 Of course. Okay, thank you. Okay. So welcome everyone. Good morning. The first talk of today will be actually a hands-on by Professor Kuan-Sheng Wu of the Institute of Physics at the Chinese Academy of Science in Beijing. So we'll show us how to use this wonderful code, Vanier tools, that can actually compute a lot of properties that are relevant for the field of topological materials starting from Vanier functions and Vanier meltonians. So thank you a lot, Kuan-Sheng, for accepting our invitation. So actually your session, so your hands-on is simultaneously broadcasted in two rooms here at ICTP. We couldn't fit everyone to a single room. So, and then there are also participants joining online. So you will receive questions from, you know, in-presence audience, online audience, and so on and so forth. Without further ado, the floor is yours. Thanks a lot, Kuan-Sheng. Thank you very much, Antimo. Antimo, yeah. Yeah, I'm Chang-Sheng Wu, and thank you very much for the organizers to organize such a wonderful summer school. It's my pleasure to share Vanier tools to you. And yeah, it's a great pleasure to have this opportunity. Okay. And this is the outline of these two tutorials in the day for Vanier tools. The first all, we will show how to use Vanier tools to calculate the topological properties, and including topological insulators, while some metal. And this is the work directory, exhaust as one. And we prepared two PDFs to show you how to run Vanier tools step-by-step and with some input files. And in this tutorial, Yifei at EPFL will also help us to answer questions. And yeah, for the second one is we want to introduce how to use Vanier tools to study the twisted graphing systems and the London levels. And we prepared one program, called the TGTBGN, okay. So it's not a serious name. And we will show you how to use this code to generate telepany model and for twisted graphing systems and also use Vanier tools to study those systems. And those are, I mean, they work directly and the two PDF tutorials. And yeah, my talk, well, I mean, the tutorial we break into two part, I mean, to each session we break into past 20 minutes talk and the 40 minutes hands-on, okay. And thanks to David and Yvonne and because they are, during their talks they already introduced a lot of theoretical background of topological properties. And including the Western loop, very face, very culture. And I mean, the Western loop is also for the Vanier-Charles Center in this session, okay. And so now we can focus on how to use Vanier tools, okay. So if, is there any, please look at this session, okay. Okay. And let's start from the capabilities of the Vanier tools, okay. At the beginning, Vanier tools is designed for topological materials. So at the beginning we have the topological, so the first part is the topological classification, okay. We can use the functional to call the final nodes. I mean, if you can define the occupant and anchor occupant, so you can use this one, this function is to look in for band crossing. If we found band crossing, then we call this gap equal zero. And then it's a metal and metal, then we can use the symmetry to define whether it's a one-cent metal or deoxymer or not one-cent metals. And then we can calculate the white clarity, by culture or by face for those faces, okay. And if we didn't find the band crossing, then it's our insulator. We call the insulator. Sometimes it's not in data insulator, okay. And then we can calculate the data number. We can use a one-cent or call the words to calculate the topological properties, okay. The two number, two number, sometimes middle, two number, okay. But this is not that motion, okay. And after the classification, and then you can also use one-cent to calculate some physical properties and the topological related physical properties. The famous one is the surface states. And you can calculate surface states in decay energy and the momentum energy mode and also all momentum-momentum-mode at iso-energy, iso-energy, okay. And also you can calculate, and these two paths can compare with our past measurements. And also you can calculate the quasi-particle interference that come compared to the STM measurements. And also you can calculate the spin texture or non-muscular conductivity or density of a state or joint density of a state. And also, recently we also developed some new functionality. For example, they calculate the magnet resistance, ordinary magnet resistance, and also London levels and then unfolding from our supercell calculation to our primitive units there. And recently we update our version that can study a very large-scale calculation simulation such as the Trista-Baliagraphian systems. And this is the capabilities and, okay. And now it's for the topological property and service data calculations will also works for the final systems. And let's introduce our methodology. The methodology we use this is, and many of us is based on the Tidebending model. Okay, the Tidebending parameters are constructed with the Hamiltonian and the overlap between two local orbitals and with the Hamiltonian. And these three requirements are needed. The first one is the autogonal basis. The basis should be autogonal with the Java. The second one is we take the Tidebending approximation that's those local orbitals are just a data function, kind of a data function, okay. And also we treat all the bases as a complete basis. All those three requirements can be made by many functions, okay. When we do the DFT calculations, we can construct the function use the great code of Vania90. And we can get the Vania functions and then we can get this Tidebending parameters, okay. And once we obtained those parameters, those Tidebending parameters, we can treat this Tidebending model as autogonal basis, of course it's autogonal basis, right. But the Tidebending approximation it's not that exact because we know that the Vania functions has and does have sub-rex, right. And also it's not complete, but in the energy range that we are interested in, this complete basis is valid, okay. And so in conclusion, that's a Vania basis, Vania Tidebending model is a very good Tidebending model for Vania tools, okay. And also of course you can construct your Tidebending model based on these three requirements, okay. The code structure is like this, the Vania tools is written in fortune and it's shared on GitHub. And yeah, these are underlined here because this name is very old name and then now I can, it's very hard to change it from to remove this one. And it's also NPS supported. And the structures like this, we have a main program, we have a main program, it's MAMF-19. And this we start from read the input, read the inputs that we call the WT.in. And then we can analyze the symmetries. Sometimes it's needed to, for example, calculate the dance of states or calculate the orbital magnet resistance, oh, no, sorry, the ordinary magnet resistance, it can reduce a lot of calculations. And then then next we read the Tidebending parameters. After those three subroutines, we can calculate the function of this that you need. For example, the bulk bands or slab bands from the surface and from the surface in 3D in 2D or and the surface data or lots of other function of this, okay. And so let's introduce two inputs. When it was the request, two important inputs. The first one is the Tidebending parameters. Of course, this is designed by the 