 Okay. Is this sound good? Is everybody in here? So I will basically continue on what has been presented before, especially by Giovanni, and sort of extend that to describe the kind of properties of a charge carrier. So I will talk about all and mobility that using the EWC. So the idea, as was presented before, is that when you apply an external electric field, the charge, electron or hole will start moving as a result of that applied field. And those charge will interact. For example, with lattice. So this is a intrinsic effect. Electron, electron, magnetic element. But also, if you have a lot of charge, you can have ionizing purity. If you have some defects, you can have other forms of scattering. In this talk, I will really focus only on electron, electron, electron scattering. So just to be clear. So on Tuesday, EWCUSA also introduced for conductivity and transport. And he talked about linear, ohmic and all anodized all conductivity. And then there was also this second order term here. And so just to be, to be clear, what I'm focusing on here is really this ohmic resistive term. And so I'm, I'm, I'm basically treating or considering only systems that have time reversal symmetry. So if you are broken time reversal symmetry, then this is not zero and then you have to conclude. So, so here we really only focus on this first term. So the lift mobility is proportional to the carrier of velocity times this change of occupation function as a result of the applied electric field. So this is the auto peculiarly on occupation function. And so to solve that, and this sort of answers maybe since in our question. So, so this is what, when you do the revision and this can be done from a very framework, you can do a certain approximation and get this iterative Boltzmann transport equation. So this is a linearized iterative boltzmann transport equation in which you compute this change of occupation as this first term. And this was the term that was presented by Giovanni, except that Giovanni had the constant relaxation time or lifetime transition phase, but there's actually this other term, which also is very important. And you can see that here you have the same quantity as here but that different band and key points. And so the way to solve this is to solve it iteratively until you reach convergence. And so this scattering rate between electronic phonon is given by this formula where the G is the electronic element, and then you have those energy conservation preserving a delta. But indeed you can do some approximation and one of them is called the set energy or accession time approximation in which you choose to neglect this second term. And then the mobility is much simpler. You just have this first term, which you can plug here and then you get a simple expression for the region mobility, which where you plug this here and then you have velocity, velocity, and then this change of occupation function, but in this case, which is not at this at zero, so it's the family directly solution function as a function of again energies. Now in most experiments, it's actually easier to measure the mobility by doing a whole experiment in which you apply an external magnetic field orthogonal to the sample, and then the electron will be deflected due to law and force on one side of the device and then you measure the change of voltage. However, in this case, you have an additional driving term because you have this additional magnetic field and so you need to account for that. And so basically now your new equation, so this is the real mobility that we just saw, and basically now the whole mobility will be the drift mobility multiplied by this whole factor. Note that the whole factor is in the limit of vanishing magnetic field, so the half just indicates the direction of the magnetic field, but not the magnitude. And so in the limit of vanishing field, this whole factor is defined as this ratio between the mobility with the magnetic field and the one with the magnetic field. And so basically you just need to extend this iterative voltage transport equation that you saw before and you just add this additional term due to magnetic field, and then this equation can be solved again iteratively, again with the same scattering rate. Okay, so in practice, the idea is that you need to compute those transport properties on a very tiny energy region close to the bed edge or close to the family level. And therefore you need to have a very dense k-point and q-point here in order to be converged. And so one way to tackle this problem realistically is to compute all your quantity on a 48 and then of course doing a Fourier or when it transforms to real space and then you can do a Fourier interpolation onto a very dense k. And in particular the electronic component matrix element is the quantity that Pw interpolate in a philosophy very similar to the 1 in 90 code and indeed Pw uses 1 in 90 in library mode for some of the quantities. So just something I need to mention is that in polar material, you will have long range non-neticities and therefore the quantity will not be, you will not be able to make them, you know, condense in the real space. And so the strategy which is the same as the dynamical matrix is to remove the long range if you have an analytical expression for it and then add it back once you've done the interpolation. And so there has been some recent development in the field in which this long range term can be expanded into a multiple series where you have dipole contribution, quadruple octopole and so on. And until quite recently in 2020 people were only using the dipole contribution to remove and add back this contribution but it was shown that actually also quadruple and this was