 Worked before. Ah, okay. That looks better. Ah, okay, yeah, yeah, no problem. Okay, good afternoon. So it's a big pleasure and a big honor to be here. Thanks a lot to all the people responsible for that. I'm not talking about quantum information. I take the spin and correlation part of the session title. So I'm going to talk about non-local correlations inside dynamical means field calculations, and I will actually do it for real materials, but I will kind of focus on a specific class of materials that is already indicated here. The nice thing of being the third force speaker, talking about correlated systems and dynamical mean field theory is that one can keep the introduction short. So you have understood that we are talking here about materials where Coulomb interactions are important, compete with the kinetic energy, and can induce completely new effects. In the strong coupling limit, where the Coulomb interactions would entirely dominate, you can induce mod-insulating behavior. That means you can localize the electrons, and you should think of these solids rather as collections of atoms where the electron behaves like in an atom and do not spread out like in block theory over the whole crystal. So if we look at the two limits, so the strong coupling limit, mod-insulator, the weak coupling limit, band picture, what happens in between? Well, in between you can think of the solid or a specific atomic site, a correlated site in the solid as a site where things can happen like in a movie. You have an electron hopping there, a second electron coming there, interacting with the first one, one hopping away. So you have quantum fluctuations locally on that given site, and this is precisely what DMFT focuses on, incorporating into the electronic structure theory description, this little movie of quantum fluctuations, local Coulomb interaction induced phenomena on a given transition metal or F electron site is what DMFT incorporates in the description, and that enables you to describe both the weak coupling, band insulating, and the strong coupling limit. More technically speaking, this means that DMFT constructs an approximation to the many body self energy, which in the general case should be dynamical, that means frequency dependent or energy dependent, and orbital and momentum dependent, K dependent, and it approximates that self energy by a thing which now becomes momentum independent or a local self energy, which is calculated from an effective problem where essentially you look at your movie on a specific atom and the bath here is mimicking the reminder of the solid. Technically that means you couple your effective atom problem to a self consistent bath in a local quantum impurity problem. So by construction, your self energy is local because it is determined from this effective atom problem, but beware, local here does not mean local in the potential in the electronic structure sense, but has a specific meaning in the many body sense, namely that it means local if you consider real space representation in a Vanier basis with atomic sites. So let me express my self energy in Vanier functions centered on atomic sites, capital R, then the self energy has an orbital in X, M, M prime, an atom side index R, R prime, and local means that I have a delta function in big R, big R prime. That means you have no self energy components between different atomic sites and the self energy is so to say associated to a given atomic site. So today's topic of my talk will be an example where this is clearly not enough, namely where we need non-local correlations and introduce inter-site components, inter-atomic components of the self energy and these turn out to be important in the example that I will show you is transim irradiate. So my further outline is to give you a short introduction into the physics of transim irradiate and related compounds and then first show you what single site DMFT gives you for that. That means the approximation of really purely local self energy and where and why it's not enough and then we will go beyond and see what non-local self energies introduce here and finally I will discuss the doped case and interesting, quite simple picture of what experimental is called a pseudogapier. Okay, this is really worked by the former student of mine, Cyril Martins, and post-doc Berger-Lenz. Transim irradiate crystallizes in the potassium nickel fluoride structure. That means you have essentially a layered pair of skite that has additional distortions. So you have a layer of iridium surrounded by ex-oxygen octahedra and then you have rotations of these octahedra around the z-axis by 11 degrees. So that additional distortion on top of the structure. If it wasn't for that, it was exactly iso-structural to the celebrated lanternum copper oxide here and also to the strontium ruthonate that Eva discussed this morning, I think. A little disclaimer, I neglect here possible additional distortions that experimentalists were discussing because anyhow the if presence should be really small. What is clear is that the compound is insulating at all temperatures. You see it in photoemission here, a gap at the Fermi level. You see it in the optical conductivity. You see it in transport. And insulating at all temperatures, all measure temperatures is important because in particular there is a magnetic transition at about 240 Kelvin but essentially nothing happens in the resistivity at the temperature. So you have here this transition schematically below it's a canted anti-pheromagnetic phase. Above it's a paramagnetic phase but everything is insulating. Our focus will be in particular here even though at the end I will also show some data for the anti-pheromagnetic phase. Okay, when you talk about irradiates you might have second thoughts when you talk about correlations. Well, usually we tell you correlated materials typically 3D oxides, 4F systems because of the localized orbitals. Now the localization of course decreases or the spread increases when you go down in the periodic table. So a 5D orbital should be more extended and should be less prone to electronic coulomb interactions. So in principle you would expect weaker correlations in this class of material unless something else happens. And of course here something else happens namely what increases when you go down in the periodic table is the spin orbit interaction. So the spin orbit interaction of an iridium atom is of the order of other energy scales hopping, span, coulomb