1.090. The input file should be like this. The first line is a common line and then this is the number of functions and number of lattice vectors and then the degeneracy of the R points. And of course, this is R, this is the band indexes and this is the hopings again. And then the input, the main input files for 1.090 is called WT.in. In this file, there are two kinds of formats. This one is called unnamely, this is a special format for fortune. I think I don't need to introduce because it's very common in Quanta Express, okay. And after you prepare these two files, you can just run 1.090 without input and output. Okay, this is the input and output we're generating with the given names, okay. Okay, and then we will show you, we will give you one example to show you what can WANITOS provide. And this is a business satellite and it's a strong topology insulator. If you look at the band structure, it's just band inversion at the gamma points, okay. You need to, in order to calculate the topology number and now we know that it's a Z2 topology, it's a 3D Z2 topology number, topology insulator. So in the input file, you need to provide a Z2 calculate, okay, here it's a missing equals two, sorry, it's a missing equals two. And then you need to set the number occupied bands and you need to set occupied bands also. I mean, all bands below the familiar is occupied. So there are 18 bands, 18 bands, okay. And also you need to set the K point that you need to plot the WANITOS loop or we call the WANITOS sensor, okay. Although, I mean, in the code, the K-match are adaptively increased in the WANITOS center calculations because in some materials, the better culture diverging close to some crossing points or I mean, so we need to increase the K-match adaptively. So in the end, you will find that the number K points is more than the initial settings, okay. And after sets, they provide the necessary and taxing this one and you can run the WANITOS and then in the end, you can get, we prepare some scripts you to plot the, there was loops, I mean, the figures, so you just use the general plot to plot this one. And from this plot, you can tell that this is a two and then I mean, as a case, because the other plan is Z to X1, for this one, Z to X0, so there's no crossing, okay. And from the textbook, we know that it's strongly topology, I mean, strong topology insulator and then you can use these six plans to define the topology number for 3D systems, 1, 0, 0, okay. And also you can get the Z2 number from the outputs from that. But I strongly recommend you to plot the WANITOS center plot because sometimes the, if the TATAPENEMODO is not the time symmetric, I mean, sometimes when you construct WANITOS the time-reversed symmetry will break. And then in that case the WANITOS center will also open some more gap here. And in that case, sometimes the Z2 number showed here is not correct. So it's very important to plot them and then to check whether your TATAPENEMODO is perfect or not. Okay, and we know that for if our insulator is a topology insulator then we know that they are the worst loop. All the WANITOS center is non-trivial. For example, here, the WANITOS center links from the zero to one when you evolve the momentum from zero to two pan. This is non-trivial and this is trivial. And also we know that there's a proof you can find in this paper that the worst loop can exactly relate to the surface states. So for example, here, this is our insulator, WANITOS center for our insulator. And then if you look at the surface states you will find that this surface state, so it's trivial. But for this one, it links, the surface data links the development to the conduction band. Yeah, this is how they are kind of homologated to each other. You can find some proof, you can find the proof in this paper or in TITOS NOCRS note, okay. And yeah, that's for a general purpose of the relation between the worst loop and the surface states on there. And for bismuth, for bismuth's solenoid you can calculate the surface states either use the slab band calculation or use the green function, iterative green function. You can calculate the KE mode or in KK mode. This is called the K plane. Also it's called a Fermi arc, it's an arc. And although here it's not an arc, but the arc is from the WANITOS methods. This is also not a very good name. And also you can calculate the texture, okay. And that's for tabloid insulators, okay. But for WANITOS methods, the first, so first you need to find the way that we have band crossings, let's say we can use the band notes, you can calculate the band notes. And once you find the wire points and then you can calculate the chirality. And also you can calculate the WANITOS center in some K plane, some plane. But in this case, it's different from the data calculation. And also you can calculate the better culture, we know that at the wire points it's the better coverage or whatever just here. But here we plot the normalized ones. We just want to show the source and the sync of the better culture, okay. Okay. And in our tutorial, we also provide titanium arsenide for other example. And you can, here one thing I want to show is that when you try to use the fan notes calculation, for example, we know that titanium arsenide does have the wire points. So it's, you only need to specify the very sparse K-mesh in NK1, NK2, NK3 to find the wire points, okay. Okay. And that's the brief introduction of the Evernual Tools and if you didn't download the Evernual Tools.kit you can just use the kit clone, you copy this one. And go into this directory and read these two PDFs and you can, there are two tasks for the first session and the first one is topological insulators. You need to learn how to plot the structure, calculate the weather loop and study the surface states. And for the weather matter, you need to first find the wire nodes and the wire clarity and start calculate the very culture, surface state and from accident. Yeah. Okay. Any questions? So let's thank the speaker. Let's see how many questions we have. I saw there was one there, raise your hand. Any other? Thank you so much for the nice talk. I have a question like, suppose we have a semi-metal, topological semi-metal like LABI, then how to choose non-occupied in that case? Like it is very simple in insulators but in LABI kind of things. Okay. To choose the occupied advancements. It depends, for example, for this one. If we want to check whether there is a topological connection between all those occupied advancements to the unoccupied advancements, all those advancements. For the number of occupied advancements, you need to get rid of the occupied for the, I mean in the election systems, okay. So for example, if you want to study this gap, then it's 18 bands. But however, if we, if you check this gap, okay. For example, here you have a full gap. I mean, at this band, it's full gap. If you want to study whether this gap is topological or trivial or non-trivial, you can set a number of capacity equals 20 because this is 20. Okay. Okay, thank you. For example, for this band, if you want to study whether this gap is trivial or non-trivial, you can also set another number for that. It doesn't matter, it is crossing the Fermi level or not, like, we just, Yeah, it doesn't matter. Yeah. It doesn't matter. Okay, thank you. That's the project, I mean, basically it's kind of, I mean, a mathematical thing, okay. Okay, thank