization the electric dipole unit volume is some value let's say P perpendicular to the surface microcoulombs per square centimeter. When I make a top surface then above this spontaneous polarization, I have then a surface charge of plus P microcoulombs per square centimeter so the size of the surface charge is equal to the size of the bulk polarization. And likewise, if I make a surface at the bottom, when the polarization is pointing up if I make a surface at the bottom, I have a polarization whose size is equal to the, I have a surface charge whose size is equal to the bulk polarization, but whose sign is now minus I have minus P microcoulombs of charge on the bottom surface for every square centimeter. And this is one could see just from dimensional analysis. So this surface charges very nice if you're for example, interested in catalysis or electric chemistry then we want to have a surface charge because it makes a surface reactive. If you want to have a stable for electric device let's say you want to store information in the direction of the polarization. Having surface charges very bad because you know that gaseous theorem this is electrostatically unstable there's a diverging there's a discontinuity in the in the electrostatic potential and diverging electric field. And so, particularly when you have a very thin film so that the surface charges can be large relative to the volume and very close together. And this can be very detrimental to the behavior of a thorough electric and so what what can happen is usually bad news people spend our lifetimes trying to figure out how to compensate this surface charge. So it, it will somehow try to suppress the polarization so for example the polarization might go in plane right because if if I have a film and my polarization is in plain they don't have any surface charge on on the surface. But split up into domains because then I have only a little bit of positive charge here and then immediately some negative charge so averaged over this whole surface, then I don't have any so much net charge. The system might spontaneously generate electron hole pairs to compensate the charge so it might make excitations of electron hole pairs across the gap so the electrons can come and sit on the positive surface and screen and can neutralize the surface charge. The holes can go to the bottom surface. And it can even form, make a phase transition even to a state that doesn't have any polarization so it can go and stabilize the power electric state, or maybe even make a completely new phase that's actually non problem. And I want to stop by showing you an example of this last case because it's a really beautiful example I think of where density functional theory calculations were able to contribute to understanding this, this topic. Okay, so this is work that was done by Julia Monday who's now an assistant professor at Harvard University and bestian bestian Grosso who's a PhD student in my group who did the density functional calculations. And here's another high resolution transmission electron micrograph of a film that Julia grew, which was made of lanthanum ferrite so lanthanum ferrite is not a thorough electric it's a non polar material. Then business ferrite the material we've been discussing, and then lanthanum ferrite again. And we want to look at the layers in the business ferrite remember when we looked at business ferrite previously we're seeing the business again when we looked at business ferrite previously. The business formed a nice kind of square array because they've all shifted in the same direction to make the thorough electric polarization. In this case you see that Julia's blown up the kind of section here. We have this pattern of two business going up. The blue is going down. The blue iron, the blue circles are the iron irons. Then we have a row of business not going anywhere. And then a row of business where to go down directly below the two the two that went up before, and then to go up where the two went down. So we looked up and said well what on earth's going on here they had these microscopy images but this kind of pattern of business displacements did not correspond to any known phase of business ferrite. Bastian was able to use density functional calculations to search for structures for arrangements of the bismuth iron relative to the FeO6 octahedra in perovskite based business ferrite that were of course higher in energy than the ground state but not too high in energy. And he was able to identify a new phase which had not previously been considered which is PNMA symmetry and has this antifurroelectric pattern of the business. As you don't see it so well from this orientation but it's two up, two down, then a layer where they're all the same and then two down, two up. And this was only 30 milliolectron volts per formula unit above the R3C ground state, the usual thorough electric ground state. And then he was also able to show using a simple electrostatic model that if your film is thin enough so here he's plugging the energy in milliolectron volts per formula unit as a function of atomic repeat units so business a business oxygen layer plus an iron two layer. For the R3C structure, which is thorough electric and has this problem with the surface charges, and for his new structure, which is anti I'll show you in a moment is antifurroelectric, so it doesn't have any surface charge. The R3C structure, the thorough electric structure, its energy goes up and up and up, as it gets thinner because of the unfavorable electrostatics, but this non polar structure doesn't care about getting thinner because it's some, because it doesn't have any surface charge and so below a certain it has what's called antifurroelectric hysteresis of the blue lines here so in the absence