 of the main building. 4 p.m. tomorrow, our terrace of the main building. What's the main building? Yeah, this is the main building. We are in the main building, yeah. And if you still want to print your poster today, the last chance to do so, please put your name on a sheet of paper outside this room. And there are also instructions how to do so. And with this, we start our first session. Chairman will announce the speaker. OK, so let's start the first session today on iron-based superconductors two optics. So we have two Raman experiment talks. The first one will be given by Professor Gersh Brunberg from Rutgers University. And he's talking about nematicity and superconductivity in multi-band iron-based superconductors as seen by Wright's scattering spectroscopy. Please. First of all, I would like to thank organizers. It's a pleasure to get back, always a pleasure to get back to Trieste. I'm going to skip the Pierce photo shoot maybe for next week since Pierce is not here. And go directly to the scientific part of the talk. So this work is done in broad collaboration. And the important people here are sample providers. Atena Savad provided most of the one to two samples. And Penjendai provided one, one, one systems. Awaj Chairman and Professor Matsuda iron-cellenites. There's a list of preprints and publications. So those are the references where the figures in this talk are taken from. And I always acknowledge the funding agency. So the motivation. So I will concentrate today on nematicity. And the question is what is special about iron-based systems, both arsenites and selenites, why we have this multipolar or the multipolar fluctuation? Why don't we see it in other systems? It's known to be in F-electron systems, in heavy fermion systems, the quadrapleodes are quite common. It's quite unusual to have them in 3D-based systems. So part of the study is to find out why we have these strong fluctuations. And the second task is to understand if they have an influence on the superconductivity. So this phase diagram is taken from our Chairman review paper. Is the nematicity universal? Essentially, the answer is that it's universal for these materials, all show nematic susceptibility, all Curie-Weiss-like. So they are mean field. There is a very large temperature range where the fluctuations are strong. And I give some my understanding of the situation. I think the important part is these 3D-based iron orbitals, which lead to three low-lying states where the Fermi pockets are made of from these orbitals and by symmetry of the iron side. These two orbitals, xz and yz, are degenerate. They are degenerate by definition. The band is narrow, they're made out of these orbitals, and they are not completely filled. They are half filled or partially filled. So they form both electron and hole pockets, but those are partially filled pockets and out of degenerate orbitals. So I think this is an important notion in that. And well, this is the pockets that have been discussed already on Monday extensively. So I'm not going to repeat those. The very common phase diagram is that there is a high-temperature diagonal phase, regime of fluctuations. Then it's a heteromic distortion, often a gap between heteromic distortion and long-range spin density wave order. So this blue part is magnetically ordered state. This red part is stayed between the broken C4 symmetry and magnetically ordered state. And the superconductivity arises here. And quite universally, the maximum Tc is where these lines come down to 0. So this is just an experimental observation. So the magnetic order parameter can be written down as a difference between the occupation of xz and yz orbitals. This is because when the symmetry is broken, C4 symmetry is broken, the splitting of this xz and yz orbital is required so that the degeneracy is removed. So these pockets get distorted. As a result, the occupancy on these orbitals is changing. Now in magnetically the material that order parameter strongly couples to magnetic order parameter, and it's in the same symmetry channel. And it also strongly couples to lattice. So the lattice itself gets distorted from square we get rhombus and the coupling between electronic and lattice degrees of freedom, I believe are essential here for this. But I'm going to skip in my talk that I hope that Indranil will talk about some of this on Friday. So I will just refer to the future talk. So this is how I see the fluctuating order parameter above the transition. So those arsenide sites, they are above and below iron plane. Those iron and what's shown here in red and green are xz and yz orbitals. Then the lattice is being distorted. The occupancy of these orbitals is fluctuating. And simultaneously with that, the pocket of Fermi surface gets also distorted. So this kind of Pomeranchic-like fluctuations arise. And the frequency of this oscillator in principle sets up energy scale for these fluctuations. I'm going to show that this energy scale is temperature dependent. Eventually it condenses, forming either ordered state or remains in the system as a fluctuation. Now, how one can probe that? This is a quadruple excitation. And very few probes can really access that symmetry channel directly. So there are four probes that I know of. This is the walk that was pioneered by Stanford group. And here what people do, they tickle the lattice, they apply strain field on the lattice, and they measure electronic response. They measure electrical conductivity or electrical resistivity. From that, they extract the response function, static susceptibility. But again, this static susceptibility is derived from tickling the lattice degrees of freedom