 So we are here in the last session and the first talk of the last session is from Professor Marco Grili and the title is dissipation driven strange metal behavior in high TC superconducting cuprates. Okay thank you Sri and the first of all of course I would like to thank Andrei and all the organizers of this nice workshop for giving me the opportunity to present our ongoing work on this issue of strange metals. So I'm sorry I apologize for not being able to be there in person I would really have liked to be there. So at this point I think probably this not needed to say what a strange metal is but just to to arrange some the stage let me just remind you that for me strange metal is a metal which violates the Fermi liquid paradigm and in particular it displays a linear in T resistivity without saturation at high temperature and this linearity when you kill superconductivity for instance goes on down to the lowest temperatures. For some 2D cases also the linear resistivity is also accompanied by some singular behavior in the specific heat which can behave as a T log T specific heat as in some cuprates or in some heavy fermions. Where the strange metal is found well in many many places here are some systems where the strange metal behavior is is found and like in the cuprates or in the nictites this strange metal behavior is found nearby quantum critical points for charge density wave or spin density waves or other critical points like in some heavy fermions. But what I would like to draw your attention to is that although quantum critical points are nearby the strange metal behavior can also occur on extended regions of the parameter which tunes criticality like here in the cuprates or in the nictites or here in this overdosed cuprate systems. So what do we need to get a strange metal? Of course the problem is not solved so in principle this is a very personal list but my idea is that essentially to have a strange metal you need two things the first thing is that we need some scattering mechanism which is very active even at low temperature and therefore the characteristic energy of this mediators of the scattering has to be very small so it can decrease with the temperature at least. And this is a quite common and natural idea which has been taken by many many people and who usually couple fermionic quasi particles with low energy scatterers due for instance to over damped spin waves or charged density waves or more recently these carriers are coupled locally in a phenomenological way to some extra degrees of freedom which form an syk model for instance but everything somehow boils down to the idea that we have itinerant particles and they couple to some low energy scatterer. Another point is that to have the real strange metal behavior we need some isotropic scattering. Isotropic scattering means that if we have some scattering which is strong only at some qc then it doesn't work. This scattering can be very strong but it is not enough to get the strange metal behavior. For instance this thing which was pointed out long ago by Lubiner Rice simply means that if I have a strong scattering only from one region of the Fermi surface to another region of the Fermi surface the so-called hot spot then there remain huge portions of the Fermi surface which are still weakly coupled in these regions the behavior is the standard behavior of the Fermi liquid quasi particles and this quasi particle somehow short circuit the transport and dominate the transport and the end of the day you find the Fermi liquid behavior so it is important that this subdivision strong division between hot and cold region doesn't take place in the system and this can be achieved for instance with a scattering which is almost isotropic in momentum space. Is there such a kind of scatterer in the cooperates? Well the answer is yes because three years ago with an experimental group of resonant in elastic x-ray scattering in a nice collaboration we found that in the cooperates the charge fluctuations have a composite nature. On the one hand at low temperature in the underdog region we find the usual almost two-dimensional charge density waves which are related to some hidden quantum critical point underneath the superconducting dome and these give rise to some narrow peak in this bluish region of the phase diagram but underneath and together with these charge density waves the experiments identified a very broad peak which survives a very high temperature and very high doping this broad peak simply identifies charge density waves with very short correlation length and just to distinguish them from the longer range charge density waves we need name them charge density fluctuations so essentially they are similar objects but the difference lays precisely in the correlation length this broad peak is huge carries a lot of spectral weight so there are a lot of this fluctuation and they are everywhere essentially in the phase diagram of the cooperates. Then if you take the standard textbook expression for the correlation function of charge fluctuations this is the standard Gaussian propagator for all the parameter fluctuations which you can find in the many textbook you find that the important parameter here is the mass of these fluctuations which identifies the minimum energy that you need to create this order parameter fluctuations and then there is the dispersion which near the minimum is of course sporadic and then there is also a dumping term which is here and which will play a relevant role later on as we will see but what is important is this mass parameter is related to the correlation length of the order parameter and the larger the longer is the correlation length the smaller is the energy required to create the fluctuation and this is why from rick's experiments we found that charge density waves have a dynamical character even at low temperature but their energy is small because they have a long correlation length why the charge density fluctuations have a slightly larger energy right because their correlation length is quite short so this is why in q space they may give rise to a broad peak the interesting thing