you. Yeah, well. Okay, so there is another question. And by the way, if you are connected on Zoom, of course you can ask a question. And I saw at least one by writing in the chat or raising your hand. Thank you very much for presentation and developing these nice tools. I have a question about maybe related to previous ones. So we heard in another talk by David Wanderbilt that it is not possible to vaneurize only the valence band of topological insulators. So I assume you must include some of the higher energy states. So how do you choose? Which states to include? And also you mentioned something that sometimes the model is not perfectly symmetrical and there can be some gap on opening where it's not supposed to. So maybe you could also comment on maybe some pitfalls of this method and analysis and where we should expect problems. Thank you. Okay, yeah. Okay, yes, for some case, for example, in the twisted biographies systems, for example, in this case, okay. For those bands, they are, if you want to construct vaneur functions only for those four bands, it's almost impossible. If you don't want to break any symmetries, okay. It's almost impossible. For one valley, it's not impossible because if you calculate the vaneur charge center for these four bands, you will find that the worst loop for these four bands is topological trivia. So it means that you cannot construct the vaneur function for these bands. However, if you break some symmetry, if you break, for example, if you break some vaneur or some C3 symmetry, you can, then it makes this worst loop on non-trivial, then you can construct a pattern model for these four bands, okay. Yeah. I'm not sure whether to answer the question. Yeah. There was one question from an online participant. What is the basic for K lines in the K path underscores lab definition? Yes, actually, that's a good question. The basis, right? The basis for the case level. It's that once you choose, because the surface is defined by the surface cut, and then for the first line is the, the first line is R1, and the second one is R2, R1 prime and R2 prime. And then with this R1 and R2 prime, you can calculate, you can calculate the reciprocal lattice right. And then the coordinates, I mean, the units for that K path slab is based on just two primitive units, primitive reciprocal primitive units, yes. Reciprocal lattice vectors, yeah. Okay, so one question was answered and two new questions were asked. Could you please briefly describe the search for the wild points? What is the strategy? Are there any problems when there are no lines in the band structure? Would you brief describe this? Okay, so the first search of wild points, oh yes, that's a good question, okay. So, we are given number of bands and this N and this M plus one, you can define a gap function. A gap function is defined at the hk, it's E N plus one minus E N. So you can get our function called G of K, right. And then you can start for a given starting K points for a given starting K points in the K mesh, then you can use, for example, a CG method conjugate gradient method to looking for a local minimal or for this G of K starting from, for example, for a given K zero, you can looking for the local minimal or for this G of K starting from this K zero and then you can get a local minimal. And then starting from another K, you can also find another local minimal. And we have six times six times six times six times and we have 216 start initial K points, then we can find 216 local minimal. And since we have the web points, so it must, so you must, so it's very easy to find those web points because the gap is just zero, right. And we need to eliminate those duplicates. And in the end, you can get all those K points, those web points, okay. So in the end, it's all it means that you don't need to increase a lot of K points here. But for the north balance systems, sometimes you need more K points, okay. Okay, and... Okay. No, I think there was a last question on four terms, but maybe, I guess that's, you know, you can maybe quickly answer that, but I guess that's a little bit more advanced topic. Okay. For bonus, yes, it's just actually, yes, we do, we do. You need to stress that there's not package it, there's another called system called system or Watson. There is a type in the TV farm, you can check online, okay. The input advanced for that. There is... Okay. System or the election or phone answer, okay. Yeah, okay, so you can specify that you're dealing with phones with a specific line, essentially, essentially. Okay, I think if there are no, if there are any, no, I don't see any other questions. So I think we can move to the hands-on. So, when Shang is... Yeah, so do I need to do something? Oh, oh, they, oh, people can just follow this, they... No, it's, as you wish, I mean, it's... Yes, I think it's easier to show, to follow the instructions, for example, for this one. Sure. The interblush insulators, you can follow, for example, see this one and then you can unzip the, I mean, uncompress, that decompress this file and then you can read it and then I think it's easy to follow it. Okay, so, you know, what we can do is that people just work on this independently and then if they have any questions, I have the microphone here and I'll go around the desk and ask her, okay. And the same for those who might be in the echelon room at the Adriatica with Stepan. Okay, maybe there is one last question, but this really should be the last one, I guess. For spread-field function calculations with semi-infinite slab geometry, do we have a way to plot separately the contribution from surface, just one layer below surface and deep in the bulk? Yes, yes, yes, do. Actually, this one, yes, it's possible, of course it's possible, but it's not implemented. It should be straightforward, if you need it, I can implement it, okay. It's straightforward, actually. Okay, so let's start with the tutorial and then if we have, you know, people have questions, we'll ask you, we'll ask to you. Yeah. That was easy. Sorry, can you hear me? Yes. I have a question about the results for this topological material calculation, which is on the page three of the tutorial. So you have the... Two, three, okay, this one? Yeah, this red plot, this Vanya charge centers, yeah. So it says that in the text that just next line after the plot, it says that it is obvious that this is a Z2 equal to one and then it refers to crossing times between the charge center and the line that you draw from the left to the right is odd. So first I wanna ask what is the line, where do we draw that line? Ah, okay, okay, yes, so in your plot, you have a blue line, right? So in that plot, I do get a blue line, you're right. Yes, yes, that blue line is an automatic method to determine the Z2 number. I mean, if you plot this plot, this one natural center is easy to change because you can get a... You can draw a line. Or just any horizontal line, right? Anywhere. Yeah, horizontal line or horizontal line or any kind of line. Any kind of line should be fine. Then you can count how many times it's crossed this WCC line. That's one, then it's one. But in the numerically, it's not that straightforward actually. Numerically, Alexey Soroyanov and David Van Beert, they proposed a very smart way to automatically tell the Z2 number from this plot. How do they draw that line? They draw that line like this. First, at this K point, you