and measuring the electronic degrees of freedom. And this is essentially static probe. This is either very, very low frequency probe or static. The next one is looking for lattice directly, either young modulus or speed of sound. And these probes basically tickle the lattice and measure the lattice. And because this lattice is coupled to electronic degrees of freedom, they extract information about also electronic part of this stability. But it's measured directly the lattice. This walk is pioneered by Karlsruhe group and has been now extensively expanded in many, many papers. There is a third probe that is NQR. So it can measure the charge susceptibility, quadruple charge susceptibility, but a very low frequency is kilohertz by looking at 1 over T1T relaxation. It can only be done for nucleus that has the quadruple moment. So selenium, for example, doesn't qualify for that. And it's quite tricky walk to extract the quadruple part because it's strongly, there's a contribution for also spin part in 1 over T1T. So those two degrees of freedom have to be separated. So it's not very convenient probe. And in my view, the probe that's made for these studies is Raman spectroscopy, which is a two-photon probe. So it directly acts as delta L2 channel, which is quadruple channel. It can measure the response function in wide frequency range. And what universally is observed is a relatively strong signal in x, y symmetry that has been noticed by many papers. And then if one does crumb as chronic out of the dynamic susceptibility, static susceptibility can be extracted. From that, one can see the curie temperature. And curie constant, the curie constant would be related to the amplitude of quadruple moment, square of angle of quadruple moment, essentially this constant C. So there's a lot of information that can be extracted. So this is 1 over chi shown here, which would look to the critical point. So very briefly, Raman spectroscopy. It's a photon in photon out probe. Electronic Raman spectroscopy generally very low signals. But once this can be done, it gives a lot of information, the particular symmetry information. And what we are going to discuss today is mainly the signal in this symmetry channel where the incoming light is parallel to this direction. So this is the shortest iron-iron bond. So this is one iron unit cell along A, sorry, this is two iron unit cell along the A axis of two iron unit cell. And the scattered light is perpendicular to that. There is another quadruple probe. If we rotate this by 45 degrees, we access orthogonal quadruple. And I will argue that there is no signal in orthogonal quadruple in the systems. And there are a few other possibilities to measure. So I'm going to skip that. And I get to the point. So the most kind of surprising thing that's seen in the system are that example is 1 to 2 here with structural transition 135 happens somewhere here. In this channel, small x, y, it's essentially no signal. So this is the second quadruple that I mentioned when the light is along the iron-iron bond. There is essentially no signal. This is non-interesting phonon. We rotate the light vectors by 45 degrees. So rotate the sample really in experiment by 45 degrees. We see a presence of very strong signal. And well, the first question is, why we see this signal? Why the light even couples to that signal? Then what can be done with that signal? What we can do? We can do chromis-chronic. We can extract from that the static susceptibility. The static susceptibility has to revise. This is 1 over chi. This extrapolated temperature, theta is the curie temperature. And the slope, which is related to A, tells us about quadruple moments in the system. To show you that this is universal, here's another sample called 2 to 2. This is the European 1 to 2. They all show the same behavior. So there is a strong signal building up towards the structural transition. And then this is suppressed. This is a phonon that appears due to broken symmetry. Sometimes we can also see an amplitude mode in the ordered phase. So that's by itself is impressive. Same analysis, same result. So it's very universe. What I'm showing here is a phase diagram of sodium 111. This is doping. This is temperature. This is structural transition. This is spin density wave transition in this material. This is separated from structural transition. And the color coded is the intensity of static susceptibility. We can see that the intensity is building up towards the transition. Then it gets reduced. And this line here is the curie temperature line extracted from the high temperature phase, from symmetric phase of the data. And it's clearly seen that the critical point of this line is roughly where the Tc, the superconducting transition, which is 20 plus in the systems, is the highest. So and there's the arguments, at least in a number of papers where people discuss that this quantum criticality could boost the Tc of the system. We went out and tried to do a check on quite unique system. This is a gold dope bar in 1-2-2. And the beauty of that system is that the superconducting dome in that system is extremely small. It really appears only here. And Tc is very low. Otherwise, the diagram is similar. There's splitting of the structural transition and magnetic transition. So we repeated the experiment, at least for a few doping. We extracted this is the line of the theta temperature. And indeed, it definitely looks that the point is here. It's just an experimental observation. So it's obviously important. Then the next question is what drives the nematic order? Why this occurs for this? And again, there are a lot of literature and many arguments. I