 Včasno se z nami je optimirat vstavljeni v delovit'u, kako vse zelo vse zelo, in prijeznaj spetanje. Kaj je inštak več, Fulio Paleari, kaj da smo priježivati, vzelo, z delovit'u, nekaj ne zelo vse vstavljeni, je nekaj nezelo, dar ne zelo, nesel vse vzelo na vrste poslutje. Daj, Fulio. Čekaj, David. Nelaj za dne občasno me glasbi. Tukaj, da jim ko se naprej tudi povdeli, idem koristim VL-om, ki kmorto šepega, in ovo je, ki se jim ovo izredali. Staj na pridem, je to je ovalo, zelo zelo, ki so domo se dovaj po povrbu zelo, z puknem jeva, si je, ki je to, ko je ovalo, je to, ki je to, t längite, vzalej. A početno, when we study neutral excitation, for example, light absorption by the electronic structure of the material, sometimes in semiconductor, the light absorption, is actually, happens with an energy that is lower than the band gap. And this is because of the electron-hole interaction between the excitered electron and the holder remains in the conduction band. Basically, this picture. In particula, it can be imagined that ljite in pinge in materijal. Makroskopik polarizacija, rapid oscillating in time is generated. And the absorption spectrum is just the Fourier transform of this polarization, so the frequencies that are encoded in this polarization end up as peaks in the absorption spectrum. This is also the path that you will take for giving a sketch for the derivation of the beta-salpeta equation, which describes electron interactions. Just to... Sorry, I should point it here probably. Well, okay. Nobody's connected to my laptop, so I think... Ah, no, now it's working, okay. So this is basically the outline. I will give you a brief introduction why we need to go beyond the independent particles picture to describe a response function like the one for optical absorption. Then we will sketch this derivation starting from the question of motion of the response function in real time. We arrive at the beta-salpeta equation and we will give you some examples of possible application of the BSE beyond optical absorption spectra, okay? So why do we need this? Well, okay, we can imagine we know more or less about DFT if we know the band structure of the system, we can also compute the absorption spectrum. So it's just a matter of knowing the wave functions of knowing the energies of the bands and then we can compute the spectrum. And this is given basically by the Fermi-Golden Rule that you can find in every book. We have the transition matrix element describing the coupling of the Konshamoi function with light, and then the possible transitions because of energy conservation happen at the transition energy between valence and conduction. However, if we apply this formula, let's say to a material like lithium fluoride, so let's say we do DFT, we also do GW correction, why not? We obtain basically the red curve for the absorption spectrum while the experiment shows this very sharp peak which even lies below this red curve. So actually there is something deeply wrong in this formula and the corrected formula let's say that allows us to describe this case as this shape. As you can see, it is a linear combination of the transition matrix elements across all possible electron-all transitions created by these weights. We will obviously explain these later on and the energy of the transition is not anymore the valence to conduction transition energy, but this new exciton energy. So these red quantities that I am outlining here come out of the solution of the beta-salpeter equation. And you see that if we apply this new expression then in this case of lithium fluoride we get a pretty good description of the optical absorption spectrum. There are even more lithium fluoride, it is pretty striking, but the best application of the BSc probably is in layered and 2D systems. I look for example here at monolayer-exagonal boron nitride again I do DFT plus JW compute the absorption, the absorption starts at the quasi-particle bandgap and it is like this potato-shaped curve but then I try to solve the beta-salpeter equation and check the difference in the independent particles and excitonic absorption spectra you see it is like completely different. All the oscillator strength is sucked at lower energies in really well-defined peaks that are ok, now you can see, basically almost like discrete states and so this is a very striking case the difference between a quasi-particle bandgap and the main peak for example is the binding energy of this exciton state which is almost 2 electron volts so this happens in such striking fashion into this system because of course as was explained by Alberto yesterday the screening of the interaction between electron and hole is pretty weak into these systems and therefore the binding energies are quite high. Ok, so now that we understood the need to go beyond the independent particles picture we can try to think about how to do this, there are several ways to get the beta-salpeter equation for example here there are kind of three, one uses the edins equations which you have already seen for GW yesterday, this is totally doable strategy but since we have already seen it yesterday we will not do it today again then there is like the schringer approach which employs functional derivatives with respect to the external potentials and we will see a version of this approach but basically starting from the equation of motion of the response function so this is an approach that can be easily extended to treat out of equilibrium systems while approach that are based on a frequency space cannot be extended out of equilibrium so this can be interesting also for applications beyond optical absorption Ok, so as always we start from the electronic Hamiltonian so kinetic term, electron-nucleos interaction and then the electronic interaction here you have the hearty term which depends on the ground state charge density and then here I just put the fork term so this is just hearty fork, ok and I do this because doing this with the DFT exchange correlation functionals makes the