 Hello everybody. It's always nice to be back to Trieste, and I'm very grateful to Andrei, Dmitri, Andy, and other organizers for the invitation. Lara gave a very nice introduction to the topic of iron base superconductors and briefly mentioned some ARPIS results knowing that there are students in the audience I couldn't resist and show a couple of introductory slides also for the technique angle result photo mission spectroscopy and it starts from actually shedding the light on the materials And this is very important point because this H nu is actually is a very Decisive factor on what you see in the end although we study electrons So H nu is nowadays produced by these kind of devices So the torch is the Einstein had hand is now something more complicated And this allows us to shed a light from different perspective for different angles with different polarizations And what is more important with different energies? the one of these Beam lines from from this picture at the end of one of the beam line This apparatus is installed at Bessie and we can can cool down the sample to the very low temperatures And this is the beam coming from the synchrotron Allows us to detect the electrons which left at different angles to the different positions here because the analyzer is placed in the Focal plane of this electronic lens and then these electrons are analyzed in terms of energy and Simultaneously Simultaneous such an analysis allows us to see the distribution as a function of momentum and energy at one image And if you then move the sample you can scan through the band structure of a solid changing several parameters You can instead of looking at just a momentum energy distribution you can look at the Just the top of this distribution and if you rotate the sample like this Schematically you can get access to the Fermi surface map So you can pick up just the top intensity and then you can get the Fermi surface map in reality It takes a bit longer than now Then the very important point is that a priori arpus depending on the direction of the light One could see very attractive images, but our job is to figure out what is the underlying reason for that And this is not always this so one has to really study the underlying reason meaning the spectral function And this is because the everything in our life depends on the motions of elections Our approaches and superconductivity as well. So our approaches to superconductivity Different and I will show you two of them which are both are self consistent one could consider the interaction between Electrons and particular suspect which means electrons and pairs in this particular case. This one neutrons Magnetic excitation spectrum from the same crystal we extracted the bare band structure from the arpus experiment Ask theories to calculate what can produce such a strong renormalization effects and our spectra and the answer was yes that if one does a simple theory and considers that the only Interaction is between elections and magnetic excitation Then one can indeed get the very high coupling constant and very high critical temperature another approach is to provide theories with the positions of the peaks of the spectral function including the orbital content and This one could use as an input for the theory meaning the where the quasi particles are which orbital characters they have and We offer them to calculate if they have a theory for superconductivity How the gap function would look like but the gap function can be determined directly from the arpus experiment So we can see actually not only where the electrons are but where the electrons are absent if the superconductivity starts for instance Meaning the superconducting energy gap and then one can compare this and say whether the theory is good or not That was also checked once in iron-based superconductors in the case of lithium iron arsenide we determined the gap going along all the Fermi surfaces with a very relatively good precision at that time and we provided the gap function to the leading groups in the field and Actually within three theories of the spin fluctuation orbital spin population and the purely electronic Pairing it was possible to explain our data. So for me, it's a clean Signature that our experiments should be more precise and I will come back to this point at the end of this talk So as I mentioned already it is very important before stating before stating How where where is a gap one has to really understand where the electrons have supposed to be and this is because of the Shading light from different directions because of very different experimental conditions It is not always possible to do In iron-based superconductors at this this situation is really complicated because of a multiband character of these materials If we start from a very big energy scale of the order of 10 electron volts, it was As Lara already mentioned the renormalization by the factor of three indeed happens, but it happens very Relatively small energy scales close to the Fermi level the natural question and how about higher binding energies? interestingly at higher binding energies we see the Relatively good correspondence with the conventional band structure calculations one electron approximation. So the Arsenic bands here is chemically shown here. I am very good in agreement then what indeed it renormalized is Very close to the