is that the rick's experiment both in high resolution and low resolution allow you to determine quite many of these parameters so essentially these fluctuations are very well characterized from experiments okay so you can get numbers from experiments for this m and for this gamma and for this new and so on okay and the question then arises naturally could it be that this charge density fluctuation which are so short-ranged and therefore immediate and in laser tropics scattering are responsible for the strange metal behavior in the cooperates and the answer is actually yes so if you take the charge response function you see that the charge density wave narrow peak suffer this lubricant rise argument so when you fold the thermosurface in such a way to my qc in order to identify the hot and cold regions you find that indeed there is a sharp separation between the hot and cold regions whereas the excitation due to charge density fluctuations are broad and when you do the same exercise on the thermosurface with this pinkish mediator you find that essentially the world thermosurface is hot so they work as a good isotropic scatter and this interaction in the overdoped region where no charge density waves are present only charge density fluctuations are there you can calculate the self-energy in perturbation theory so the effective coupling that you need to fit for instance a transport of is rather small the dimensionless coupling is around 0.4 0.5 so potential theory works well and you do find that the self-energy for the itinerant furnace dressed by this charge density fluctuation has exactly the marginal Fermi liquid like form so all the properties of the marginal Fermi liquid as a phenomenological theory can be reproduced thanks to this microscopic charge density for pressure mechanism what is interesting in transport is also that this charge density fluctuation now have a characteristic energy omega not of order 100 120 so 10 millivolts and precisely at this energy which is found with the ricks experiment we do find the deviation from the linearity so transport experiments and ricks experiments are consistent even in the deviation from the linearity so and in conclusion it seems that at least in this regime of temperatures above tc the superconducting tc we are done because we have observed well characterized fluctuations and we use them for transport and simply with first order perturbation theory we fit the transport okay both in the linear and then the upper curvature part but there is a problem because if you switch on a magnetic field we know that the linear resistivity goes down and proceeds down to very low temperature down to two kelvin in the scoop rate okay and therefore since the charge density fluctuation at a mass of a 100 kelvin this fluctuations as they seem to be unable to explain this this mechanism down to the slowest temperature so we have to think at something more so we are facing now a bottleneck because on the one hand to have a very low energy scatterer which can explain linear resistivity down to a few kelvin we need very low energy and therefore one is tempted to use a very large size so to approach the quantum critical point and take an increasing size but if we take a large side then the interaction becomes peaked around qc and therefore it is no longer isotropic and the lubularized argument kills us kills the strange metal behavior so what is the way out well the way out can be provided by this landau dissipation term so this is the term which describes the fact that this charge fluctuation can decay into particle of pairs and now if we look at the characteristic energy of the fluctuation this is not only given by the parameter n but it is actually n over gamma okay so this is the relevant energy scale so we can find the situation in which psi stays small so we stay away from the quantum critical point so we are near the quantum critical point just to have a lot of fluctuations but we don't go on top of it so that psi stays finite and possibly rather small and the small frequency characteristic frequency is not due to psi which increases but is due to some mechanism which makes gamma increase if we take just by hand gamma larger and larger we see that the spectral density of the scatterer becomes smaller and smaller and therefore we can extend the linear resistivity down to lower and lower temperatures okay so this is the area so the main take-home message is that instead of using the critical slowing down using the diverging psi we want to keep psi finite so we stay a little bit away and possibly over extended region around the the critical point and away from the critical point and use some mechanism additional mechanism which makes gamma increase so the question is now why i gamma should be should become large one possibility is simply that if you switch on for instance a magnetic field then the superconducting gap is killed and of course you have many more particle holes to damp this fluctuation so the lambda damping naturally increases when you kill superconductivity but the point is that if you want the linear resistivity to go down to the lowest and lowest temperatures then we need a larger and larger gamma if this is the good idea and therefore we need a diverging gamma and therefore just to have the closing of the superconducting gap is not enough so we thought at a toy model just as an example which is only valid in 2d to provide at least in one case an example of situation in which we can realize this increase of the lambda damping parameter gamma and the idea is simply related to the fact that in any standard metal even clean metal you have some impurities and if you have particle holes of low enough frequency and at low enough temperature smaller than the scattering rate due to impurities then this particle hole do not propagate ballistically but they start to diffuse scattering with impurities and this object here if you resum this if you make an infinite resumption of this impurity scattering processes you end up with a diffusing pole which can dress the charge density fluctuations okay so this is the idea the charge density fluctuation