equation a bit more clunky but it's totally doable in these lights it's like this just for simplicity let's say and then of course from this electronic Hamiltonian of non-interacting single particle energies we can get the eigenvalues and the block functions and from the block functions we can also get the charge density at equilibrium we already more or less saw these the other days but the quantity that we are interested in is the response of the system when an external field external time-dependent field is added to this Hamiltonian and then the situation becomes like this we have our equilibrium Hamiltonian we have the external field but then we also need to account for a change in the electron-electron interaction because now the Hamiltonian gets an induced sorry the density gets an induced component which is time-dependent because it is induced by the time-dependent field and so the functions of the density must also change a little bit so before we have to add these pieces here which adjust the difference between the equilibrium electron-electron interaction and the time-dependent ones ok now of course we can get the density matrix of the system this time time-dependent not anymore necessarily at equilibrium you can get it for example as a time-equal limit of the single particle Green's function and then we can finally get to the quantity that we are really interested in in this presentation and today the response function which is here the variation of the density with respect to the external field so we would like to find an equation of motion for this response function which includes electron-hole interactions sorry of course the response functions just as the charge density can be expressed from the position basis to the single particle basis which would be the constant basis if you did the DFT calculation and then actually we will mostly work in these basis where N1 and N2 and N3 and N4 are single particle indices ok so now well the equation of motion for the density matrix is pretty simple no it's just the Eisenberg equation of motion so it's the commutator of our operator of choice this time the density in the fullamentonian of the system but then we can think about a way to transform this into an equation for the response function we just take the functional derivative of both sides with respect to the external field by doing this so this side becomes an equation of motion for the response function but then we have to kind of compute the functional derivative of these commutators and the let's say the most difficult part of this is computing the functional derivative with respect to the electron-electron interaction parts of the Hamiltonian for example let's consider the time dependent heart term we can actually immediately rewrite it just as a functional identity making the functional derivative with respect to the external field appear here we did nothing basically not just an identity but now we can apply the chain rule here to transform here this in a derivative with respect to the density so we applied the chain rule but now this additional term is just the definition of the response function so we basically transform this variation into some kernel let's say which is then a tensor product with the quantity that we want to find the response function we can do the same things also for the other part of the electron-electron interaction in this case the fork part the sum of the two will have this shape basically kind of two particle kernel it's two particle since it depends on four single particle indices now we will see better what this means later and then this is much easier to calculate as we will see in a moment in fact for example this is the hearty term so basically we have a density loop and the coulomb interaction here we can just replace here the single particle basis expression for the density so this goes out of the integral and we just get basically the density matrix product with the matrix element of the coulomb interaction keep in mind that because of momentum conservation this term will be only evaluated at zero momentum or the momentum of the incoming field at the end of the calculation we can do so in the end we arrive at this expression it's the same as before and then the functional derivative is pretty easy in this form this is a time dependent hearty we just get the coulomb matrix element basically we can do the same for the exchange part of the self energy this is just a fork term so here I wrote rho to maintain consistency we can also call it the Green's function at equal times of the system and this is still the coulomb interaction but here we have a problem in our treatment because if we just keep going so we do exactly as we did for the hearty term so we rewrite these in the single particle basis now we have a problem because this bear coulomb interaction is bare, it's not screened and therefore it will give wrong excitons so we have to actually replace this with a screened version of the interaction in order to avoid the over binding of the excitons and also to be consistent with what we learned yesterday the GW case in fact we just replaced V with the statically screened electronic interaction and the screening, the static screening is in the RPA approximation so this is exactly the GW approach now this is transformed it's not anymore pure exchange it's not anymore the fork term but it's the screened exchange approximation for the electronic interaction that is commonly used to compute excitons is the so called hearty sex so hearty screened exchange approximation now we can continue after overcoming this obstacle now we can write the screened exchange part also in this way notice the different sign with respect to the hearty part we can compute again the functional derivative that we need to get to the equation of motion neglecting the functional derivative of the W itself now W in principle depends implicitly on raw because of the screening but this is an higher order term we don't consider it and then we get this simple expression