think we came across a very interesting system which may give some resolution to that question. And the system is so-called 1144. It's a close brother of calcium 1-2-2 system. I showed some data of that earlier. This system has a body-centered unit cell. So those sites are equivalent. They are both the whole calcium sites, blue. What's in this system is it's a layered system where every second layer of calcium is replaced by potassium. So these sites are not equivalent anymore. The unit cell is not body-centered. As a result of that, this plane, so the irons are exactly in this system, half distance between these calcium layers, this plate shifts. So it shifts up and down in this new unit cell. And as a result of that, the site symmetry of iron is reduced. So it has the S4 axis. So it's a C4 with inversion invariant in this system. This symmetry is broken in this system. So as a result of that broken symmetry, this xz and yz orbitals are not degenerate anymore. So the degeneracy is lifted. And when we look in the spectrum of that system, so red is in the superconducting state and superconducting transition in the system is high, 35 degrees, we do not see. And that's the first system we studied and observed that we don't see huge difference between this x, y, b2g channel and the orthogonal b1g channel. They are both very weak. They don't show any pneumatic enhancement. Red shown in the superconducting state, this has to do with the gap, pair breaking excitation across the gap. But above the superconducting transition in pneumatic phase, there is no anisotropy between those steps. And the argument that I have here is that because the site symmetry is broken on the iron side, the orbitals are lifted. And we can't do this anymore because the sample, by the way, remains the diagonal, all of us, it's an entirely tetragonal sample. But these two sites altered. So here, the occupancy of xz orbital is larger. Here is yz orbital of larger. But on the same site, there is a gap. So those are split. And therefore, this type of fluctuation costs energy. So this is strongly suppressed. So maybe that is an indication, or at least strong indication that the generality of partially occupied degenerate orbitals is essential for these pneumatic fluctuations. Now, I want to flash a few slides what happens in the superconducting state. So I'm talking about sodium 1011 sample. This is the sample that does have this pneumatic fluctuation. I showed you the phase diagram. So the low frequency response in that interesting B2G channel appears, builds up towards the superconducting transition. But there is a signal. It's a relatively strong signal. But it's a very broad feature. So if I do a Fourier transform in time domain, look on that, what excitation is in time domain. It's just a relaxation behavior. So it should relax on sub picosecond scale if we would do pump probe experiment and try to look for this excitation. So it's a broad feature. It's a relaxation feature about this transition. But what is interesting, what happens if we cool the sample below the transition, below superconducting transition. Now the gap opens up here. And we get where we had this relaxation behavior. We get a beautiful mode. This mode is very, very strong. It's a collective mode inside the superconducting gap. The dotted line is a superconducting gap, as it's seen from one particle spectroscopy. And of course, this is a very well-defined mode. So in time domain, it would have many oscillations. Beautiful mode. So what is it? It's kind of indication of that pulmonary type of oscillation. When it was over-damped here, we saw essentially only very broad blah. But now when we remove the damping, it's ringing. And this is true observation of pulmonary type oscillation of the Fermi surface. So in B2G channel. Now I should remark that this happens only in the sample where the low temperature phase is tetragonal. So we didn't break the C for symmetry. So this is only the fluctuating regime. C4 is not broken even in the superconducting phase. That was a question. And well, if we go to high doping in that system, if you increase the doping from that critical point up here, then this mode gets weaker and weaker. And the reason for that is that it gets more and more lower than with doping. We looked also whether this is universal for the entire phase diagram. Again, back the phase diagram from our chairman's review paper. Five minutes. Good. This collective mode is now shown in potassium doped samples. So it's on whole doped parts. So it's similar. If we go to phosphorous doped sample, and this is isovalent substitution, this mode can be seen. And this is a different mode of different origin in the symmetry broken state, in C2 symmetry state on this side. And with doping towards the critical point, the energy of this mode softens. This is the gap roughly as function of doping. This is the energy it condenses. But the mode is there. The remaining five minutes I'll concentrate on iron solenoid, because this probably is the most interesting part. This has been discussed on Monday. This generally has been also discussed on Monday. So important thing I emphasize here is that it's a consensus between model calculation and ARPES that in broken symmetry phase in TS, there are two pockets, and they all they are talking to each other. So there is an elongation of the large pocket around gamma point in one direction. Here it's in opposite 90 degrees rotated in this case. Phase diagram from Chairman's paper, pneumatic susceptibility, very strong observation. This is, again, this theta line. This is Tc, in this case, quite flat. This is the structural transition line. And if