again decays in a particle hole pair but at low frequency and low temperature it decays in diffusing particle holes notice as I said that you don't need to have a strong disorder but just a few impurities is enough because all that matters is that you have at small temperatures more frequency finite impurities scattering rate and if you dress the charge density fluctuation with this diffusing pole then you find that in two dimension this lambda damping parameter diverges logarithmically with t so when you decrease t you have a diverging lambda damping okay so for instance if you calculate in this two-dimensional case the specific okay thank you if you look at the specific heat as due to this charge density fluctuations which are electronic fluctuations of course but still you can consider them as all the parameter fluctuations like in the standard person means theory and you apply the usual machinery to calculate a specific heat contribution due to this other parameter fluctuation you find that there is the standard logarithmic term and a prefactor gamma now the different thing with respect to the standard quantum critical theory is that usually in this theory the quantum critical theory is this is this log which diverges because the mass goes to zero because psi diverges here we want psi finite so the mass stays finite and this log term is just a finite correction but this gamma due to the effect of this diffusive mode is dressed and it is this gamma which diverges logarithmically with t okay so this is just another way of finding some logarithmic divergence of the specific heat which could match this divergent uh logarithmic specific heat which is found in some nearly two-dimensional systems like cerium copper six gold and uh lanthanum strontium copper oxide with a new denian and new rock in the open color so what are the conclusions uh incorporates the charge density fluctuation work well at high temperature so above tc there is no problem essentially the we are done because we have uh fluctuations which are well identified we they are experimentally uh explored and characterized we use from experiments this charge density fluctuations and we do reproduce the transport even the deviation from linearity uh in transport experiments now the question is what happens if we want to extend this linear behavior down to the lowest temperatures as it occurs when you you apply a strong magnetic field then we need that the lambda out ampere parameter gamma grows larger and larger and in this way one can keep psi finite the correlation length is finite so the idea is that we stay close to the quantum critical point but not too much and still we can get thanks to the diverging gamma a smaller and smaller energy and we can adjust this bottleneck and we can avoid this bottleneck having at the same time a small energy for the scatterer and still an isotropic scattering okay now the slowing down of the show range fluctuation is something which can proceed and give rise at zero temperature even to glassy phase so this is something which is somehow reminiscent of what Andy Millis, Jörg Schmalian and Dirk Mohr did in the case of quantum grief phases where they found that if you introduce the damping the lambda damping the instantonic tunneling processes which flip the order parameter inside the quantum grief phases these are made rare more and more rare and they eventually get quenched so essentially this is a similar phenomenon so the take-home message overall is that in order to find a consistent description of the strange metal behavior is that we not necessarily have to find to go to the quantum critical point but we rather should stay away so that the large psi is not obtained and we keep gamma psi finite but we look rather for large dissipation so this is the message I would like to convey you and the new idea since this problem is open since many many years is just to try to keep open minded and try to explore these other possibilities because in this way we can get finite ranges of strange metal and we can get somehow at the same time low energy scatterer and isotropic scattering with this new perspective and at this point I conclude simply showing the people who helped who worked on this idea in particular the ancient roman groups with Sergio Capral and Kallavi Castro and the young PhD student Giovanni Miracchi then the ancient romans were helped by a barbarian from Germany who is good cyborg and of course we also enjoyed a lot our collaboration with our friends experimental it's from Milan with Giacomo Gringolli, Lucho Braicovic and the young fellows Yingying Peng and Kazua Pang of course the experiments involved many many people like new books about chimer that you did that call my salutes and hang out so thank you for your attention thank you thanks Marco let me first take questions from the chat so would you like to so so I see pierce has has something to say pierce would you want to unmute yourself so I'd be happy to Marco thank you for a very nice talk and one of the things that was observed a long time ago by Serrini in Argentina is that in a large number of heavy electron systems that show log c over t you could parameterize them by a pre-factor you could write c over t as s over t star log t star over t and if you did that you found that s was very similar for a wide range of materials with different values of t star there's a very nice if you compare for example the quantum critical system terbium rhodium 2 silicon 2 with the quantum critical system cerium copper 6 gold the c over t is when rescaled this way drop on top of each other with the same pre-factor s of order one third log 2 and so my question to you is what happens in your theory do you get a universal pre-factor because that's a really important observation in the heavy electron no the answer is no we we use the coupling between the itinerant fermions and the the child density for patients incorporates as a fitting parameter so as a matter of fact we do find a rather moderate and small coupling but this is a fitting parameter so there is no reason in our theory why this coupling which is then g square is entering this