so to bring everything together now for our question of motion of the response function we get basically the commutator with the non interacting Hamiltonian then the commutator with the external field ok and then we get this part that we just computed which contains this W minus 2V which is the electron kernel now we can actually in practice like what does this mean for example the first term is pretty easy just this commutator we can apply H0 on the left and on the right and we just get the differences of the single particle energies in this case in the case of the field so remember that we are in linear response so we are at first order in this field therefore for the raw we can use the ground state value the equilibrium density and then we apply this also in this fashion to the left and to the right of the states and we get the equilibrium occupation of our system instead of here is the difference of the energies here is the difference of the occupations and then the last complicated term actually is stated in exactly the same way so is basically the same steps after we do this we finally have a simpler expression for the response function the equation of motion for the response function now consider that since we now are explicitly the equilibrium so we have used the equilibrium quantities in the evaluation of the commutator now actually turns out that the chi is just dependent on the differences of the two times and then here we have finally this k which is what we computed before just put it together in a single variable w minus 2v now the difference in sign plays an important role because the w acts as an attractive interaction so this is the binding term this is responsible for the electron bound state appearing below the quasi particle band gap of the system and instead this partial contribution is normally much lower in value in magnitude than this in the semiconductor of interest to us so in general when we have this kernel we can find bound accidents ok so now let's switch to a different basis which is the transition basis as we can see we are now explicitly considering transition from the valence band so n1 is now a valence state to the conduction band so n2 is a conduction state so we can just label this double index with a single index the transition index and in this way we kind of simplify a little bit this equation because now it depends on 2 indices instead of 4 indices ok perfect now finally we are most at the end we can just do the Fourier transform of this since in the end it depends just on the difference of the times we can Fourier transform this and then if you ok try to do if we put k to 0 then it means we are putting to 0 the electron interaction and then we need to go back to the independent particles k and indeed if you do it you end up just with chi equals to this quantity so it is written in a kind of compact form but you can recognize it is the same chi not independent particle response function that we discussed yesterday but now we have an additional term this kernel and therefore finally we can write it as probably as it is most known the beta-salpeter equation as Dyson-like equation and this is kind of a kind of a diagrammatic representation this is the response function the box represents the fact that the electron and holes are interacting in a complicated way to this box we have first a non-interacting case the bubble diagram and then we have the interacting part ok and this is also the point of arrival of the other derivation approach that I outlined in the beginning the one based on Edin's equation in the end you get to this expression very good and of course the kernel is composed of these two terms that we just described perfect now we have to solve it so normally when you have a Dyson equation you try to invert it and this is what we are also doing here we try to factorize all the term with high on one side and then if we just keep omega alone we see that what is left as kind of the form of an effective Hamiltonian for two particle states so if we just call these h let's say then we can kind of invert it and place this on the other side of the equation ok so this we called h and then we invert it and we get something like this formally written so you see this actually starts looking more and more like a propagator like a green's function because in a green's function in a supercar space typically is the inverse of omega minus it's a relative Hamiltonian and in fact this is kind of the point here because now this Hamiltonian contains all the information that we were after at the beginning for example to describe excitonic corrections to optical absorption vector the eigen values of this Hamiltonian that is what is technically diagonalized inside the hambo give the exciton energies and instead the eigenvectors give the exciton coefficients that we were discussing before so now we can write this in this new lambda basis which is the exciton basis in which it is diagonal obviously since we diagonalized the two particle Hamiltonian and therefore finally if we want to go back to the transition basis we just have to perform a change of basis so basically we arrived at the end and we basically see that we have reduced let's say a problem that started from a complicated equation of motion for the response function to an external field of the system to basically just linear algebra problem just diagonalizing this effective Hamiltonian which contains enough diagonal part that encodes electron interactions in these hearty screen exchange approximation so these are all of course not time dependent, not frequency dependent all static interactions and this now this effective Hamiltonian that we need can just be computed with the techniques that we already know so for the energies here the single particle or quasi particle energies we will use DFT plus GW or various things the wave function we will use typically the DFT wave functions the conSAM wave functions and then we just have to compute the RPA screening to compute the W the statically