we do Raman, again, like in all the systems, in this geometry, we see very low signal. In this geometry, we see strong signal. If we get close to pneumatic transition, we get very strong low frequency response. And the focus of my remaining three minutes is going to be this feature, which is a gap that develops in the spectra in the pneumatic phase. So this gap develops in XY channel. So it's in a quadruple channel and cannot be seen in other experiments. So this is the spectra above the transition. And this is spectra at 205 degrees. If I pull the sample towards the transition, I can clearly see two features. There is the slow frequency feature, and that's kind of our friend that I discussed before. There is another feature here. Just above the transition, this feature sharpens. I'm talking about pristine iron salamide in this case. And there is another feature here. We can see it's an overdone feature. Now I pull the sample below the transition, rapidly develops suppression in this green response. You can see that there is some remanescence of this feature here. And this is suppressed. It's completely suppressed already at 20 degrees. This data can be decomposed into components. This reddish line is our friend, cause elastic response, everything I spoke before. The blue line is if I subtract the reddish line from my data, I get this response. So the shaded blue line is this. This is still above the transition. Then the gap develops, this suppression. And I was wondering what the origin of this gap is, whether it can be seen somewhere else. This is data from Sergei Bereisenko's paper, EDC, around eight point. This is splitting of these XYZ orbitals that is required below the transition. Temperature dependence, they're splitting. But look on that. This is very broad feature above the transition. Very sharp quasi-particle peaks, at least up to this energy scale. This energy scale is here. It's a quarter of, it's 25 milliolectron volt. So at 25 milliolectron volt, quasi-particle peaks are sharp. There is a strong suppression in Raman response. What happens if we go to hide X value on this phase diagram via the diagonal phase, where there is no broken C4 symmetry? Everything is very similar. We can see, we can decompose into components. The drastic difference is that in this X equals zero point, a nice gap develops in tool for dope case where there is no broken symmetry. There's still strong building up quasi-elastic peaks so the matic fluctuations are getting stronger and stronger up to zero temperature. Not surprisingly, but also in this feature there is no gap like suppression. So there is a big difference in this bluish in the low frequency part. So how one can explain that? If one remembers that there are actually two pockets in this system, then there could be a two type of fluctuations. One is in phase between gamma and n point. Another will be out of phase. And we are told, we can't determine it from Raman, but we are told by Arpus that this one is favored because the XZ and YZ orbitals flip when Arpus looks for the bands around this point and this point. One of them, one of these fluctuations could be much slower than other. So there are two competing order parameters and this seems to be the favorite. So this is the slow degree of freedom. This is the fast. Ginsburg potential just plotted here along two combination of order parameter and they contribute to these two features above their transition. So if we now cool the system below transition, then we condense in one of the states. Well, that would be the consistency with Arpus. This is the degree of freedom. So because of that, the quasi-particle scattering apparently goes away, gap develops. So we have still this oscillator. This oscillator is now gone. Instead of that, we can have a collective mode here, amplitude collective mode. That would be the oscillation in the border with this potential. This is a summary paper, a summary slide. Yes. Let me go through the summary and I'll get that because this is a really nice slide. What's shown here is phase diagram. This is temperature. This is frequency. Raman shift. This energy scale roughly this 400 corresponds to 25 millivolts. There is a suppression in the enigmatic phase. This is being seen for all doping up to the critical doping and not seen beyond the critical doping. It arises from strong feature that is roughly peaked at 500 millivolts, 500 wave numbers, I'm sorry. Now, these fluctuations are suppressed when the symmetry is broken, when C4 is broken, and a gap develops. Interestingly, the magnitude of this gap, this gap, it gets smaller and smaller with doping and all can be scaled on a universal plot. So what's plotted here, T in units of TS, gap in units of KBT, KBTS. So the gap is mean field for 4-ish ratio. And the solid line is delta of T, which is A minus B over IA plus B, just the tetragonality order parameter. So it all comes together on one plot with the exceptions of interesting things that happen below TS, TC, I'm sorry, superconducting transition. And what really happens below superconducting transition, this is now pristine sample in the gap, develops a collective mode, not very strong because the old signals are here very low, but there is definitely a collective mode. And now this mode, unlike in that data that I showed for sodium 111, arises in the superconducting state with broken C for symmetry in C2 state. So it must have an amplitude mode origin, which again can couple now, that's for you Lara, couple to superconducting amplitude mode and interesting things can come out from that. OK, so I'm done and I'll take the question. Thank you. Thank you very much. Good questions.