also presented by the channel is something important. There is also an additional term of the same order in cubes which are px here if you want to properly do the interpolation. So I'm putting some, I'm just flashing some input variable from EPW which you will need to set in order to activate those things. So when you put LPOLA in EPW what it will do is it will subtract this long range term and then there is no flag for quadruple but if there is a file with that exact name that contains the quadruple px then it will also add the quadruple when it does this subtraction. And this is just to show that in silicon, in principle it's a non-polar material so you wouldn't expect to have a fully dipole term but you actually have a quadruple one and you can see that the electronic kinematics elements which is computed on a course grid maybe a 666 or a 12 for 12 cannot be well interpolated if you don't subtract this long range quadruple and the circle have direct GFP calculation which are not far from the grid that you've used to do the interpolation and so in order to recover those discontinuities finite discontinuities that you have you really need to add this quadruple term. So now I'm just going to give you a few tips that will be useful for the hands-on. So in general the code scales as a square, the number of one-erised van therefore you always want to minimise the number of one-year function to the bare minimum that you need and so in general it's much more efficient to treat the electron and the hole separately so if you want to do both or endowed mobility or connectivity it's better to just one-erised the variance van or the conduction van and then do the calculation on that than to do both of them at the same time that would be more expensive than the sum of the two. Another thing like I said is that because of those energy-conserving deltas, this is the Boltzmann contradiction and all of those energy-conserving deltas corresponds to those four mechanisms in which you have an electron which is in the state Mk and can absorb or emit a phonon and go to the state Mk of vice-versa you have an electron that comes from Mk and goes into, you have out and in by absorbing or emitting a phonon those are the four possibilities and as you can see from the occupation function if they are the same sign so for example this is one and this is one then the resulting zero so you always need to have one on the same on each side and as a result typically the contribution will be all only the state that are very close to the van edge and so there is a input variable which is an f-stick window it's a window for the state that you are considering in an EPW calculation and this is a variable that you should converge on and you should take the smallest variable the smallest f-stick such that your result don't change if you want to do whole mobility, if you want to compute the whole factor in principle you should also do a conversion take a B field and then make it as small as possible the contribution should linearly go to zero so in the implementation we compute the derivative with a second field by finite difference which means you can input a finite magnetic field however the theory is only valid in the linear case so you will not be able to describe a lambda level and so on but you can describe some properties that find that field if you want but the whole factor is defined in the limit that goes to zero so if you don't want to do this conversion just take a very small value the unit of this is Tesla so it's quite a big unit so like the reasonable value would be 10 to the minus 10 to the minus 8 takes two implementation for the velocity the velocity VME 1A is the one that was presented by Turani so this is using the 1A scheme the same as in 1A90 and then there is also dipole which I can explain with this you can have different broadening for the delta you can have the Gaussian broadening and so on but if you put zero then it will use this adaptive broadening which is quite convenient because when you have a fixed broadening and then you densify your grades it will converge to a certain value but then you have to also convert decrease the smearing and converge again and so if you do adaptive broadening basically the smearing will decrease as you increase or densify your grade and so you don't have to do any conversion with respect to smearing due to numerical tests it was found that it was more efficient to use the same k-point and q-point but the implementation allow you to have grades that are commensurate but they need to be commensurate because you are solving the iterative solution so you need to be able to connect the k and the q so the grades need to be themselves commensurate and so this is just to show you the type of convergence that you can see and in principle you have to converge on which you started to do interpolation and also the fine grade and this is the convergence of the whole factor in green and on the right side you have the mobility are very small but basically what you can see is that this is an inverse scale that's 1 over 60 and so on and as you progress to the left you get more and more converged and so you have those quantities sometimes converge quite slowly so you can also extrapolate if you want to speed up the convergence I will now just show some results so does this theory work do we have to use experimental mobility but the first thing I want to say is that in general the whole factor is not 1 and it's also time to adapt and so in many experimental studies they assume the whole factor is 1 and they say that the intrinsic mobility of the material of the drifting intrinsic mobility is the same as the one we measured but it's not always the case so here for