Fermi level. So here this factor three four sometimes even even larger factor And this is nicely captured by the DMFT calculations so We know that there is a very strong renormalization, but still the system according to these Cartoon is not as high not strong that strongly correlated that we should talk about the Really more insulated we are not in this regime. It's not just pure metal, but there is a very strong renormalization which still There are still quasi particles remaining in the system very well-defined was a particles and they are living at the Fermi level So but if we dope the system even close to the half feeling We still have very nicely defined Fermi surfaces very sharp was a particle. So we are far away from madness in this sense One can call this Lower harbour band already this this formation, but existence of these excitations is Still there they still exist the orbital renormalization can be the renormalization effects can be orbital dependent and this is another complication in iron-based superconductors This is iron selenium which has been mentioned already It has very tiny Fermi surfaces and if one looks in the center of the brilliant zone one Realizes that actually the bands these are experimental values compared to the theoretical ones and these big numbers are the factors of Renormalization so factor 3 is not always universal It could be 3 to 4 but x y band for instance in iron selenium is renormalized by a factor of 9 So this orbital renormalization this renormalization can be orbital dependent another complication And this is another language how to call the Fermi surface shrinking we call it blue red shifts because this is a different space this is momentum energy space and If we can pay experiment with the theory you will see that Constructs of the dispersions which are responsible for the whole like Fermi surfaces in the center of the brilliance on an election Like Fermi surfaces at the corner of the brilliance on are shifted with respect to each other Simultaneously blue and red shifts occur and this results in the shrinking of the Fermi surfaces with which Lara mentioned in in the previous talk If effectively you can draw the Fermi level if you can still use the band structure calculations In the case of iron selenium This looks like this We have again the theoretical bands and we see in the experiment that for instance The tops of these bands are now below the chemical potential and the electron Bottom of electron bands are much closer to the chemical potential another complication is that Temperature with the temperature this situation tends to come back to DFT results So the shrinking tends to disappear not completely with the temperature and here show the temperature Dependence of the spectra in the center of the brilliance on you see that when upon heating up this bent clearly moves up and this is rather strong effect one could see it in the shift of the energy distribution curve of this peak and If we go to the corner of the brilliance on you'll see that upon hitting the sample up the electron pocket The bottom of electron pocket is going down Meaning that the Fermi surface is getting larger. So if we compare this too, so the the blue and red shifts tend to be smaller when the temperature rises up and This can be expressed in terms of both energy and momentum This is the situation at lower temperatures. This is higher temperatures It tends to go to DFT, but doesn't reach the DFT conditions with a large Fermi surface is still still another another complication but Probably think which which is good for superconductivity that if we are moving these constructs from the DFT Approximation where the Fermi surfaces are large then we Bring these singular Features to the Fermi level and the singular features to when they are the Fermi level seem to be very important for the superconductivity only because they have a very high density of states and Schematically it is shown that in lithium iron arsenide the top of this bent hits the chemical potential This is schematically shown as a black sport here in one to two This critical region is at the chemical potential resulting in this propeller, which is a place where the density of states is very high and in 111 in in terms of single crystals the highest you see the both of these singularities are at the Fermi level and Yeah, well you can add up these temperatures and see whether this is important for superconductivity or not still another complication is spin orbit splitting spin orbit splitting is a very tiny effect and usually people do not consider it But since there is iron in the system and one does expect Splittings of the order of 20 milli V we decided to check whether this is the case and iron by superconductors and Indeed in this material it was easy to resolve it directly so one could go to the particular point at the case space and Usually Xe Yz orbitals if there is no spin orbit interaction They should be degenerate unless there is another effect, but this This splitting could be seen also the different positions of the brilliance on Where the electron pockets supposed to cross with in the absence of spin orbit interaction? We clearly saw the splitting and actually we detected it in all main members of the family of high-temperature Superconductors iron base high-temperature superconductors. You see this is LDA result This is the scale