of any electric field. The polarization, the measure polarization is zero, but when you apply an electric field it switches to a polar state you take the field away it switches back to this non polar state and again in the other direction. And these antifurroelectric materials are very important because they're candidates for very high energy storage so this is my first example of a density functional theory calculation being used to to engineer materials that might contribute to saving the world in terms of affordable energy and climate action because one needs of course if one has an alternative source for energy to have a way to store it and antifurroelectric there are candidates. Okay, I wonder are there any questions Sandra I see the see the number ticking up in the chat but I can't see the question so if anybody wants to ask anything I kind of I don't see questions in the chat for the time being I asked everybody to write their questions in the chat if they want to ask questions so I'll keep monitoring that. Okay, I'll keep going I'll give you like a 10 seconds to kind of breathe because now I'm going to do a totally different different example. Okay, so that was our first example designing new antifurroelectric materials based on the understanding about polarization that we're able to gain from our electronic structure calculations. I want to introduce another concept now and this is going to be the finding happens. So if you're waiting to see how electronic structure calculations to make you happy. So I want to go back remember to this simple polarization lattice we had just plus minus plus minus charges the centrosymmetric lattice that was it was non polar, but it didn't have zero as it's as any of its allowed values. And business iron oxide in fact is analogous to that very simple example that we looked at earlier in its centrosymmetric form. So when business right is in a non polar para electric structure for example it's in the ideal cubic perovskite structure. It's polarization lattice doesn't contain zero it contains the heart quantum. Oh, sorry. And I can illustrate this here is perovskite structure business ferrite in its ideal cubic structure with no polarization so the iron is right in the middle the positive iron is right in the middle of the negative oxygens. The business are exactly at the corners in a square and so there's no dipole. If we look at the charges of each layer. This layer in the unit cell has one business and one oxygen, it's business three plus oxygen two minus so it has a charger plus the electronic charge. The next layer one iron iron and two oxygen irons, the iron is plus three each oxygen is minus two. So the charge in this layer is minus one electronic charge and so on. So if I look at the layer charges for unit cell, I have exactly the same situation as in that simple cartoon we did earlier I have plus one minus one plus one minus one equals based and we saw already that such a structure has a polarization that doesn't contain zero. Okay, so the polarization. Yeah, if I work it out then for this unit cell, then I have a charge of plus one at position zero I'm working out the polarization out of the plane in the z direction, have a charge of plus one at position zero. I have a charge of minus one. So minus a position a over to where is the unit cell and I divide by the volume to normalize. So the blue square is my unit cell, I have a charge of minus one at position zero so that contribute zero, then I have a charge of plus one plus a plus a over two and I divide by volume to normalize and so on. So I have this polarization lattice that contains the half polarization quantum but doesn't contain zero. As a result of this then because my business ferrite in its centrosymmetric phase doesn't have zero as an allowed value of its polarization. This means that there is a surface charge associated with the polarization, even in the centrosymmetric power electric phase. You can see that also just kind of maybe it's even more conceptual to think of it in this cartoon way. This layer which contains business with an oxygen is a positively charged layer. And so if I put a surface above that, I'm going to have a positive surface charge. There's nothing to do with any further electric polarization it's because of the internal layers of the material. Likewise, if I make the surface just above the FeO2 layer, I'm going to have a negative surface charge associated with putting the surface just there. And if I work out the values of the surface charges in the ferroelectric units, what I find is that the surface charge associated with the business oxygen surface is plus 50 micro coulombs per square centimeter. And the surface charge associated with the FeO2 surface is minus 50 micro coulombs per square centimeter. That's if I convert one electron per unit cell into ferroelectric units. And if you remember back to when we first looked at the polarization in business ferrite, the spontaneous polarization in this 001 direction, the polarization that comes from the ferroelectricity when the business ions displaced relative to the rest of the unit cell, that also had the value of 50 micro coulombs per square centimeter, right? I want to emphasize this completely coincidence. Business ferrite is the only material I know where this happens. It's completely an accident, but it's going to lead us to some very interesting, I don't know whether to call it physics or chemistry, very interesting kind of physical chemistry as an outcome. So this again, just to recap, this surface charge is coming just from the way that the atoms are layered. It's there in the centrosymmetric phase. It's nothing to do with the ferroelectricity. But then we have in addition to that a surface charge that comes from the ferroelectricity. Of