example you have some material in which the whole mobility increase with temperature some of them in which it decrease they say more or less constant but you can see you can also have lower than 1 which means that the whole mobility will be lower than the previous mobility and so it's quite important to take this into account if you want to compare your result to whole mobility data and so this is what I've done here so I'm comparing calculated mobility on the bottom with experimental mobility now all of those are quite simple material but I must say that some of them have been investigating very long time ago so maybe it would be worth to reinvestigate those simple material also experimentally so in general we overestimate the mobility and this is expected because the only scattering mechanism that we have is electron form scattering but like I said there are other scattering in an experiment that can reduce the mobility so this is all the result for those 10 semiconductor in which I both have the electron and the whole mobility and this is within this self energy relaxation time approximation so just to be clear the self energy relaxation time approximation is not the same as constant time relaxation the constant time you would have just a constant value here we don't have a constant value it's just that we don't solve it iteratively and so I'm not showing it here but with constant time relaxation I think one would be completely off to be honest then if you solve it iteratively you have this iterative bolstering approximation and those are the red result and in that case in general the mobility increases so getting a bit further away from experiment and then if you compute and multiply by this whole factor then in most cases even a bit more and here you have the mean absolute error and the mean relative error you can see that you increase but this is what you expect you expect to overestimate but that's it so maybe there are still some approximations that could be lived we could try to see if we can do better but in general what we find is that we overestimate experiment by something like a factor 2 in some cases then we can also look at what are the dominant scattering mechanism and so for that we can plot the spectral decomposition so this is a contribution as a function of frequency and so when you integrate on this you get the scattering rate and so you can see here that you have some material which are dominated by acoustic scattering so this is the one you would expect silicon, diamonds, cubicle or nitride those are very stiff materials so you would expect acoustic scattering and then you have materials like germanium arsenide arsenide and so on which are optical scattering dominated in some times very strongly so I've shown a general framework to compute the drift and hold mobility which can be derived from a monopoly framework and I've also studied what I haven't shown here in very detail but the whole of different approximations of the velocity the whole of including or neglecting quadruple in some cases can be important spin-off with coupling in general it's important for whole mobility but not so much for electron mobility and the reason is that you have a splitting of the the generacy in the valence band so even for silicon you have 50mV splitting and because the transport properties occurs very close to the band edge maybe 200mV on the band edge if you start having splitting due to spin-off with coupling then this impacts the mobility so in general for p-doped mobility or productivity you always want to have spin-off with coupling okay so this is just a list of current EPW team members so the channel started this journey which is a paper and then starting implementing the code and then hoxana margin joined and worked on the superconductivity and the nitrogen and so on and then the team is drawing and so maybe in the future you can also participate to this electron phono and join it and if you want more information this is the website, we have a follow-up it's also part of the Potomac Espresso distribution so if you download Potomac Espresso you will have EPW included and here are some references and that's it, so if you have any questions I'll be happy to answer so watching on the zoom is that not that yeah you want to ask about the benchmark data so to which extent the result is sensitive to the choice of the exchange correlation functionals because the gap is underestimated then maybe the affected muscles could not be right yeah so here is basically the impact so the relative effect on the mobility but this one okay so thanks for the question so yeah so basically here we looked at basically all the possible approximation that we could compute and the effects on the mobility so this is the relative effect and so all the dots and the squares are both for the electron and the hole for the 20 possible mass here and then the strongest approximation is this local velocity approximation which I haven't talked about then your dipoles, you know the couplings etc so lattice is the difference between the experimental lattice and the PVE lattice which was the choice for this but then we also looked at LDA so this is the choice between LDA and PVE and this is so it's not so big so 0.04 and then this is the change that we see for different pseudo potential with the same exchange correlation function so this is using different pseudo potential lattice so you can see that in general the last here are relatively small I would say but it's also true that I didn't test let's say MetaGDA or other exotic functionals I mean things like W and so on will have a bigger effect but at least I would say PVE, PVE or LDA, I understand that one the effect is not too big does