find the largest gap, for example, here. This is the largest gap, right? Okay, that's where the blue line starts on our plot, right? Yes, yes, that's the largest gap. The largest gap of line is just to draw a random line to count how many times it crosses that line between the WCC and that line. So it's automatically... Yeah, I don't know if you can bring that plot, but I cannot share a screen. So on my screen, that line starts, as you said, where you have a largest gap, then it moves sharply down and then it crosses one set of the charge centers, and then it jumps back again to the top, and it's kind of after a couple of zig-zags, it flattens. So I was thinking like, what is the rationale for... Yes, you can draw any kind of line. It's never see the genu. Sorry. No problem. We're a bit ahead. Strange. Yeah, I mean, the point is that it doesn't matter how you draw that line. You can draw this line here, here, here, here, it doesn't matter. But then why they had a special algorithm for generating this line, if it doesn't matter how to draw that line? Because that largest gap is fixed. If you have a van der Tijer center, that one is fixed. That line is exact. Okay. Sometimes you can ask, okay, I can draw a line here, just a fixed line here, right? But that's also fine, but sometimes you forget the number for this line. For this line, if you draw a line here, it's very hard to count how many times it's to cross this line. So it should be more or less obvious, right? Yes, yes, it's not that obvious here. But if you have a line, for example, it's zig-zag like this, then it's very easy to counteract. I see. Okay, so that's probably the reason why we have that zig-zag line, that in my point of view, what it does, it connects one on the left side, you find the largest gap, and then you find the largest gap on the right side, and then it is trying to connect these two regions with a very obvious number of crossings, I would say. That's also fine, that's also fine, but we have the same problem for example here, and this one and this one, sometimes it's just to hold it in the line thing, it's not easy for you. Okay, but this horizontal line cannot have a slope, right? Sometimes, yes. But for example, if your line here, then it's easy to counteract. I see. Yeah, maybe it should select your line like this. But the largest gap is a kind of fixed one, and it's exact for WCC, for WCC approach. Thank you for answering. Yes. Okay, there's a question when we can play to this level. Yeah, there is. I see, it's possible you can play to this level. Yes, of course, of course, yes. They thought that one, that being, just okay. Actually, the weight is stored here. And how to use the broken homes? Okay. Do we include, okay, they have slab. Yes, I think you, in the documentation it's called, it's called the slab, slab, okay. Okay, slab, I think it's called the slab of binder calculation. Actually, we not only have slab of binder calculation, we also have slab of plain and slab of band of wave function calculations. Okay, and then the demo's asked me how, can I explain how to use the blue team? How to slab, okay. So if you want to use it yourself, you can, if you, I mean, you can read the UK slab of F19. Okay, it's here you can, I mean, give a K and then you can get the, the harmonia and then you can diagonalize it. Then we found the energy stored in the, in the aggregate and this one. But if you want to, to, to, to just use the, to use this UK slab, you can use the slab of binder calculated you can show to get the, to get the clothes. Okay. So, I think it's, it's stored here, right? It's here. It's this clothes. Let me open the. On Shang, we also have one more question from here. Yes. Yes. Audience in the room. Yes. Hi. Okay. Yeah. So I have a, some questions about the, the twisted bay layer graphing thing. Mm-hmm. So. No, for the twist of value graphing, I will answer there for the next session. Okay. Perfect. Yeah. Yeah. Because I will let the content for the next time. Sorry. Okay, thank you. Okay. I'll just say ask me to set the layer-specific contribution. Please guide the home should do purpose. Okay. Okay. For the, okay. I will show you the, the code for the website. The F-19 for the, this is our code to show you how to get the eigenvectors for the slab calculation for given k points. Okay. And the, the wave function is for given band and a given case stored in, in the website. Okay. And so you, in the input file, you need to define a single k point to D and that you can find the read input. So it's, it's, it's written here. You need to, you need to specify kind of here, single k point to D, direct the zero, zero, or you forget the zero, zero point five or zero. It's just one k point. It's in, in fraction coordinates. And with this k points, then then you can construct the Hamptonian read with this function. And then you can, and then you need to diagonalize it. Here it's the, we called us, this is a function from the, from the lab pack. You can diagonalize it. And then in, okay. This is a precise, it is a wave function. Okay. And then you see here, this is the, this is the percent, this is the wave function. And then, for example here, you want to get, this is a perceptual is the square. I mean, no, they know the square root of the norm of the percent. So you can, you can get, get the perceptual from, for this, the sliver and this is the band. So you can, you can get the, this is for one step or two steps a second. But for example, if you want to, if you want to get the, the atom layer result or atom result, you need to define another one. You need to define another, another percent. And yeah, because the wave function is, because we know the basis of the wave functionalism. The way, the basis for the, the wave function for the sliver is that, we have a, we have one sliver, second sliver and the third sliver. And for each sliver, you have a number, you have number of atoms, right? And the time, you have number one functions, then I mean the dimension of number one function, for each number one function, you have the look, you have the position of the atoms, right? So you can get that. Yeah. That's it. Very strict, restricted, and very strict, that, let me check, our loop. This loop, this percentage is for the slab and the band, number select of the band. It's number select of the band. Yes, yes, yes. Yeah, right. That's it. In this, in this routine, this, I mean, in all the puts of, I mean, this percent, ABS of text. So you see, they, the output is based on the slab, one slab. I mean, the weight on one slab of the second slab of the third slab. Yes. If you plot that they, if you plot that they will function for that band, I mean, if you check the, for example, these key points and then select this band, and then you will find that it's like this. I mean, the weights are just a lot, let's add the boundary. Do you see, Oh, that's okay. That file is created on, okay, let me show you, 3D wire symmetry. I have, okay? No. If you check, if you check, they, I mean, the examples are on your tools on GitHub. I mean, there's an example is called 3D wire model. And there is a fortune, fortune code to, to generate that's a 3D Watson or 3D, I mean, the type of a model. It's, it's, it's designed like this. It's very simple. This, this is a parabolic band. And, add opens that gap along X and data, X and the Y direction. But, data and open the gap along the Z direction. So