course, in practice, they're both there, but we can as a thought experiment decompose them into these two contributions. Okay, so here's another cartoon. Here's my slab of business ferrite. I've put an ethio to minus surface at the top and so I have a surface charge from the charged layers of minus 50 micro coulombs per square centimeter. I put a business oxygen layer at the bottom. So I have a surface charge coming from this charged layer of plus 50 micro coulombs per square centimeter. And in addition, in ferroelectric business ferrite, in its polar ferroelectric state, I have a spontaneous polarization in addition to this, whose size is 50 micro coulombs per square centimeter. So you can immediately see then depending on how the polarization is oriented relative to these surfaces, I can end up with a net surface charge that's either very large or cancels out to zero. Right, so I 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 charge layers from this half quantum polarization. So, if for example, if I keep the same orientation of the business ferrite I have the ethio to minus surface at the top, and the BIO plus surface at the bottom, and I polarize it in the up direction if I just leave the film sitting there it will do this spontaneously. Then the surface charge from the polarization exactly cancels the surface charge from the layer, and I get a net surface of zero. And so this is where we find happiness in our electronic structure calculations this is a really happy electrostatically electrostatically completely content surface right there's no surface net surface charge there's no diverging electrostatic potential. This I can make a very, very thin film of business ferrite provided I choose this combination of surfaces and this orientation of polarization, and it's electrostatically stable. This is completely remarkable I mean I think this has not been. It's very, very difficult to make a thin film of a thorough electric and not have it want to explode. And business ferrite it happens spontaneously because of this unusual cancellation. We should have realized this in pre history when we first made this calculation and I pointed this out to you earlier that the total polarization was normally when one calculates the polarization of a thorough electric ones only interested in the spontaneous for electric polarization this was indeed what we were interested in at the time, but the total polarization can actually be zero because the total polarizing this calculation one has of course all the irons there so one. The system knows about the internal charged layers and business ferrite in its bulk thorough electric state has a can have a total polarization one of the other values is actually zero this manifests in these happy services. The converse of course is if you try to switch the orientation of the polarization business ferrite. It's even more unhappy than in a conventional thorough electric because you have the surface charge from the polarization. Adding to the surface charge from the charge layers and it's doubly unhappy than it as it would be otherwise. This shows up in an electronic structure calculation. This is a calculation of the density of states as a function of energy the family energy shown at zero. So this is the balance band and this is the conduction band layer by layer through these slabs. Let me start on the right hand side this is what a thorough electric usually looks like a thin film of a thorough electric. You see there's a strong internal electric field which causes the bands to bend. You can also see that the top of the valence band starts to overlap the Fermi energy at the top and the bottom of the sorry, the top of the top of the valence band and the bottom of the conduction band. This is making holes up here to try to compensate the negative charge and making electrons down here to try to compensate the positive charge. So this is a typical thorough electric slab with the net polarization in the happy configuration. There's no internal electric field because there's no surface charge. Okay, so this results I'm showing you now and then the next couple of slides are going to stop after a couple of slides or if you're getting tired. The result of a really lovely collaboration over the last couple of years together with Chiara Gattinoni who was a Marie Curie postdoctoral fellow in my group and is about to start her independent assistant professorship in the University of London. Marta Russell, who's beautiful electron microscopy data I showed you earlier who's now a microscopist at MFA, the Swiss National Materials Lab, and EPAC FA who was actually a master's student in my group who's now a PhD student actually growing things on. She moved over to the dark side and decided to make examples. And these two papers came out just in the in the last months, one discusses a lot of the kind of technical interplay between this layer polarization and spontaneous polarization if you're interested in the technical side. But I'm going to show you next is an application of this, of how these happy thorough electric surfaces can be helpful in in water dissociation. So generating generation of hydrogen for fuel cell and energy applications and also water remediation so for cleaning up water. So back to the saving the world question. Okay, so water splitting. So remember we have two kinds of surfaces now we have happy surfaces which are charged neutral and unhappy surfaces extremely highly charged and what we found again with our electronic structure calculations is that on the happy surfaces water molecules like to absorb they absorb stably onto the happy surfaces which is what you would expect right if you have a neutral surface you're likely to be able to absorb a neutral model. On the unhappy surfaces, we