interactions in this compound. And as we will see this is actually an essential ingredient here. If I look just at the atom in the cage of the oxygen I have a splitting of the 5D shell into T2G and EG but now if I add my spin orbit coupling it has been pointed out that the T2G shell is split again into what people like to call a J-effective one half state and a doublet of states usually called J-effective three half states. And it has been realized about 10 years ago that this kind of splitting by the spin orbit interaction is actually a crucial element here. So a cartoon picture tells that even if coulomb interactions are relatively moderate if you apply them to a narrow J-effective one half band here you can split this band in upper and lower hubbub bands and obtain a more insulating state. So the recent literature I will not go through don't worry. I will just focus a few highlights to motivate you further to investigate this compound. One of the intriguing elements here is the close similarity to the cuprates as has been pointed out in different contexts here by Central and one who argued that the fact that it is described by a single orbital model namely for this J-effective one half state should indicate that it should be close to cuprate physics and maybe, maybe, maybe become super connecting. Experimentalists were then hunting in photo emission here for Fermi arcs. And even if the Fermi arcs got closed here to ellipses the quest of finding super connectivity is still open but until now super connectivity remains elusive at least in the sense of direct proof in terms of transport properties. Okay, so far on a brief, very brief literature review. So our focus will be in the first place the paramagnetic phase here at high temperature. We start from the experimental crystal structure and for that crystal structure we perform just DFT calculation. The result is here with the T2G states here with the reminiscent XY band going down here which is larger band with oxidant states down here and the colors here are just a guide to the eye to indicate that slowly you might start to see that there is some package of band up here and some package of band here even if there's no reason not to continue the band here and this one here. Note that there is four iridium in the unit cell and that these dark colored states here would therefore correspond to a single band per atom. Okay, let's first analyze this band structure a little bit further. As a theoretician I can switch off things selectively and I can play. So let me undo the distortions and undo the spin orbit. Then I just have a band structure which looks very similar to the one of transient mothonate and I can selectively switch on either spin orbit or distortions or both and you see how the back folding of the bands comes in by the distortions of course and some rearrangements by the spin orbit coupling. What is important for us is now to see where are actually the bands corresponding to dominant J effective one half or three half character. So let's take this band structure and let's project it on the J effective one half and three half orbitals. The results are here. This is the J effective one half. These are the three halves and here you see that while the three half one half states are indeed below the Fermi level, the three half three half are still quiet around at the present at the Fermi level. That means they still carry a spectral weight. So at the DFT level strictly speaking this material is not yet a single orbital system precisely because we are not talking just about levels but the dispersion and the overlap here leads to still occupied three half states. So if I look at the numbers then I would say that if I do just LDA with the spin orbit coupling here the three half one half state is full but this is not completely half filled and that is not completely full. So there's some charge too much here missing here. However, now I do my DMFT calculation and the result is actually in the first place that I clean up the three half states at the Fermi level and I have a charge transfer here from the J effective one half to the three half state so that now both three half states are indeed filled with two electrons and I end up at the end of the calculation with a state where I have a half filled J effective one half state. So that means starting just from the J effective one half single orbital model is a bit too quick but after doing the calculation this is actually what turns out to be the result. So when the system actually itself reduces effectively the degeneracy starting from all three T2G states, putting the correlations and then goes to an effective single orbital state. Let's look at the spectral function. So this is the total spectral function and these are the one half and three half resolved states. So for the three half of course we don't need to plot the empty part because there's nothing, the three half orbital is filled. The one half is half filled and in the total spectral function also you see the gap opening here. So we get the insulating state in the parametric phase. Okay, I think I don't need the pedagogical introduction to what is a spectral function. You can think of it very roughly up to matrix elements as the quantity measured in photo emission or inverse photo emission. Where do I take out or where do I add an electron in these processes? Okay, so we get the insulating state but how comes? And in particular, let's look at the little brother. The little brother is transim rodate. Isostructural, isoelectronic. Exactly the same thing. Apart from the fact that rhodium is a 4D transition metal and not a 5D one. The properties are completely different. Namely, transim rodate is a nice paramagnetic metal. So first sanity check, what happens if we apply now our technique to that thing? Okay, let's first do the DFT. If I look at the band structure, the T2G manifold here seems a bit more narrow than its transim rodate. That's worrying because you would think that correlations are stronger here. However, spin orbit splitting is smaller, so we don't know. We assess the Coulomb interactions and at first sight, surprisingly, but at second sight, actually quite logically, I can come back to this. They are slightly smaller. And if we do the calculation, this is already the total spectral function. We indeed end up with a nice metallic state here, bands cutting the Fermi level. The blue dots are extracted from experiments from Felix Baumberger's