you, you, you, you, you, you have the, you have the two icons along the Z direction. Yes. It's here. It's just a very simple model. Very simple, very simple model. I think it's already shared on, on GitHub. Riyang, is that clean? Okay, welcome. You're welcome. Hi, I'm a bit confused. Got it. Okay. That insulator, it's, so it's called up with a quotient, right? It's, it's, that insulator is, it's defined by, at each K point, we have a gap. So we call the kind of insulator. It's kind of a band insulator. No, it's also not a band insulator. So we, topological band insulator or what? I don't know. So how can we, how can we define that? This insulator is different from the band insulator. Since it's, it's, it's a gap at each K point. But, so it means that we have a dollar gap everywhere. But we sometimes, we don't have the, sometimes we, we don't have the indirect gap. I mean, this is a, this is a real definition in the, in the, if you want to add the topological band, the topological properties, because the topological properties, we only need the energy gap at each K point in, in the, in the K plan that you want to study. Okay. Is it possible to read the data index without reading the one year poll? Yes, yes. The data index is already in the, in the WDOT. Yes. That you see, you can read that here, here in the, in this PDF, you can use this one to, to read it. You can search a data number for six plans to all data number. You can search data number in WDOT. We have it. Okay. Sorry, can we take one question from Leonardo Roman Trieste? Yes, yes, yes. We're just trying to understand how the, this plot of any HR center was generated. So still back to the third page. Sorry, progressing slowly. This one? Yes, exactly. So on this plot, what is the K on the horizontal axis? So we have, we have KX and KY, right? Well, it's like this. It's defined in the, let's go to that. When you calculate the WDOT center, you need to integration along our K vector, right? This is the dependent in the K plan block. This one. This integration direction. So along this direction, you can get the value along the Y direction for this plot. That's the WDOT center on this direction. And for each K points, along this vector, the third vector from zero to, I mean, zero, zero to zero, zero point five. So here, the K is this zero, this is point zero point five. So this is the- For this plot. Yes, this is the point five. I see. So this would be in the Y axis, right? Yes, yes. This is the KY, exactly. This is the KY. Okay. Actually, it's not kind of KY, it's steps. Okay. Here, here is the KY. Yes, of course. Here is the KY. Because it's auto-connected. Okay. So there's second axis. Yes, the second one, yes. We can buy this one. Okay. And I know that the tutorial it's, there are many contents in this tutorial and yeah, maybe most of you didn't finish it, or I mean, all these two PDFs. But in this, I mean, in this summer, I would like to introduce them in more things, more functionalities in one year to you. So I'm sorry that I want to go to the next part. Time, Guan Cheng, you can move to the second hands-on. Okay, okay, okay. Thank you very much. I'm so sorry. It's, there's so many things. Okay. That's fine. And okay, the second part is for the quick twist of biographies systems. It's very hard to recently, right? And yes, okay. I suppose that most of you know this name of twist biographies, you put two graphene sheets onto it and make a twist. And then you, if you look at the band structure, you will find that this is the band structure for graphing, they are concave above. If you make a twist angle, you will find that they, we still have a direct points here, but the band width are very small. I mean, it's much reduced. And there is a magic angle and actually in all calculations, 1.16, but in the experiment is 1.08. You will find that there's a very flat band here. Okay, this is called the flat band. Okay. And recently, after the experiment on twist biographies, there are lots of numerous other set up for example, twist monobiliac and the twist double biliac. And also a mirror symmetric twist trial graphing or other genetic stacking configurations. If you look at the band structure, you will find that there's, I mean our flat bands and flat bands. But here in this band structure, there's a flat bands, I mean, together with a linear deluxe band, okay. And in this case, we have a deluxe band and we have flat bands and the other deluxe bands with higher clarity, okay. And so, and we know that after by decreasing the twist angle, you will find that the unit cell are increasing dramatically. This is a table for, here is a table. Oh, sorry. And this is a table for the twist angle and the number of atoms in the unit cell for the twist biographies. You will find that at the magic angle, we have 11,000 atoms in the unit cell. Okay, it's very huge, okay. If we want to generate the, if we want to store the independent parameters, I mean, as in the original one year 19, I mean, in the original format, it's almost impossible because we need to store, I mean, 11,000 times 11,000 elements. And also we have one, two, three, four, we have seven our points. So it's very, very huge. And we know that most of the hoppings are zero because we know, I mean, the bases are very localized. So there should be no hopping between this, I mean, between the center to the next part. So, I mean, most of them are just zero. So we don't have to store all those zeros, right? And so we propose another format, we call it a sparse format. We based on the original format, we call it advanced format. So we add another line at the second line, it's called the number of non-zero lines here. We move all the zero lines of that one. And but we, the other format is the same, but we remove all the non-zero, we remove all the zero elements, zero lines here. So, and this is what we call the sparse format, okay? And in order to start the crystallographic systems, the crystallographic systems, we prepared a code, it's called the T-G-T-B-G-N, it's called the crystallographic type of any model, it's shared on GitHub, and it's also written in fortune, it's very simple. And in that, for this code, you need to prepare our input file called system.in. And in this input file, you need to specify how many number of layers, for example, in this case, that's three layers, okay, number three. And this is a twist index. This twist index is defined from the commensurate twist, it's called, you can read the paper here, in this paper, the angle, the relation between this index and the angle is like this, okay? And a special case is zero, zero in the code, if you set the M equals zero, then it means the twist angle is zero, so there's no twist, okay? And also we need to provide the twist angle area input. Here we have three layers, right? Three layers, and the twist angle, it's like this, this unit is this state, okay? And the other, it means the first layer pattern twist, the second layer twist by our state, it's, I mean, this is counterwise, counterclockwise twist. And this data, it means there's no twist, so it's based on that, too. And the stacking configuration, stacking sequence is the ABA, because then we know that in graphene, we have two candidates for stacking, this is the AB, this is called the bonus stacking, the other one is the Robohedron stacking, ABC stacking, okay, so we only accept the collector's ABC. And we also, in this