still have adsorption there's still a negative adsorption energy but this time it's it's for the dissociated ions of water and of course the OH minus ions. So I've turned this round I'm sorry adsorb on the positive charge of surface which is the business I had that on the bottom before I apologize for that. And the H plus ions absorb on the negatively charged FE. So you could then envisage a cycle for effectively water splitting in which when the business ferrite slab is happy water molecules absorb on the services. So we have a shift for example with an electric field, the water dissociates into the ions, and the positive ions stay on the negative surface the negative ions leave, and the positive ions leave the positive surface and keep the negative ions have a very effective way then of splitting the water into its constituent ions. Then you let the film relax back. The ions the charged ions are released or stepped off the surface and no longer wants them, and molecules are reabsorbed. So one has a nice cycle for water splitting. I want to show you some, I don't have the data to show you for this yet I can tell you it's been done but it's not yet published by our experimental colleagues, but I want to show you something related, which rather than water splitting where the goal is to generate hydrogen. The goal was water remediation. And so this is the work of Salvador panators in the mechanical engineering department at ETH, and Salvador took these very nasty toxic dye molecules, this is a vial containing this cartoon of molecule molecule called Rotamine B, which is what's used to dye your genes and ends up of course in the water supply wherever your genes are at dye. He mixed this solution with bismuth ferrite. You can see not beautiful pristine thin films of bismuth ferrite, just bismuth ferrite nanoparticle crystallites or micron sized I think crystallites. And when he did that, he found that the bismuth ferrite broke down this nasty molecule into its constituents into small molecules like methane and carbon dioxide and water which are not toxic. And we think that the mechanism is very similar for the water remediation as I showed you for water splitting. What was nice, I'm not sure that it's useful particularly but I think is rather cute, is that this process is strongly can be strongly accelerated using magnetic fields because of the multi ferroic properties of bismuth ferrite and so this was also a kind of nice, nice feature maybe not particularly useful but it was kind of fun. Okay, I'm going to just quickly skip to the end because I had another example in case I had time but I don't so let me skip to the end because I have some homework for you. I'm giving you a long deadline I tried to work out roughly your guys age so when you're likely to retire so you have to summer 2065 so when you were long and exciting careers. Your job now is to pick one of these sustainable development goals or more than one if you like and use the skills that you've been learning during the school and during the rest of your training your electronic structure theory methods and think about how what you're doing can contribute to solving the to reaching these goals and saving the world so I showed you some examples of how our electronic structure calculations are helping with water issues and also both energy and climate action I skipped over device device physics and yeah so pick your own and go off and find your goal that you'd like to work towards. So that's the end of my talk I'm very happy to take any questions and very best wishes to all of you for your ongoing research successes and particularly making nice electronic structure calculations with quantum express. Thank you thank you very much Nicola for this beautiful introduction overview of the theory of modern polarization modern theoreticalization and these nice examples and now we can all contribute to save the world, just by sitting in front of our computer. I don't see any question for a time being Alexander is there any question on YouTube please post it. I'll start myself with a question. This actually has to do with with with temperature temperature effects can be can be can can can be relevant in some of these materials I mean I was wondering whether you know there is any theoretical approach what would be the standard theoretical approach methodology to include also the temperature variable in in in these calculations. Basically by making effective Hamiltonian so one can make makes an effective Hamiltonian and extract all of the parameters from density functional calculations and then solves solves a model. I mean in principle I guess one could do, you know, have an issue molecular dynamics and and for electric phase transition I think it would be perfect it would be really challenging but yeah usually by either kind of some kind of lattice family a function type model or you know post land theory and extracting the land our parameters from, from effective Hamiltonian from density functional calculations. These are quite high so business example I showed you the business far right, the curie temperature is really high actually so even at room temperature. And it's not very different from from zero carbon so it's, yeah but of course it's it's very relevant if you're interested in lower temperature materials so whether curie temperatures are much lower temperature for sure. Yeah. Do you guys learn about an issue and do this week did you do that and in this room. I think we did with there was one session on a permission be yes. We have a question from Ludovica. Are you. Yeah, you're a muted now go ahead. Thank you. Can you hear me. I can. Yes. Thank you Professor for this interesting talk. And I, I want to ask you a question about this particular phase anti ferroelectric