screen interaction in the screen exchange approximation and that's it basically this is what kind of Yambo does in the next lecture Davide will enter into much more details about this and about also other technicalities so now I'm kind of skipping over many things but I thought at least in this way I can give you kind of initial understanding of what we mean and we say we derive the better equation we solve the two particle Hamiltonian we get the exciton information now I come to the last part in which I want just to give some examples of how we could use the BSE we could use an excitonic picture beyond or in addition to simple optical absorption not so simple but optical absorption measurements I think our guest speaker today will probably give a much better overview but still I will give you some examples so the first natural extension of what I said is okay so far you were implicitly considering the case of optical absorption therefore of macroscopic fields in which the momentum of the incoming field is much smaller than the extension of the deluene zone of the system but what happens if we instead we want to consider excitons with a finite momentum well then we would need to diagonalize the excitonica Hamiltonian for each finite momentum a different Hamiltonian for each momentum this is kind of similar if you know phonons to what is done in the matrix in the phonon case and then we have a q-dependent exciton basis and this describes you see a non-diagonal transition indirect transitions for example from a valent state at k minus q to a conduction state at ck so it's basically indirect transitions and when you solve the BSE at finite momentum for example compute exciton dispersion relations of what you do when you compute a phonon dispersions this is for example an example done with Yambo we are solving the BSE at values q's values transfer momenta in the deluene zone of monolayer MOS2 and basically we get the dispersion of the values excitons is a very badly made plot but just to give you an impression of what can be done but physically inside we can actually get from this paper maybe you will talk a bit more about it but I just want to mention some interesting things that can happen when you study exciton dispersion for example this is monolayer MOS2 and this is the exciton the first bright exciton of MOS2 da exciton it turns out this is a doubly degenerate exciton and when you go away from q equals 0 it splits and it has an interesting dispersion that goes parabolically and this is determined by the screen interaction that kind of gives this parabolic dispersion but the other one is dominated by the macroscopic component of the heart interaction which gives this linear behavior at least close to q equals 0 and another interesting case is this one of solid pentasin as you can see this bright exciton has kind of different energies at q equals 0 depending on the direction in which you take the q equals 0 limit in particular if your direction of q is parallel to the polarization of the incoming field so let's say it's a longitudinal direction you have a higher energy than the case in which the opposite case when the direction is orthogonal and so you have kind of a transverse direction and this is the so-called longitudinal transverse splitting of the exciton states maybe you know it from the phonons again the energy with the phonons is very nice maybe you know the L-O-T-O splitting longitudinal optical and transverse optical mode splitting this is a kind of a similar effect well obviously this ties into something that is very important at the moment for research which is basically ultrafast out-of-equilibrium experiments for example pump and probe experiments in this experimental setup what you do you first excite, create excitation in the system with a pump pulse then there is excitation and relaxation dynamics and then at a certain time you probe the system with a second pulse and check the state of the system and in system where excitonic effects are very important you kind of see complicated signatures in this pump and probe spectra for example this is a time-dependent arpes it means it's a kind of arpes that can probe also empty state also conduction states while regular arpes normally is confined to valence levels but here we don't see kind of a no parabolic conduction band or anything we see this blob and the authors of this experimental paper they say okay this is actually below the quasi-particle band, this is a kind of an exiton blob and actually if we wait a bit of time we start seeing some signal here and this could be because there is some kind of transfer of exiton from here to here for example some kind of complicated scattering process between exiton and phonons that could kind of move and change the momentum during the relaxation process of these exitonic states instead to the right we have another very interesting although very complicated type of experiment this is called a multi-dimensional optical spectroscopy and for example it is very useful to measure the broadening of the exiton peaks in general experimental sample you have many imperfections over the spatial distribution of the sample so it's not a perfect crystal you have defects, you have like distortions and whatever and this causes the various energy level to be a bit misaligned for example in absorption experiments but also in luminescence experiment and these adds a lot of noise to the broadening, to the width of the peak but with this technique you can actually remove all these noise and get to the true or so called homogeneous line width of the system which is the one that we compute when you do first principle calculations here you see the main diagonal is the line width of an exiton peak including these inomogeneities and instead the cross diagonal is the homogeneous line width so it's pure perfect crystal line width more or less of course this is a very difficult experiment and you see this is basically the cross section in the homogeneous direction and people found that the line