code, you can also provide a postcard, for example, in this case, you generate a postcard, but you want to relax it with the lamps, and then your lamps will give you another postcard, and then you can use that postcard to generate the type of model, okay? But in this case, we don't have the postcard, and we generate a postcard here. And also we need to specify, okay, sorry, here it's not correct. HR generated, whether you generate the type of model or not, okay, here true, it means we generate the HR data, and also we need to specify the format of the HR data sparse or the original dense format, okay? This for some means that we generate the dense one, okay? And also we have HR cards. This is the hoping cutoff, if it's smaller than this value, then we set to zero then, okay? And in this case, we use 2.81 EV for the pie bond hoping, and this is the HR cards for, I mean, our points, because if the index M is larger than one, you can always set it to one because the unit cell is very large, so there's no hoping between the home units to the next, next hoping, okay, to the station one. But if the index is zero, then it means that you, there are only two items in the home units, so the HR card should be eight, so that you can cover all the longer hoping, okay? So, and the type of animal hoping is adapted from this paper, and we use a set custom model and, okay. Okay, and to run this, it's very easy, you have this file and run just right, and then you can generate the WT.in and HR data, and some information where the running information can be obtained here, okay? And we combine these two subroutines, these two programs, you can get the band structure for the twisted biographies system, so for example, these are twisted biographies systems with M equals four, that the angle is the 7.34 degree, okay? And once you calculate the WT.in, you can, when you plot it, you will find that this is the flat band, it's called, I mean, also quotient, it's not that flat here, okay? But we call the flat bands, okay? And if you check the band index, it's from one to one to one to four, okay? And one different from the previous WS loop calculation is that you can use, you need to select those bands to get the WS loop, and this is described in the tutorial, okay? There's another card to select these bands, okay? And you can get this WS loop, and you can compare with the PRAR paper, and it's written in the tutorial, that's a USC, that's an MTR, okay? And also, once you plot the band structure, you will find that it's kind of complex, right? It's very hard to tell the information from that, except in this part, okay? But when you look at the APAS measurement, you will always see that the bands, the measurement looks like this. So it means that we need to unfold the bands from the tricep allele graphing to the primitive units of graphing. Actually, it's kind of a projection of the wave function to another plane wave defined by these unit cells, okay? This is called the band unfolding, okay? Then you can compare these bands to the monolayer allele graphing and the bilayer graphing compared to that, okay? And, okay, the next part is the longer-level spectrum. And now one of those can study the longer-level spectrum by applying the magnetic field. If you apply the magnetic field, in the calculation, you will find that, I mean, in the terabinic calculation, it's very easy to use a passive substitution that's the magnetic field. Once you choose a fixed gauge for the magnetic field, you can get this gauge and then you can calculate the phase that is associated to the hopins. And then this will change the terabinic model a lot, okay? And in our case, we choose a periodic longer gauge and this is defined by the hasukawa in this paper. And then here is the calculation for the graphing system, okay? This is the band structure. And actually this band structure is obtained from the DFT calculation with the one-year-ninety. So it's a little bit different from the band structure previously that obtained from the standard custom model, okay? And if you apply the magnetic field here, for example, if the flux per this unicell, it's one quarter, you'll find that the bands are quantized into London levels. See, the London level, London level, London level. The bands just split into two. And actually it's not, because the magnetic field, when you apply the magnetic field, actually it's not a kind of linear response. It's not kind of a linear response. So you cannot treat it as approximation to the bands. Actually this phase changes a lot. See, if you look at the London levels, it's very hard to tell some band characters of this band. So it's indeed changing a lot, okay? By changing this file, I mean you can change the magnetic field so the flux will change. And then you can obtain the offset butterfly. This is called the offset butterfly, okay? Then here is the offset butterfly for the twist double-balliography, okay? For the twist double-balliography, you can also have the flat bands closer from the level, for example, this one. And this flat band is well-supported from the remote bands, okay? So you can just start in this band. And actually for twist double-balliography, you have two configurations, AB-AB and AB-BA. If you look at the band structure, it's very hard to tell the difference, right? However, their topology are different. If you study the Western loop for these two, you can do it, I mean, after this tutorial, straightforward actually. But it needs a lot of time, I mean, the computational resources. You will find that the Western loop are totally different, okay? If you look at the... And we know that if the band topology is different, it also means that the operator magnetization is not different, right? And since the operator magnetization can couple with the magnetic field, so we can... It's not that's a... a knowledge that you find this two-language work plots are totally different, okay? And also, many tools can... not only calculate the... I mean, this half set of butterfly, we can also do our integration to get the vanilla diagrams, okay? And then from the vanilla diagrams, it's easy to... I mean, to... If you look at the slope, it's easy to get the chen number in the level gaps, so, okay? And in our tutorials, we prepared the two... also two tasks. The first task is... is to study the twisted biograph... to twist the graphing systems. You need to learn how to use that TG... I mean, that code to generate the type of band model for twisted biograph and use many tools to calculate the band structures, okay? And also, you can... you can calculate the Western loop. That's okay. And also start the band unfolding. And also... But in the tutorial, we don't use the twisted biographing to study the lambda labels because the system is so huge and it's impossible to write in this version machine. But instead, we use graphing as a model. We study the lambda level of the graphing. But graphing is a 2D system. So there's no dispersion around the magnetic field, I mean, around the data direction. And also, we prepare another model. It's called the 3D Western Metatowery Model. It's, I mean, in the previous session. In this model, you can apply the... you can study the lambda levels around the key paths. I mean, parallel to the magnetic field. You can study the carol... the carol mode that's induced... I mean, that's caused by the wire points. Okay. That's all. Yeah. Okay. I would like