phase. Are you shows us and I was wondering if I get, if I get the question is that this this layer is not really grown in this particular configuration. It's right. My question is, if some others behavior can be tuned the discovering other interesting phases with some external tuning of this phase, for example strain or other type of growing of this of this tractor for the devices. Yeah, so that's a very good question and so I'm one of the really appealing aspects of thin film growth is that one of course can grow the material on a substrate that has slightly different lattice constant and strain the material actually quite a lot up to a few percent. And this has been done with business ferrite. And so it's known the face diagram is a function of strain is known, and other things happen that are also very interesting to me. So for example, if you compress it a lot you end up with a giant polarization out of the face you get it out of the bank in a new phase, which has a different symmetry and a giant out of pain polarization. This particular phase that the one that we looked at we pull it up again. It's not very strain dependent. So the experiment has not been done but we. So this is only been grown on lantern for it has a rather similar lattice constant and a couple of other materials that have rather similar lattice constants, but computationally bestian actually looked at the strain dependence. We found that actually over a reasonable range of strain. It doesn't change its relative energy a lot. So I think with this, this particular phase. Actually, we don't really want to modify it anymore we're kind of quite excited to have it as it is and it's fairly robust to moderate moderate changes in strength that's absolutely a very good point and then I don't have a picture here bestia major phase of strain electrostatics and saw how we've you modified one of the other and get into different regions of the phase space. Very good question. Okay, thank you. Now the ice is broken and there are several questions coming. I guess. You are muted now. Can you ask the question. Yes. It was said that the polarization of the solace has multi value when we calculate it. I can picture that what is the meaning. This whole meaning of the multi value of the polarization. When it's when perform the experimental it makes sure in many was to or anything I can picture is. Thank you. I'm not sure I could, I'm not sure I could hear you very well was the was the question what is the meaning of the physical meaning of the multi value. Yeah, this is a good question. So I can tell you how I think of it. And without a kind of. Gary, whoops, I forgot to show my screen without. I'm not sure how rigorous this is but this is the picture I have in my head so he is seeing my my periodic solid again. Okay, let's imagine so here's my my periodic solid. Let's imagine I take an electron say off of this and I am. And I move it by one unit cell right so I do a thought experiment I pick an electron off an and I move it to the and I'm in the next unit cell. When I do that. It's a periodic solid so every and I am moves. It sends an electron one unit cell to the right. So at the end, nothing has changed right my physical system is exactly the same. But when I take a charge and displace it by a distance are my polarization has changed by the charge times the distance I've moved it divided by the volume. So that's saying that's how I think of the physical meaning is that I can always change the polarization by any amount by any integer times the charge times the lattice vector divided by the volume. And that doesn't change the physical system. I don't know if that helps but that's that's for me how I kind of reconcile this strangeness with kind of technically. I have another question Christian, you're muted now. Yes, thank you. I want to ask, I want to first thank you, the ICP member of the organizer and the lecturers. My question is to know how the solution effect is done in one to express so is it empty seat or SPC. And for the molecular absorption or favorite with water. How is it. Ah, so yeah, I don't think we did these either in quantum espresso they were also done with fast, I have to confess I'm really sorry that we are doing some kind of quantum espresso. So the water absorption was done with. Oh, I don't remember the exact acronym of the functional, but one of the functionals that describes very nicely water. But you can look it up. It's detailed in the paper, but it's a very good point for for water you have to be very careful to have a suitable functional that's appropriately describing the hydrogen bonding and so on there and there are now many nice modern Functionals that do this and I'm sure many of these are also available in quantum espresso and the kind of practical qualities of the calculation it was a very large supercell so we could make a slab of business ferrite. We had to force the polarization when we wanted to be in the unhappy orientation, we had to kind of basically lock the polarization in the unhappy orientation otherwise we wanted to switch back the other ways that was a little bit complicated. Yeah, and then of course make sure to have a functional that's appropriately able to appropriately describe both the water and the ferroelectricity of business ferrite. And I apologize I don't remember the name of the function. I have a question from the YouTube chat about the choice up to the potentials whether there is anything that you can recommend the terms of choice up to the potentials ultra soft PAW for calculation polarization. In general, so I think that you know hopefully your choice of pseudo potential shouldn't matter right I mean you should always give you the same same answer. Of course every pseudo potential you take one has to test