which is predicted by LDA and this is the size of spin orbit splitting detected experimentally by arpus And you see the trend is the same the scale is lower But we got used to that We got used to this that the scale close to the chemical potential energy scale is kind of three four times smaller in particular The spin orbit interaction in iron selenium is is very high So that's probably why this This additional feature which makes this material probably a little bit different Whether spin orbit interaction is important for superconductivity summarized here it turned out that Those portions of the Fermi surface which are supported by the spin orbit split bands Where spin orbit split is a large? Turns out that they support the largest superconducting gap. So whether it's just a sedental or whether it's interesting effect Probably theory should decide but we just noticed experimentally that this is the case last complication and This is the I mentioned in all these complications because the theoretical treatment of the system with the two parabolas and two circular Fermi surface is extremely simplified. That's why always mentioned all these factors Perhaps because they have to be taken into account as well. This is a three-dimensionality and along the gamma to Z in all members except of probably 11 Except of 1111 which is pretty two-dimensional We see a strongly dispersion band in life as it disperses for more than one electron volt in One to two it also interacts with all three whole pockets here in the middle Which is important and even in iron selenium. There is complications because of this three-dimensional band this is Three that square minus r squared bent and it has been detected experimentally We did it for lithium iron arsenide in this case the scale is a photon energy Changing the photon energy. We can access different perpendicular momentum in the system and in this case we could resolve this bent directly and This which also means that Arpus is not as surface sensitive technique as people used to believe because if we would take this this Information cannot be taken from the topmost layer because according to uncertainty principle our resolution would be then the full Brilliant zone will not be able to see this dispersion. You can clearly see this kz dispersion meaning that the Probe in a distance the electron escape depth is at least ten units also along the kz direction this 3d band has also been determined in has also been determined in iron Selenium doped with tellurium material the interpretation was a bit different but since There is a spin orbit interaction in the system also spin polarization is Expected so this bent is also present so three-dimensionality is another important feature of iron base superconductors Now knowing all these complications. We wanted to address the question of energy and momentum scale of pneumaticity which probably one of the most interesting feature features in iron base superconductors and the story started from The multiple reports actually our first study on iron Selenium where we didn't observe Strong influence of the pneumaticity the the multiple reports with the energy scale of 50 60 up to 70 million electron volts Appeared in the literature So we decided to readdress the problem and it turned out that the this energy scales came from two initial studies of iron base one to two where the scale reached up to 70 mili V and So do one one one everybody was talking about the Lifting of the energy this degeneracy between xz and yz orbitals and this is a very huge effect Which you cannot overlook in arpus usually so we decided to now You see the energy scale is of the wood of 60 to 70 mili And this is a summary of the literature at that time Which we wanted to to readdress the iron Selenium High precision measurements and iron Selenium actually didn't surprise us because we saw the blue red shifts we saw the usual Fermi surfaces and at that time It was very difficult to resolve the structure near the corner of the brilliant zone So this small feature this electron pocket basically two electron pockets crossing each other But if we compare this to the conventional band structure calculations We saw surprisingly that actually there is nothing strange happening So there is one to one correspondence between the features of course There is experimental scattering here at higher binding energies, but General picture is more or less standard So we we have not observed any dramatic splittings and this is the lowest temperature where the pneumaticity scale should be the largest and This band structure calculations are actually tetragonal phase without taking into account any kind of Pneumaticity then we Went to the region of interest this is the corner of the brilliant zone and we asked our theories to calculate how the Autorombicity simple a is not equal b effect would influence the Spectra with influence experiment because our spot size which probes The surface is larger than the typical domain size so we should see the overlapping of the domains and This is the picture which came out the red line is a tetragonal phase and upon entering the Autorombic phase the green and blue components should appear and as you see conventional band structure calculations Do predict that one should see this kind of Splittings here, so this is mostly XYZ bands. This is a mostly XY character and indeed we