width of the exiton peaks can be reduced by one order of magnitude between inomogeneous and homogeneous so this is quite important experimentally and where's the theory in all these well these are very difficult experiments to reproduce theoretically in a very convincing way let's say there's a lot of discussion about the important role that exitons certainly have in this kind of experiments but how to model this is pretty difficult here we can see some examples on the time dependent R-PES case on the left you see this is just a model so it's not first principle simulations and it gets what we kind of expect from experiment also this is the valence band this kind of dashed parabola is the conduction band but we don't have this we have these exiton blobs below the conduction band and on the right you see instead the calculation done with the hambo by Davide actually of kind of the same thing this red parabola is the conduction band of lithium fluoride and then this energy the distance between the bottom of the parabola and this blob is the exiton binding energy and at the exiton binding energy there is this kind of signal which is a bit deformed with actually replicas of the valence bands so this is a kind of another complicated out of equilibrium process who can attempt to model it using the Bethe-Salpeter equation another important topic is exiton phonon coupling this is also a difficult concept to get around but for example it can be used I will give you two examples one example is to reproduce phonon assisted optical spectra so optical spectra that are determined by indirect band gaps mostly in this case we have bulk boron nitride and photo luminescent signal actually this is cathodoluminescent signal is determined by the emission, the recombination basically of some exiton at finite momentum and they can only recombine emitting light via the help of a phonon of several phonon modes and these are basically the satellites the phonon replicas that assist in this recombination because it turns out that for example the strength of this exiton phonon interaction is kind of proportional to the second derivative of our response function including the BSC with respect to atomic displacements along the various phonon modes another way to compute merge of the first principle types of calculations density function perturbation theory which is used to compute the phonons and many body BSC which is used to compute the exiton and then by doing this merging you can also get the exiton phonon and in this paper you see here this is not a band structure this is an exiton dispersion also of bulk exiton boron nitride and the colors represent the authors calculate as the relaxation times of the exitons so basically how much time typical time the exiton takes once it is excited by a pump pulse to relax and go to lower and lower energies so ok this is more or less were some examples from the literature of course this is a difficult problem as is the problem in general of non-equilibrium quantum mechanics in these condenser matter systems in many things that can be done here also a kind of a fundamental level I will give you just an example of something that we are trying with Yambo when you compute the phonons this you will see this better tomorrow you already include inside the phonon calculation the contribution of the electronic-arter interaction to get reasonable phonon frequencies but this contribution is also as we have seen inside the exiton so what we are trying to do now is to remove this double counting so for example to see what happens if we compute the exiton phonon coupling strength like removing the art interaction for the exitons and as you can see from these plots of the matrix elements these were done also with Yambo the orange is the one with the double counting and the blue is the one without double counting you see qualitatively we have of course the same structure the same symmetry, the same phonon modes coupled with the exitons this is monolayer molybdom disulfide but we can have also pretty different intensities as you can see this is not the final answer but it is just to say this is a very complicated problem there are many things to be studied many interesting approaches both theoretically, purely theoretically but also from the experimental side and from the explanation of the experimental signals there is also much to do so welcome to this field if you are interested and with this just conclude with a summary what we have seen that the independent particle picture is failing in the case of many semiconductors especially layer materials two dimensional semiconductors to reproduce important spectral features because we are not including in the standard treatment the electron interaction these we can get it in a very general framework in which we try to model the dynamics of the excited electron system out of equilibrium and for example from the question of motion of the response function then we can kind of recast it in a kind of effective to particle Hamiltonian form this is the standard better approach and this yields the exitonic picture that as we saw can be used to kind of improve our understanding on a variety of spectroscopic phenomena with this I thank you for your attention and before the end I just let me give you some references so basically if you are just interested in like learning about the derivation that I sketched in my slide without maybe too much context I would just suggest these two papers, the bottom two so these are papers in which this kind of derivation that I have shown is done very well with all the steps and everything if you are more interesting in also learning in the context of how one can do many body, physics in a time dependent framework of course there is the book of Karanoff and Beim and then there is the book that we already mentioned many times the book of Gianluca Stefanucci and Robert van Leuven honestly I don't know which one is more difficult Karanoff and Beim are actually ok, try the first five chapters of the Stefanucci then