in in the situation that you're using it in. I think what's maybe more delicate is the choice of exchange correlation functional. And so this has to be carefully tested that it's appropriately describing the ferroelectric polarization because you think about you know this polarization when the onions and cations move off center this is quite a, you know, a delicate description of the bonding process between the transition metal and the oxygen and so that also has to be chosen quite quite carefully, but I don't have any, you know, hopefully all potentials should give really the same answer and these days you guys are kind of fortunate these days you because you have the libraries and they're often very well tested so we have to have to make our own in the olden days and then it was then I guess you really knew what you were getting. Okay, we have a very last question for one of the students, Stefano Baroni. With this, Stefano, you can unmute yourself. Well, I said, I will rather give up my question and leave and leave more room to participants. Yeah, I think we're essentially done with the questions. There are no further questions for the participants so I think you have a question. Let me just, let me just ask the last one. So, Nicola, first of all, thank you for this spectacular lecture. I think that we all enjoyed very much. So the difference between a happy and an unhappy surface, if I understand correctly, is the volume contribution to the total energy of the system that takes a term that is the square of the electric field times the volume, right. So if you have a macroscopic field in your sample, you have an electrostatic energy that is E squared times the volume, right. Yeah. And in order to neutralize, in order to make the surface happy, it would be enough to neutralize the surface with some charge rearrangement, right. So in the happy, sorry, go ahead. No, no. So in the happy surface, if you like, there is no surface charge because the photoelectric polarization is neutralizing the surface charge from the, from the layers, or if you like in the happy situation. The polarization is actually zero, because the spontaneous polarization cancels the layer polarization. So there's nothing to neutralize. We probably have a different conception of happiness. I thought, I thought the opposite. I thought that when you have that take, take, take a non a non a polar system, take a system a ionic system, and if you have a polar termination of your of your of your ionic system. You could have in principle a surface charge that would give rise to to to a bulk energy proportional to the square of the internal field, right. Exactly. Yeah, yeah. And then the happy and this is usually compensated. And this is usually compensated by a local rearrangement. The surface atoms and surface charges that costs an energy proportional to the surface. And that compensates a volume, a volume about energy so eventually it is always favorable to rearrange the charge at the surface, paying a small price to make a little a big gain in the volume. Yeah, exactly. Yeah. In the happy situation, you don't have to do that you don't have to pay that price, because the surface charge that's coming from those ionic layers, basically the polar surface is compensated by the polarization from the federal electric. Yes. That's why it's happy, whereas in the unhappy surface, you still have to in practice of course you have to do something like you reconstruct the circuit you add extra surface charge, have a metallic electrode to screen it adsorbed positively charged. Okay, okay. But. So the mechanism is similar to what I was describing, but starting I was describing what would happen starting from a non polar system. For instance, the central symmetric ionic system, and you are describing exactly the same mechanism for a system that is intrinsically polarized because it is a ferroelectric or whatever right. Yeah, but the difference between happiness and happiness is just a local rearrangement at the surface of atoms and charges at the surface right. You can always pass from happiness to unhappiness just by swapping a few atoms or by adding some charge at the surface. No, because in the unhappy. Well, yeah, if you add well, I know I don't think so because if internally you, let's say you have, you keep your surface planes, the same surface planes, say, to the top of the bottom to go from happy to unhappy, you really reverse the polarization. So it's like, in one case the business of all moved up. In the other case the business of all moved down relative to the other layers in the unit cell. So it's, it's the polarization. From the point of view, from the point of view of bulk symmetry of bulk symmetry polarization up and polarization down are two different realizations of the same broken symmetry they have the same bulk energy. Yeah, they're the same bulk energy. Okay, so they're the same bulk energy, but you've changed their orientation relative to the surface. So for sure, you could pass from happy to unhappy by putting half a model half a unit cell on the surface so you can say up and FEO two minus and I'm happy. If I put a layer of business oxide on the top, then I become unhappy. Yeah, exactly. In that sense, you pay so the difference from happiness to unhappiness is cost a surface price, not a bulk price, because you do something at the surface and you pay something per unit per unit surface. So doing something on the surface, you pay a surface price, but then you gain or lose a bulk energy, because you switch an electric field on and off. Right. Yeah. Yeah. So, Stefano Nicola, can I suggest that perhaps you can do this discussion. I want to make sure we have a we have a happy ending to this. So, okay, we discuss later. Nicola, I will ask you the question in