to take the questions. Okay. Okay. The first question is that is the TBG called restricted only to graphing? Can one simulate that for other things? No. It's only for graphing. It's always... Yeah. It's only for graphing. We also have a question from here, from the room. Okay. Please. Thank you for the talk. And I will ask you about the unfolding procedure for twisted ballet graphing. And what I want to ask is when you unfold onto the primitive cell of maybe single layer or bi-layer untwisted graphing, what are the meaningful physical quantities that you can measure as a function maybe of the twist angle doing unfolding for different twist angle? Yeah. That's a good question. Actually, the unfolding that we did is that we want to compare with our past measurements. And in the past measurements, usually we use the laser. We apply the laser onto the graphing sheets. But for the... When you apply the graphing sheets, usually you can only get some information from the top layers. Right? Then... But sometimes you can get the information from the bottom layers. But the more... The primer information that you obtain is the top layers. Okay. So... And... And actually, the unfold is kind of to measure the weight between the plane wave defined by this one, by the top layers, by the top graphing lattice onto the mori cells. So... Yes, that's... Yeah. Yeah. So the bent... So the bent unfolding is that we want... We... We... Because here it's a double... It's a bi-liography. So if you look... If you look at the unfolded bent, you'll find that the bent structure looks very similar to the bi-liography. But here, see, you will find some gaps. These gaps are induced and induced by the mori potentials. Yeah. Thank you. Any other questions from here, from the room? We have one more question from here. Yeah. Hello. This is maybe a little bit unrelated to the topology stuff, but do you have some way to maybe look at the effect of relaxation in the lattice? So when you twist at small angles, you have some big relaxation to minimize the elastic forces and you get some sharp domains, but do you have some way to maybe, you know, include this effect and look at its effect on the bands? Because this is static geometry, right? Yes, yes, yes. Yeah. That's... So we need to use lamps. Yes. We can use the classical molecular dynamics method. So we can... Here in test bi-liography, they already... there are already some classic potentials for the graphing systems or even graphing HPN systems. So you can use lamps to generate the relaxed crystal structure and use this code to generate the HPN model and then you can study the band structure again. And then you will find that after the relaxation, these flat bands are more isolated from the remote bands. Cool. Thanks. Hi. Thank you. So I have another question. So in the way you defined the Hamiltonian for the twist, you only have to define the pi-bond. So is there any way to modify the on-site potentials or the sigma-bond? I'm sorry, two... So in the system generation you have to specify the... let's say the value for the pi-bond of the PC orbitals. Yes, yes, yes. So is there a way to modify the other ones, like the sigma-bond or the on-site energy? No, the sigma-bond... You can change that code, actually. The sigma-bond is... I think it's kind of fixed. In my code, I fixed it. But you can relax it. I mean, you can set yourself by... You see this... P, P-pi, with sigma zero. Sigma zero. You can set it yourself here. Okay, I see. Yes. Okay, so sorry. So just another follow-up question. Then... I mean, this would be... So I mean, how do you build the type of the model for the twist? So you build one for the... for the bulk, let's say, and twist the thing, and then you twist and kind of repeat all these hopings to make a supercell? Or do you do this in another way? No, no, no. First, you generate... you generate... a unit cell, right? For example, like... once you generate this unit cell, once you have a unit cell. Then you... if you have a unit cell, then you have all the... all the R, right? All the distance between these two... these two atoms, right? Between each pair of atoms. And then you can use the... the slight cost model to... to get the hopping between each atoms. Each pair of atoms. Okay, so you also get hopings for the interlayer, right? So, like, from one layer to the other. Okay, guys, thank you. Also, we have a VPB Sigma, right? Otherwise, we only... we only have the VPB pair. And then pair it down. Thanks. Yeah, welcome. Yeah, and the same... there are several questions in the chat, but I will answer them later. And, okay, you can... we can start... I mean... the tutorials. I mean, from these two... with these two PDFs. Okay. You can ask... Juan Shenk, do you hear us? Yes, I'm here. Please ask a question. Actually, I have two questions from previous exercise of topological semi-metal case. Suppose we want to define the surface card for along 0, 0, along 1, 1, 1 direction. Can you please explain that setting? This is for 0, 0, 1, but I want 1, 1, 1. Oh, 1, 1, 1 direction, right? 1, 1, 1 surface, right? 1, 1, 1 surface. I am unable to understand the surface card setting of that case. Okay. For 1, 1, 1 surface, it's... so you want to... you want to 1, 1. 1, 1, 1 surface, right? For the 1, 1, 1 surface, you need to choose... you need to get two vectors that perpendicular to this direction. So I assume that it's a cubic system. Okay. 1, 1 direction you will have... you need to specify 1, 1, minus 2. The first one. This one is perpendicular to this line, right? And then the second one is... it's... 1 minus 1, 0, right? So you only need to specify this two. That's enough. This one is also perpendicular to that one. Yes, okay. Okay. And does the surface states depend upon the veneer functions we choose? Like I found the veneer... choice of veneer functions near the Fermi level do affect the surface state properties. Like in this veneer tools, how should we choose how many veneer functions we should choose near the Fermi level to get exact surface state properties? To choose veneer functions or what? Like suppose we are getting band inversion near the Fermi level. So how many bands below the Fermi level we should choose? Oh, okay. To calculate the surface state you don't have to choose the number of states. I mean, it doesn't depend on the number of bands. Sir, it varies a lot. Like in LABA system itself, if I choose suppose four bands below the Fermi level, then I was not getting. So then if I took two bands below the Fermi level, then I was getting the surface. You mean the YEEK is lack of... Like mainly the giraffe point. Mainly the giraffe point I want to say. Like I was not getting the surface states. Like if I choose all the states below the Fermi levels. It's not only in one case I found it in many cases. So that's why I asked like does the choice of linear functions below the Fermi level affect the surface state properties? You mean in the setting of WT.ing or... Yeah. I mean, did you change your type of model? I mean the HR data? Yeah, I need to choose that. I need to change that only. Like I decreased the bands below the Fermi level. Like it's like the inner frozen window which we use for constructing linear functions. Like how many states we should choose? Okay, I see a point. I see a point. Okay. That's a little bit to how do you construct the linear functions, right? They... When you construct the linear