resolved all these Features here and even the evidence for the splitting which we believe is a true pneumatic scale so this is the influence of auto-rombicity to the system simple structural thing and indeed our spectra Clearly showed that there are two peaks which are separated. There are two big Sets of features which are separated by 60 milli eV But one cannot interpret this as a difference between XYZ because the difference between XYZ if one wants to speak in this language is this small one and if one goes to the center of the brilliant zone then one sees that Something indeed strong happening something happening, which is indeed stronger than the band structure calculations predict So we went from the corner to the center of the brilliance on now and one sees that the Difference between the green and blue features are much smaller than we observe it in the experiment So this splitting is not predicted by the experiment Therefore we indeed believe that the pneumaticity as of electronic origin But its energy scale is not 60 to 70 milli eV but rather 10 to 15 milli eV Since I already mentioned that XY Orbital XZ and YZ orbitals are non degenerate at the center of the brilliant zone because of spin orbit interaction one may ask question how do These two effects coexist in the center of the brilliant zone and the answer was very interesting because we can switch off Pneumaticity by heating up the sample above the transition temperature and still we observe the splitting So spin orbit interaction is there and it was 20 milli eV but below Where both pneumaticity and spin orbit interaction lift the degeneracy we observe the splitting of the order of 25 milli eV and I just told you that we can attribute 15 milli eV only to pneumaticity close to the Fermi level and We first was surprised how this can be but then we realized that one at squares and this is perfectly fits The scenario when both effects leave the degeneracy between XYZ one has to be One has to also notice that people are talking about XYZ splitting But since spin orbit interaction is sizable there of course mixed and there is no clear XYZ in the center of the brilliant zone Already at this point I would like to say that Z factors for these two bands are exactly the same this Yeah, this this Exactly this was suggested by Oscar Buffett He's in the audience and Raphael Fernandez that in the corner spin orbit should be zero That's why we started from the corner and we saw the splitting due to pneumaticity, which is 15 milli eV Their spin orbit didn't contribute 50-60 was a mistake. I think many our press group now acknowledge this Not our mistake so About coherence factors both XYZ have essentially the same coherence factors and I will come back to this point later on so the different one should of course differentiate between the orbital composition and between between the orbital composition of a Fermi surface and the coherence factors of These orbitals so with the iron Selenium was more or less clear Sodium 111 we also have good data, but this one I'm in acknowledgment in In this paper, but the paper is done on our crystals. This is a very beautiful work We're accurate one which also showed that correct Consideration correct interpretation of the situation in the corner of the brilliant zone Where is a good map place to measure pneumaticity has shown that the Pneumatic energy scale is not exactly is not this distance between these two peaks but small splitting which arises afterwards and energy scale of this pneumatic of This pneumatic order of the order 10 to 15 milli as well This was the most interesting for me to check because this is where everything started and You showed five minutes. No, no, no This is barring one to two Straightforward barring one to two no superconductivity nothing just barring one to two parent material for iron base superconductors and Again, we had to readdress it because we we didn't notice it before and this was a good to do because the quality Has improved that this is the overview for the surface map This is a small brilliant zone and we can now zoom in using the different excitation for to an energy And you can see it with this kind of precision the best way to compare with the quality of 10 years back We had this kind of map from this barring one to two and this is what is available now So our first step is always to compare to the conventional been structure calculations And then to see what is what is exotic what what deviates from that? So this is a brilliant zone and if you now compare To the Benz structure calculations I show the the Benz structure calculations not as line the only thing I do here is Integrate over KZ and there is a slide broadening to two Experiments so these are df. This is dft and this is the Fermi surface of the magnetic calculations Usual dft approach of course there are domains in the sample and this is the superposition of these two domains and when we Got this data. We realized that there is a certain degree of agreement between this and we thought to maybe and There were a lot of discussions in the literature the barry one to two is completely cannot be explained by a dft And then this is something strange going on, but this kind of agreement was From my point of view remarkable and then we compared the underlying bands Of course there are a lot of bands because of the folding of course There is a strong