person the first time we meet. Very good. Nicola, thank you very much. Thank you. There are there are dozens of thank you messages in the chat. Yeah, so thank you very much again and we'll close this session now and I guess I will leave the floor to Elisa if she's connected. Yes, I'm here. Yes. So Elisa is the big boss the director of the Max Center of Excellence so she's going to give us some closing remarks. Thank you, Elisa. Thank you. And actually, yeah, I don't really see myself as the big boss and I see many big bosses there of real work. Just try to say a few words to finish with the school which in my view I even if I didn't follow it all is really an exciting event. Before that, let me just tell you, I think going to a school is somewhat becoming part of being part of a community. And even if you didn't get it in person, in a way, what I think is that you will be discovered in a number of years that the people that you met here, you may keep finding again around I kept finding my schoolmates of some summer school in conferences in panels in committees in faculty meetings. I think this is an opportunity that you have had to network with many people meet many colleagues, but then also start meeting scientists and have it at such an international level and and having the opportunity of meeting top people I think by the way, because we are at ICT P and Sandra and the others are here I think one of the big reasons why I think we should be all be grateful to ICT P is that they share with Spanish press and many of us the attitude that in the schools you don't just go and pray the low level things that people should like to should have. The idea is keeping the top possible level of speakers participants in the world that can tell you about what they do and I think that's what I think our community should be very much proud of and ICT P is helping a lot in that direction worldwide. But so let me just tell in this case you had a lot of opportunities I'm sure you will realize already now and you realize even more as time goes by, but one. Okay, let me let me put that in numbers first so so that you can see and thank you to even who just provided last minute the summary of the numbers. The numbers are breaking all records for ICT P but also for for max in terms of numbers of people who applied to be to participate in in this meeting and then the fortunate. And who apparently are very happy about about their experience they they come from many countries in the world and that this is a really an experience of international interactions and and I think you had keynote speaker lecturers and tutors from a very provenance and also very high level I was especially happy of one number which I didn't see here, and this is that out of this 125 participants more than 50 are women and more than 42%, which is something that for a long time didn't happen and I was very happy to see happening here, so this is becoming more and more diverse, not only in terms of the geographical distribution but also in terms of who we are participating in in in all this. And one point that I that I wanted to highlight here is that with respect to to to normal schools here you have a very special opportunity to mix users and the developers of codes. People who are so you're not just mixing physicists chemists and material scientists are whatever but you're most mixing people who know about computer science and put the hands in the codes that you're using. And also, together with people who just use the codes and make their science out of their codes, and you also I believe had the opportunity to see the process in the making when people put together their codes and this is partially the result of a community of students. The postdocs who before you work that putting together putting into the codes their science their algorithms, their computational solution so this is also really an opportunity of being part of that community and you will keep seeing them in the forum and you know the correspondence and it's actually very nice that you will have access to people who are the developers and you have seen them faces. The reason I'm pointing out this aspects of developers is that very recently the nature of this process of developing codes is changing a lot. Here in the center of this of this slide, you have a picture which is meant to point out the big advantages in performance that that you get now together. This is from quantum express so today, the numbers that that even put there is that on 24 GPUs. The quantum express was today three times faster than it was on 3000 course of the latest generation. And, and you've been able to see that because it was made. The technologies that were made available to you through the use of the virtual machine, creating your, your configuration in your lab and so on. So you did what I want to point out here is that there has been a big effort that was needed for that, not just in developing the science and the codes from the community of developers but also in making them available in an efficient and also in a practical way to everyone and this is something that is becoming more and more difficult along the year. What has happened in the last year, I think behind the scenes and I don't know if all of you realize that is that there has been an increased complexity in the architectures that we are using to calculate. It has been more and more heterogeneous for example with GPUs and other type of of strategies, mostly made in order to have greener computing so also taking in some sense also care of how to make the world better but anyhow, it was a need imposed by the market of of supercomputers for example and of your computers that people would have to take care more and more of how their codes would be evolving in time. And