that answer the question? No, yes I know that for instance the gallium arsenide the mass will be a factor of 2 or 3 wrong for the conduction band if we use so that would propagate right into the solution some point in fact so of all those materials indeed the electron mobility of gallium arsenide is extremely sensitive because it's quite wrong in DFT, it's super small is 0.05 or something and so for this one and for this study we use the experimental effect mass just for the electron of gallium arsenide so this is expanding the paper but because it was extremely sensitive indeed so this will completely but I think it's a bit of an extreme case with a very small completely underestimated very high effective mass indeed that's an issue so you may maybe a suggestion would be then to use some more accurate theory for the effective mass and then use more like a faster theory for the rest of the calculation so would that work for work? Yes, in a way so this is something not in this study but that we done before is for example to compute the effective mass with GW but actually the GW in many cases doesn't change too much the effective mass but in fact this is a very good point is that in DFT or GW they don't do an extremely good job at describing the effective mass in general compared to experiment so even silicon I think if I remember the heavy hole in the 1-1-1 direction it's wrong by effective 2 in DFT GW as a thing compared to experiment and so I think people don't look enough at that issue so this is a real issue that in some material the effective mass is really slightly predicted yes and so of course this one will have an effect a strong effect on mobility so we need to indeed try to improve the effective mass at every point Thank you Yeah Yeah I mean that particular This is dipole Sorry So this second dipole Can you tell us a little bit more about what is the definition of dipole Oh no this was neglecting of quadruple if you want So it's only using dipole when I do this long range subtraction So if I use only dipole and not dipole but quadruple Oh no sorry The first one Oh local velocity So I haven't talked about that because before in EPW there was a third option for the velocity and that was the velocity in the local approximation so it's basically computing the velocity neglecting the non-local part of the potential contribution and this was because then it's much easier to compute and this was the original implementation but it's an approximation and since now we've implemented the non-local part and with one year there is no reason to use this one so we are not providing this option anymore and this is to show that it's bad somehow Yes How does the in GW that the electron is wrong because it's not the electron can you do that here you know like electron interaction would change Yeah yeah so that's a very good point so the real part of the energy will renormalize the band structure this is completely true so in the case of silicon this band renormalization is quite small I think it changed the effective mass value 0.0 3 years from here but it could be that in some materials the change is bigger in general the main change is an opening of the band up so for the zero point motion renormalization and so in general it closes the temperature but there are some material in which it opens but in most material the band up will close this is a zero point motion and as you increase the temperature it will close even more and of course this is K point dependent so this could change of course the the effective mass and this is the mass enhancement factor that we've seen before so it depends on the material against this answer Yeah and also I think you could change that from the behavior of ability to manufacture because it is the difference between computer that measures ability to use the factor then it will be the difference will be counter dependent it is due to the inferiority that should be paid also right? Yeah Yeah indeed and I should I should emphasize that basically I think at least like this one I mean there is one or two material with particularly this one maybe this one where I mean the experiment is from the 70s and I've only one paper I mean I wouldn't rely too much I mean it could be simply that the experiment needs to be redone or it's not very pure things like that so we would need to investigate those material more but in general we sort of overestimate quite systematically I don't know if I have so here as you can see so this is the temperature change to the reduction of mobility both electron and hole as you increase the temperature this is not on a large scale so you see these things and yeah the dots are all the experiments but you see I mean what was it? Yeah you only have one I don't remember this one you know it's 69, 83 and I couldn't find the maybe there are but I couldn't find more recent experiment so in general you see that quite old so I would really hope and I would really like if an experiment is re-investigate those things with high purity and so on but I think that would be very valuable to sort of benchmark of theory a bit there yeah so if there is no more question I think we can start with the first tutorial so at the entrance you will see that there is two of tutorials in paper format so if you haven't already taken them just go at the entrance and take one so the reason we think of it is that we found that it's quite useful you can write on it and also you can log in and then just follow the instruction and so yeah Roxana will start the first tutorial and we will do it with you and I will if you have a specific issue you can raise your hand and I will come and yeah that's it so you can all start with the I can start with you so this