you tell me how it is and ok, it is really thank you for your attention so thankful you for this very nice talk so I recall you the first part was really focused on the Betis al Peter and what we can do with the Jambo code, computer excitons and absorption and then there was a second part which was more motivational to say you have the exciton, you can do much more there is a lot of physics you can explore and now the session is open for questions and I also remember that there will be a prize for those who are in presence and we call it a prize for the best attitude and doing questions is part of a good attitude in the participation of the school so we welcome many questions Alberto so first of all thank you for your nice talk and I hope this question is not out of topic but if you start from a GW bend structure you can also compute the finite lifetimes of the bends so is it possible to consider these lifetimes within the Betis al Peter equation? ok so this is actually a much deeper question than I hoped for but ok, try to reply just to say if you just plug in the complex part of the bends in the diagonal part this would be totally wrong ok because the BSc rest on the fact that you are using inside single particle well defined single particle states so you do not use the full spectral function that you get with GW you just use the spectral peak you just take the quasi particle energy and that's it otherwise it becomes all inconsistent then consider this if you put some kind of imaginary part of the let's say the electronic states inside the Betis al Peter equation which will describe the broadening relaxation and so on then the two particle Hamiltonian is not anymore pseudoimitian does not anymore give real eigenvalues and then you have to ask yourself like isn't it possible that I'm including something at the independent particle level that could be maybe cancelled if I include also dynamical interactions in the kernel this is actually the case so you cannot include higher order treatments just in the single particle case you kind of have to find a way to also describe in a consistent way a dynamical part of an electron interaction I don't know if this is clear or not but more or less this is there Thank you very much That was really interesting A question about the interactions that you include when you describe exit and phonons in two different ways one is the Bernadi-Tangali way that you showed exit and phonons from the kind of Hedins perspective from coupling excitons that you solve with phonons like here and you get lifetimes and the other is by real time GW real time propagation where you also include interactions with phonons so can you comment about the interactions you can include or not include in the two cases and I admit I will talk about it a little bit later but I'm interested mainly about the real time propagation part So I think in both cases what it boils down to is that you add the dynamical part of the kernel which depends on the first order on the phonon propagation so it's a kind of so basically you add for example the interaction of the conduction band of the electron with the phonon of the valence with the phonon and then the cross interaction between the two is called interference terms so it's a kind of first order correction in the phonons where the phonons are dynamical but then this correction is not if this makes sense re-summed in a dison-like way, it's just kept at first order and this I think is common to all kind of approaches this one, the equivalent one that was there at PLVG Kudatso and also kind of a real time approach however if you start your derivation because you can start your derivation and this is what was done here and also by Kudatso at the Bensal-Peter level like I have kind of the excitonic propagator I have the excitonic Hamiltonian now I kind of perturb it with an additional term with the phonons and then you get this go to the beginning of my slides and put electron for interaction inside the main general electronic Hamiltonian in this case you would be away from the standard artisex approximation, you will have to include a kind of vertex function in the phonon so you will have basically the GW interaction more or less is the artisex approximation plus a kind of fun type self energy so g times the phonon propagator times the vertex and this vertex will have to include all electronic interactions so also kind of an excitonic at the excitonic level within this vertex and if you do this it comes out very similar to this but with an important difference that basically is this one that the excitons since the vertex that you will include in some types of energy is the vertex without the heart interaction so it is irreducible vertex then you get excitons like this without the heart inside, with only W inside so you get slightly different and depending on the system Hamiltonian and then this is basically the difference for example for MOS2 in some unphysical exciton phonomatic elements in unphysical because these states are too far away to interact with a single phonon energy not because the calculation is wrong so you can see there can be kind of an effect so there is a difference and we are now finishing our work with Andrei Amaini in which we explain all of these very well with all the cases and yeah it remains to be seen what these entails for the future then in the next few minutes I don't know so yeah thank you for this very advanced discussion I mean here we are discussing things which are really different years of the present research I would like to have much more basic questions for the students I have a short question here as far as I know the YAMBO code can also use the Redesal Petri equation to calculate Magnon spectra to calculate sorry spectra from Magnon's oh ok, ok, yes could you say a few words on how the Redesal Petri equation can be extended to the magnetic interactions yeah so no I'm not doing that because the expert is Davide so I think he will probably talk about it a bit in his lecture there will be a