interaction the gap opened up and so on but even if one shed the light at a particular Angle what could what could still see most of the features and if one compares with the Benz structure calculations again. These are now simply integrated along the KZ because we we measure along zero zero one and One sees that basically all features are reproduced so Conventional magnetic calculations of the barry one to two taken into account blu-red shifts of course Qualitatively reproduce all the features which are seen experimentally of course with the present quality then How about three-dimensionality if we change H new I said that we can address different KZ's in this case indeed This is what you expect erratically if you measure near the gamma point. It's just a very small window of integration along KZ This is a t-point and this is a z-point you see that going with photon energies You can partially get this dependence, but still there is a mixture from different KZ's So in this particular case, we are not that good in KZ resolution, but still Effectively we can address different KZ by varying Photon energy this is along this line and by going from First brilliant zone to the next brilliant zone because an arpus one if one goes to Higher momentum in plane momentum using the same photon energy one effectively lands at the different KZ value So measuring this one this map with one photon energy. This is one KZ. This is completely different KZ So this that's why one cannot compare the diagonal cuts as people usually do It's it's a dangerous thing so one cannot look at the electronic structure along the diagonal because you effectively change the KZ and KZ dispersion is very strong in this material, but anyway that there is a certain KZ dependence and the best point to measure pneumatic effect is of course P-point because this Brilliant zone is different from one one from tetragonal ones and Only two peaks in EDC. I expected at P-point and this P-point It is when we measure the spectrum there one does the same as I showed in the case of iron selenium and we saw that Exactly the structural a is not equal B Reproduces the picture we cannot go down to very low temperatures because this system has SDW this system has a very strong folding There are a lot of features coming in which are still in agreement with the magnetic calculations Which do not take into account any nematicity. So in order to estimate pneumatic effects one should Know the energy where to measure and this is effectively P-point and if we now look at the momentum scale The the splitting is not very dramatic And if one goes to energy scale looking at the EDC these two peaks are basically there They're a little bit broadened by this sort of obesity, but there is no dramatic effect again We analyze the approximate analysis and we extract something like 15 milli we also in this case and Since yeah, this I show very briefly the now coming to the gap knowing all these details knowing where to measure the gap we I go to the I skip this because this is Detail and we go to the Superconducting gap as a function of K now we know where to measure at which Fermi surfaces and this is already kind of Technicality, but in the end we get the distribution of the Superconducting gaps on the on the different Fermi surfaces We should take into account that they're actually four electron pockets here And we accurately determine the another trophy of the gap Also in the center of the brilliant zone, of course it is a two-fold symmetric now because of pneumaticity But we can do it. We can summarize it here for as a function of KZ For both electron like Fermi surfaces and whole like Fermi surfaces This line is great because the Fermi surface is really tiny So one probably for the quantitative things one should probably address the laser ARP is dated because we can do it only Approximately and I Mentioned before that lithium iron arsenide was a very good candidate to test the theories and my conclusion from comparison with previous Theoretical studies required more precision. So we went for this higher precision briefly flash you very Prelim not preliminary, but manuscript is not yet submitted. This is the new precision of iron Selenium you can resolve the gap. You can see the non-occupied part the gap Where of two mili v is not a problem we can see it in unoccupied part as well with such an earth One could go to the Fermi surface now like this was this precision without any kind of Symmetrization we can determine the superconducting gap in Every of these thousands of a point the same holds for electron like pocket a briefly flash the first result Which was very surprising no photos, please gear and This is a very surprising for us, this is a two-fold symmetry So this material is not iron Selenium where you have or to our own big distortion where you have strong gaze not equal to be this is lithium iron arsenide very tetragonal without any Big science of anything when I mentioned all but the gap on all Fermi surfaces is to fall so now We are back to to the theory tests so we can now provide our quasi particle type binding fit or was Renormalizations blu-ray chiefs for dimensionality and even with temperature dependence So if you would like to test your theory, please let me know and I would like to thank all the people who contributed to this particular study and To you for your attention Questions