this has become something that is very difficult to be done by individuals, by individual teams even even by a big team like quantum and that's why you finally will learn what is this Max that you saw in the title of your school. Max is an effort that was co-founded by the European Commission community in in by Europe basically which is devoted to working on codes and on more generally on the whole ecosystem of materials design. I'm able to run in an efficient way at the exit scale so towards the new generation of computers and also to be able to to be used in a simple way that people be trained to use them as in the best possible way. And so this is co-founded by the European Commission and of course by the teams of all the people who work at this and just to let you know and also to thank all the people who contributed to that to work together with the European Commission. It is all the supercomputing the big supercomputing centers in Europe. Very importantly, it's all the the institutions and teams that have worked in developing the codes. So here you see the codes that are involved here. It's quantum espresso below here almost hidden is YAMBO working for especially excited states related to excitations, I would say in general. And then CESTA changing the basis sets, FLIR again mostly working for for a magnetic system and with another electron basis we everything became switched. CP2K, I won't mention them all big data and the AIDA platform that you have learned how to help you organize all you do in an automated way. So and the people in the teams that develop the lead developers of these institutions and of these codes put together so I started to work together in order to try and work on these open source codes where the idea is that you want to make this available to the community that people can see open source. And the idea is that people do all the best to readjust their codes, which means re-structuring their codes, separating the role of the people who will have to adapt to the new architectures with respect to the people who think, have to think of their science and their algorithms. So working to really prepare, rewrite those codes they had been put together by generations sometimes of professors, students, postdocs, people like you for their thesis and so on, but they're not always they were or they are completely in shape to take advantage of the new architectures. So there was a big effort by these people in the codes and the supercomputing people to push that evolution. And the help was also coming from the technology partners and from some institutions like the ICTP and like SICAM and SICAM and SICAY which represent our scientific community and some other partners who basically helped in this big effort which is lasting already for more than five years and we hope it will be continuing. So this is where this name Max comes and the commitment is to continue working in order to make the other codes and especially quantum espresso and the codes that will be related to it as efficient as possible, as performing as possible and also evolving as much as possible to do all the new science that is becoming possible with the new supercomputing architectures, for example, enhancing the capability. Some time ago, just looking at spectroscopies would be extremely difficult because we wouldn't be able to look or looking at phenomena, some of the phenomena that Nicola was talking about would be almost out of reach and we are trying to implement new capabilities, new science, new tools and also much more efficiency in the codes that come with the new architectures. So this is where this Max comes from and where I think some support to the school came, but the school would not have been possible without all the quantum espresso team and all the ICTP team and all the people who supported your tutors, your hands on sessions, all the speakers and all of you. I know you've been contributing a lot and I hope you also managed to interact a lot. So I wish this remains in your memory as an important moment in your education and also in getting to know other people that you will meet again in your future. That's all. Thanks. And I should say, Nicola gives great talks and she also motivates all of us to use quantum espresso for the best, so special thanks also to her. You're welcome. Thank you. Yeah, I'm not sure I should take over now, but I guess it's since I was chairing the session at the beginning, I guess I would probably just say thank you everybody for joining for contributing for attending for participating. And I think we can probably declare the school closed unless there is some further comments, Stefano or Lisa or even or I would like to make a final statement. Okay, Stefano, go ahead. So a very short one. I am really pleased and even moved to tell the whole truth by the enthusiastic reaction of all the participants to whom go my first heartfelt thanks. And I would like to thank individually the organizers who have made this event such a success. Tony cocal from New Biana, Alessandro Stroppa from L'Aquila, Bayran from Shanghai, Ralph Gebauer from Trieste, ICTP, but above all the two heroes of the school are the two events. And Gerardo who is smiling in this very moment and even Karny Mayo who have made the impossible possible and real. You don't know what happened behind the scenes, but we've had a few moments of real panic. And thanks to them, none of you perceive anything. Thank you very much, even and and even last by not least the supporting institutions, the ICTP in the first place, since the Quantum Express Foundation, and of course our main funding source, which is the European Commission. Thanks to all and best wishes for a successful and happy scientific career. Thank you for being with us. Thank you. Thank you.