slide on that so maybe we can check if there are questions from the audience of online hello just please hello a very nice presentation and actually I am curious about the ARPS plot that you have shown for excitons and what is the material actually you have chosen ARPS exciton plot so if I understand correctly you are asking me about which materials I have shown in these examples yeah yeah ARPS plot ah the ARPS so this one this one should be transition method like arcogenide tungsten something I think tungsten diselenide WS2 and I just want to ask here you have shown you are saying that this is the exciton when light is interacting so there must be many so is it a single one how are you explaining this exciton so you are still your question is still about this figure the left one is it a monolive? yeah ok thanks since this is a layered system in transition method like arcogenides you still have strongly bound excitons also for bulk systems so basically here they had some independent way to determine the position of the quasi particle bandga then they did this time dependent ARPS and they saw basically this signal this very weird looking signal below what should be in their determination the quasi particle bandga and therefore they assigned this to an electron all bound state they say ok this is an exciton and this is kind of this experiment ok then I've seen a nice question from Inizio Marinho from the online audience can unmute yourself so otherwise I do the question myself so the question is about the screening he says so we are doing all these complex BSc theory but then we still use the RPA screening so why do we do that well I mean let's say it's the simplest approximation and the most consistent with the many body treatments in general that are implemented in codes also you may think of this as a kind of improvement with respect to the RPA screening so the RPA screening is already a small improvement with respect to just the independent particle scales and then we kind of add even more physics inside it and from RPA it becomes BSc either the step before to go to the step after that if that makes sense ok and then I know the question from Rajet Dut if I spell it correctly if you can unmute yourself as well Rajet Dut thank you very nice presentation actually because we are talking about the exaltonic states so I'm wondering whether these exaltonic states can be used or to study the metallic optical optical spectra or is it it can help us to understand the metallic system as well ok so in general it's kind of a bad idea to try to apply betasalpeter to metals exactly because of the screening problem so metals are very heavy screen a gap and dynamical effects in this screening are extremely important while here the way we are taking electronic interaction is just at the static level so most likely if you try to do that you will get wrong results also even I mean in addition to the dynamical screening dynamical effect problems there are also some details inside the exaltonic Hamiltonian they didn't discuss about that need to be adjusted basically I'm referring to what is known as the thumb dunk of approximation this is a standard approximation that simplifies the exaltonic Hamiltonian but doesn't hold for metals maybe you will understand more about this in the talk of Davide Davide's talk in which he will explain these blocks of this Hamiltonian much better I mean much more basic answer is that in metals the screening is so strong that usually you also do not bind so you don't have excitons but you could have kind of modifications in the absorption sorry if I can add on that what you say is totally correct but still there are literature calculation on metals there is a famous paper in the still alloy group showing the existence of bound excitons in metallic current nano tubes so there is work on that and there are cases when you can find interesting results I would say in semi-metals not in metals semi-metals you are correct Any more questions from the audience here? I think Enesio Marino Junior asks to read the questions Yes, I think we already did that so I wonder if everything you said is also valid for core excitons is the physics still the same? I think generally yes but maybe Davide, you can answer to this I would say that in general for core excitons the electron binding energy is even more important because the oil is pretty much localized so it tends to interact a lot and there are at least two groups that worked on using beta salpator to describe core excitons and you can do that and it works pretty nicely We have time for one last question before the break May I please? Yes, sure Can we do bi exciton calculation using Yambo? There was also one question in chat box Same So in Yambo right now there is no response and charge excitations like that Ok, that was quick and also I see a raise the hand by Nea Kapila Sharba if you want to do your question I am sure they asked the hand in my hand You wanted to say something about bi excitons? No In Yambo we can calculate no linear properties You are calculating bi excitons functions and full point response functions You cannot disentangle bi excitons from single excitons but there you have free body interactions in uncontrolled way This is a type of simulation that the user can do like running Yambo So let's say the standard implementation of the BSE in frequency space you directly compute the response function and that is just for excitons In the real time propagation you can go beyond the linear regime and you can have much more effects somehow but in the implementation that we have at present in Yambo we linearize the kernel dependency with respect to the interaction so I think you will not capture bi excitons and these kind of effects but maybe we have to discuss so Let's say that at least the real time propagation formulation will be prone to include more easily these kind of effects OK, so time for the coffee break I think We are perfectly on time and we have half an hour of coffee break We will assume in half an hour