functions you... I mean, for example here in this case this is a bit of a satellite. Okay. We want to study the band... First, we need to study the band topology of the systems, right? We also want to reproduce the band structure collector closer to the Fermi level, right? Yeah. So we need... So it's... It's... So we need to... First, we need to do the fat band calculation system also called the band collector studies. For example, you project the band structure of the systems to the orbitals of different elements, right? Okay. So for the BISMA satellite if you look at the band structure you will find that the BISMAs P orbitals and the saloon of P orbitals dominate the energy bands closer to Fermi level. So it's... So it means that when you construct the linear functions it's not related to the bands and below the Fermi level but you need to construct a good type of band model that can describe all the band collector for this one. And maybe your question relates... Another question, for example, here we have the BISMA P and saloon P orbitals, right? It's a good type of band model but if you add BISMAs S orbital or saloon S orbital these two bands together then we will have more linear functions and then you will ask whether their surfaces are the same or not, right? Are you asking that question? Actually, this is clear like it is in deep velocities of no use to the surface state properties of topological insulators. BISMAs satellite I didn't face any problem with the BISMAs. I felt that like you can see here below the Fermi level from 0 to minus 5 you can see a large number of states. Suppose there are 15 states so suppose like now if how many states should I choose to get the exact surface state properties? I found that only by choosing 2 or 3 I was able to get but if I choose more than 3 or 8 but it was a hit and trial like I need to iterate every time that how many states should I choose to get the direct point? Okay, I see your point. Okay, so yes for direct same methods usually because it's a method so the orbitals are not that localized right? So usually we need more linear functions to get I mean to get more localized orbitals so sometimes you need to get more orbitals. I mean if the band structure for example for the BISMAs satellite if you only calculate, if you only construct two bands, I mean four bands close to the Fermi level, you will find that the function of the spread are very large right? The spread are very large so in that case of course the surface the surface state calculation But in that case I was getting the correct result Yes, I think I mean at the beginning you I mean in the one year tools the approximation is that it's a telebending model it should be kind of a low class, it should not be very very extensive for example across to four or seven units there it's very very very very spread it's not easy to to get the right the surface states Okay sir, thank you so much Yeah, you're welcome Yeah, Stepan Stepan you ask can I calculate the lambda levels of two stabilizer only for the lower bands Yes, it's we can calculate the lambda levels for that actually actually Yes, actually it was not me just told you through with under my account Yes, actually it's like that You can calculate it but it's it's more tricky actually because this lambda level I mean these flat bands are not the topological trivial they are not just topological trivial so the link from the remote bands the contact with the remote bands Hi Qansheng, this is Antimo I actually have a question for you Yes, it's a bit general so the machinery that you developed for the unfolding that you're showing with this tutorial on Twisted Biographies would that work with any Supercell Vanier Hamiltonian Yes so it's very general you could do it with any Vanier Hamiltonian of a Supercell Yes Here you see I prepared for example the diamond the carbon vacancy diamonds or silicon topo diamonds Yes, it worked Fantastic, excellent So really any so you take any say cell whatever it is and you select any smaller cell that can be integer and you put it into the original one and it works Okay, whatever is the result but it works Yes Okay Any kind of unicellar? Yes, you can Yeah, just But the point is that the unicellar you choose it's kind of you need to make sure that there is there is you have a map you can say the pre-middle cell if there is no match then there is no weight Yeah, absolutely There is no requirement that it is somehow similar has the same number of atoms or like I mean to make sense it has to be No, to make sense the other thing that technically you don't realize is that you don't unfold it Yeah Yeah, so there is another question from Yeah, it's very similar if we have some atomic distortion in the supercell then can you unfold that system? Yeah, that's a good question Latest distortion There is I mean in the code if you look at the and unfold You mean distortion of lattice vectors or atomic positions? Atomic positions You also need to to do distortion for your primitive cell otherwise there's no match, right? No, but this is for what you're showing is the lattice parameters but the atomic positions, you know, they're not they're not needed here, right? Yes, I mean the lattice vector should also be should also should also match That's for sure But I guess the question was more like suppose the lattice vectors do match if you can have, you know just distort in the in the supercell you distort the atomic positions you can absolutely unfold back Yes Yeah, you do it with this here and here it's just with vanille functions Yes, yes I mean here is kind of a limit kind of a limit actually in the in the in the vast, but if you have the way in the real space then you can get like any kind of unicellular it should be okay but in the type of animal it's kind of limited actually because we treat the other You can distort it but only slightly so that it finds which was distorted to which Yes, yes You had an 8x8 supercell with, I don't know, 8 say 2x2x2 with 8 atoms and then you unfold the cell which has no atoms I don't know You cannot do it, right? No It's not like in the DFT where you have real space and you just set just the form of the primitive unicellular and that's it Yeah One more question Can I ask one more question? Sure To follow up on the question on the Landau level So is the effect of orbital magnetization included in the Landau level of magnetization? Sorry, what kind of effect? Orbital magnetization Orbital magnetization Yes, it's automatically included actually because they pass substitution we are giving you that orbital magnetization I see, thanks a lot You see, I mean the orbital magnetization actually is a kind of orbital effect I mean that's I mean, when you apply the magnet field here they flux just a couple to the orbital right So it's automatically included Okay, can I ask is there a possibility to conduct self-determination that's a good question we are working on that at present, no I go to the ground and then come back up maybe we are not speaking from here Okay, so maybe in a couple of minutes we can stop with Hanson there is a coffee break between now and let's say 5 plus 11 and 11.30 as usual, those who are who are the Leonardo building and need to come here to the Adriatico building, they can take a shuttle bus that leaves 11.30 and and I think we should thank again for the great tutorial Thank you Thank you very much Thank you Thank you