gamma term there is no reason why this should be universal and be the same in different systems I think this is also related to the universal or non-universal debate of the plantian behavior so the slope is in the scattering rate is nearly proportional to t with the pre-factor of order one or not this is an open question as far as I know and I'm glad I really would like to understand this better and definitely thank you for your suggestion to look also at this entropy yeah universal so but okay so in our theory there is no reason why this what is that the slope of the this came up interestingly enough in the context of a cerium system cerium rhodium germanium and which is a ferromagnetic strange metal and one of the questions was whether the log t was coming from ferromagnetic fluctuations or was non-ferromic liquid behavior and the pre-factor was much too big to explain it in terms of uh a coupling to spin fluctuations around the prairie surface it looks more local in character so the pre-factor is a very important signature of the possible origin of the log t behavior I think anyway yeah yeah cheers nice talk thank you we have a question from the audience let me just add one thing if you use a given coupling g to fit the the resistivity then essentially the same g works well for the specific heat so different things seem to be consistent but this g is a fitting parameter there is nothing universal in it in principle but I think the same problem is for syk models for instance they also don't have any universal coupling is that right I don't know if abyssal fatter is is around maybe okay can I come in with another question maybe quickly I think I understand the idea that low line charge density fluctuations would give rise to linear and temperature resistivity but your dynamics of the charge density fluctuations it also has dispersion right there's a q dependence and so I'm just wondering whether that shouldn't give you a different power law and the second question quickly was whether spin fluctuations in principle would follow the same theory yes so the second question is yes so the the spin fluctuation would work as well I mean if you are close to a spin density way quantum critical point to the same ideas should apply the idea is that you simply stay a little bit away from the quantum critical point the interaction is mediated by some broad momentum and then this comes to the first question so there is a momentum dependence in this charge density fluctuations but since the the peak is broad this means that the momentum dependence is not that relevant so the pre-factor nu of q minus qc square is such that altogether the dispersion is what matters is really the fact that they have a finite mass and then there is a small curvature of the rate which is rather soft as moot so it is essentially like an optical phonon I would say but it is overdone yeah just want to quickly jump into discussions that had with Pierce about the pre-factor and completely it's important so I take a hat as a organizer and try to connect previous talk in your talk and in previous talk when Prave was talking about Garkov-Mirik Burkhodarov then that's the expression of tc with form energy as a pre-factor but with scattering lengths instead of interactions in the exponent and in your case I guess it's very similar station you start with the coupling but then nothing prevents you to screen this coupling in a particle whole channel generally replaced by scattering lengths and that quantity does not grow if coupling goes up it's roughly like g divided by one plus g some number so at the end of the day you get pre-factor for linear in t term which is some constant of order of one but constant yeah this is a very good point thank you yeah I could agree okay we have a couple of comments from the from online I'm just going to quickly look at them so John Cooper uh let's see oh we have uh Chung Hao Chung who says I wonder if your cdf scenario also accounts for the Fermi surface reconstruction in the strange metal region near the critical doping of the cube rates which has been observed in experiments i.e. the Fermi surface volume changes from a smaller to a larger value with increasing doping across critical doping x critical equals 0.2 and that no in the sense that thank you for the question but let me go back to the other transparencies here you see that there are actually two objects which are present in the in the phase diagram on the one hand there is this broad peak this broad peak as a short correlation length is nearly momentum independent because you see this is really broad momentum space okay so it is momentum dependent but not that much so the momentum dependence is not important and therefore it can hardly affect momentum dependent properties like the shape of the Fermi surface what instead is very effective in changing the Fermi surface shape are the charge density waves and indeed it is quite well known that charge density waves when they become nearly static in this can you see the cursor in this low temperature under doctrine here there you do know that the charge density wave can change the shape of the Fermi surface and reconstruct it in the presence of strong magnetic fields finally concerning the pairing this broad peak is so broad that essentially in the wave disappears and it is repulsive after all whereas the charge density waves mediate a strong pairing in this regions of the Fermi surface in the hot spot of the Fermi surface well sorry I can no longer change okay so there is a strong attractive pairing here due to the charge density waves and this can account why the gap the superconducting gap can be larger here so spin and charge density wave in the underdoped region and optimally doped region can cooperate for the pairing but the charge density waves the picket object here instead if you go here in the overdoped region where there are charge density equations only then they cannot neither change the Fermi surface shape nor mediate pairing because they they are repulsive thank you very much we need to move to the next speaker so thanks very much Marco for a beautiful talk thank you the final