group. Okay, here's also the orbital resolved picture. Where you see that, oops, where you see that what happened is that there's one of the three half states which sank below the Fermi level, and this has also been noted by other authors before. In the two remaining orbitals, you keep charge. So the effect of degeneracy is reduced from three T2G states to two T2G states, and one is actually eliminated in the process. Okay, you can enjoy the nice Fermi surface in comparison to experiment. I will not do that on this. Just let me point out, so why is transim irradiate insulating and transim aerodate is not? Well, if you have a two orbital model, you need a much larger coulomb interaction to localize the electrons because you have more kinetic energy. So the suppression of the effect of degeneracy helps actually the system to go towards the insulating state. This is akin to what we found many years back actually with Eva in a series of vanadates and titanates where for different reasons, for structural reasons actually, one suppresses the degeneracy in these titanates and then induces an insulator there. Same theme somehow. You suppress the degeneracy, kinetic energy is lowered and lower u is sufficient to induce the insulating state. Okay, this is very nice, but let's look a little bit more in detail at the spectral functions and let's compare with experiment. So this is actually photoemission, experimental data from Luca Pavetti and Veronik Pouet. And the first thing to note is that they measure the first Boolean zone and they measure the second Boolean zone and find something quite different. So by definition, this is not present in just a theoretical spectral function which has to be the same in the first and second Boolean zone. So the difference here is a matrix element effect. One can rationalize this to some extent, I will not go into the details. For the moment, let me just retain that we should measure something at features where we have something here and at positions where we have features here. So let me just see if I can roughly get the sum of these two. Well, the answer you see here is no. So we nicely have these parts here which correspond to the three half states, but we are completely missing here the dispersion of the J effective one half state. So that is not at all well described in this single side description. So this is where the theme of the non-local correlations comes in. Let's extend our theory to just as a minimal model, include inter-iridium fluctuations. So let's include iridium-iridium self-energy and we do so by really having a minimal model that is a dimer. The minimal cluster here is just two sides. And surprisingly, first side, surprisingly, this indeed fixes the problem. So now the result here shows you that we get nicely this very dispersive feature here and this survives from the three half states. So the details of the spectral function, in particular the dispersion, indeed need here this cluster description because the inter-iridium fluctuations seem to be important. You can compare more in detail with experiment by looking at cuts now. So we fix an energy and look as a function of K and this is experiment theory, experiment theory for different energies. So this agrees now very nicely. Okay, so now things are working so nicely in the pure compound. Let's become crazy. Let's start to dope it. So let's start to put electrons into the system. Now the system becomes a metal again. You have states around the Fermi level here. And let's look at the comparison to experiments. So in experiment people pointed out that, okay, around the endpoint there were very steep features, waterfall-like-ish stuff that was puzzling in the experimental papers. Let's look what we get around the endpoint. So let's zoom in and let's plot in the same way as experimentalists do. So you should compare this one to this one and this one to this one. So the waterfall-ish-like picture is just here these, if I go back, the part that you had around here because you have two features actually showing up. Okay, let's look again at the spectral function and now around the endpoint. So you can see that what happens when you put electrons and they go here, that means you form an electron pocket around the endpoint. And this is actually of the form of an ellipse, precisely as experimentalists had seen it. So this is the theoretical Fermi surface and this is the experimental one. So now let's look a little bit further because experimentalists were saying here, there's a pseudo-gupt. If we follow spectral weight on the Fermi surface and we look at the range of energy, at low energies, they were saying, okay, here if I look at angles, this is what they call zero degree and then 45 degree. So you follow the Fermi surface here, you plot the onset of spectral weight, they find a depletion right at the Fermi level and they give you the size of the depletion as a pseudo-gupt here. Let's do the same thing in theory. Well, we have spectral weight here and here and we have a pseudo-gupt. Okay, here also some kind of pseudo-guptish like feature. Well, where does this come from? Well, to some extent, let's look here. What experimentalists do, they take the spectral function that they measure and first they symmetrize it, particle-hole symmetry. And that means that actually if you do that on such a spectral function, which is not particle-hole symmetric at all, you will just pick up this band again up on the other side of the Fermi level and it looks like you have a pseudo-gupt. Second issue is, and this is what we got from our cluster, DMFT, because we were actually taking care of not breaking the symmetry, so we do the cluster twice in both directions and average in such a way that we do not break the point group symmetry of the crystal. And that means we actually, in the theory, get a kind of superposition of two ellipses, meaning that at the very end, you have a depletion coming precisely from these inter-side fluctuations that you can interpret as the antiforomagnetic coupling between the iridium. Okay, so now my time is up, despite of the fact that... Oh, okay, so it's my five minutes. Okay, okay, I stopped late, you realized, right? Okay, okay, nevertheless, so my time is up, so that means I don't show you the antiforomagnetic face, just enjoy that the experimental points are on top of the theory and I don't show you barium, that doesn't matter, you can ask me over coffee. So I let you read my summary, thanks a lot.