 is Avishar Patel and he will tell us about strange meta. So please go ahead. I think that you can also see us in the screen, okay? Great. Yeah, looks good. All right, so thanks for inviting me and I'll be speaking about a body of work which has led to what we would like to consider as a universal theory of strange metal behavior from which arises from spatially random interactions. So this is just a quick recap of strange metals. I suppose a lot of people are already familiar with strange metals, but what they are is that there are several two-dimensional or layered materials which have strongly correlated electrons and they are displaying their phase diagrams, compressible metallic phases that are unusual and they are unusual in the sense that unlike land of Fermi liquids, they have electrical resistivity whose temperature-dependent scales linearly with temperature as opposed to T square and this often occurs near some kind of quantum critical point. The exact type of quantum critical point differs between different materials, but there's usually evidence that there is approximate quantum criticality to strange metal behavior. So in the T-linear resistivity in and of itself is not that unusual because one definitely can find it at high temperatures where phonons are activated so above some debi or block reconnaissance scales, but what is very interesting about this and these strange metals is that this T-linear resistivity extends down to very low temperatures. So for example, there's this result on NDLSCO cuprits where the superconductivity suppressed by magnetic fields and the T-linear resistivity extends down to temperatures below 10 Kelvin where the phonons are certainly not playing a role and there's also this very beautiful experiment from last year on magic angle twisted bilayer graphene where again the linear T-linear scaling of the temperature dependence of the resistivity can extend down to temperatures that are like 40 millikelvin where there are no phonons and this T-linear behavior and the resistivity is often accompanied by other signs of strong interactions like a T log T specific heat which implies a strong temperature dependent to normalization of the quasi-particle effective mass. So this low temperature T-linear behavior is definitely a signature of strong interactions. So since this is a strongly interacting metal and not a land of Fermi liquid, what is usually done when it theories is to consider a Fermi surface coupled to coupled to some bosonic mode that can mediate strong interactions between electrons. So such a bosonic mode is inevitably gapless at low energies and there's no screening and that that bosonic mode comes from critical fluctuations of order parameter near a quantum critical point. So you couple your electrons to that bosonic mode and there's a very old canonical theory, I think was first pointed out by Patrick Lee in 1989 that if you just do self-consistent early Ashburg equations for the fermion and the boson propagators in two special dimensions, one will find that you get a fermion self-energy that's omega to the two-third which destroys quasi-particle peak in the spectral function and you have a metal which is without quasi-particles which is a non-firmly liquid. But you know if from the point of T linear resistivity this theory is rather useless because what happens is that it's a translationally invariant clean system and because of that there's a conserved total momentum and you heard of a finite charge density so you cannot there's no way there's not a compensated metal you just have one fermi surface at finite charge density so you can't excite currents without exciting momentum and because you can't relax momentum that means you can't relax currents and you get you get an infinite DC conductivity up to you know like vegan clap processes that would occur if you put it on a lattice which would give a T square resistivity at best so there's no way you can get T linear resistivity out of this. So in order to get you know this pretty large T linear resistivity down to very low temperatures you need to be able to relax momentum and the only reasonable way you can do that is to consider the effects of disorder and impurities in the in your system and that can cause momentum non-conserving collisions and relax momentum. So one can naively try to add disorder to this theory of the non-firmly liquid metal the simplest thing to do is just add a random potential term for the fermions and if you do this that changes the low energy structure of the fermions green function and because of that if you do your Eliashberg theory again you get a different kind of land-out damping for the boson you get z equals 2 boson with this diffusive propagator instead of z equals 3 and then you get a different kind of fermions self-energy in two dimensions which is not omega to the two-third but it's a less violent omega log omega frequency dependence plus of course a constant that comes just from the random potential itself and this this omega log omega fermion self-energy leads to a quasi-particle decay rate that's that scales as energy so you if you do this calculation finite temperature you find that it scales as temperature and just this this omega log omega self-energy also produces this t log t specific heat however from the point of view of transport you know what what happens is that your fermion boson interactions the fermion scatter of bosons that that are mostly close to zero momentum because the boson propagator is pq at near q equals zero and those are for momentum conserving forward scattering processes that don't relax any current or momentum and you don't so therefore the this fermion boson interaction doesn't give a transport scattering rate that's linear in temperature even though you have a quasi-particle decay rate that's linear in temperature so we need we need something more than just you know just this this very naive treatment of disorder in the problem and one way to well what we figured out is that you know having just potential disorder is not enough and actually in in your material and whatever disorder is intrinsic to it will also affect or the interactions between between electrons so one can there are like stm measurements on on q-prates which show that like the superconducting gap can vary quite dramatically between between different regions in space and that that that is sort of evidence that the interactions that lead to superconductivity are also varying quite dramatically so that's the disorder in the interactions and one can also think of this from a hover type model that you have a t and a u a hopping and a hovered u and if you have disorder in your hopping then that that leads to disorder in the spin-spin exchange coupling that's derived in second order perturbation theory so instead of t square over u now you have t plus delta t square over u and that leads to delta j and delta j is delta t over t so one one that that you can have a random exchange interaction that way and if you decompose that with the hovered stratomics transformation you get a random boson mass but you can also rescale your bosonic fields in a spatially dependent way and transform that random mass disorder in the boson to actually a random a disorder a random coupling between a random yukawa coupling between the the fermions and the bosons and this in in this this theory this this leads to considering a random g prime shift in in the uniform yukawa coupling so take the same theory as before but now we add this this spatially random yukawa coupling and so if we do that we can again do our ali ashberg theory and compute compute the fermion self-energy in two spatial dimensions and again it's omega log omega but now there are two sources of omega log omega there there's one that comes from the that's the previous one which comes from the g interactions and now there's also the the randomness in the g interactions gives another omega log omega term so basically the coefficient of omega log omega is affected by the randomness in the interactions and boson is still still got this diffusive form which is q square plus mod omega so this this looks very similar to what we just had with only potential disorder but for transport this this random interaction this this randomness in the yukawa coupling actually makes a huge difference so if we you know try to compute the conductivity within within perturbation theory people it's compute conductivity by resumming self-energy and and vertex corrections to the to the current current correlator so they're usually just these these four diagrams with the self-energy and the the ladder diagram and then these two aslam as larkin diagrams so what one finds is that you know the the g interaction it continues to just induce forward scattering between fermions and bosons and therefore it it just cancels the most singular contribution just cancels between between the self-energy and the simple vertex correction and what but the g prime interaction is not forward scattering anymore because but it's disordered so you can actually have large angle and momentum relaxing scattering and yeah so then what happens is that the g prime interaction doesn't cancel between self-energy and vertex corrections and therefore you get a transport scattering rate that that is similar to uh it just comes from from the self-energy contribution and while these aslam as our larkin diagrams in in the limit of life's furby energy they only they almost cancel each other and you know they only produce a scattering rate that's energy square over the fermi energy so that's not not important for for the most singular piece so now you do now have a t-linear piece that comes from comes from the g prime interaction doesn't cancel with vertex corrections in the transport scattering rate so one gets a transport scattering rate which is a residual resistivity which just is just determined by the potential disorder it's just v square and then we have this this correction which is linear in energy so that would be linear in temperature you know you know finite t calculation and that's g prime square times t so yeah at at low temperatures as as t goes to zero this this g prime square t term is smaller smaller than than the residual piece which is like what you you could see like this twisted bilayer graphene experiments for instance and you know one can also compute ac conductivity at finite frequency and then there is this mass renormalization in optical conductivity which has this this log form which is also in there there is also experimental evidence for this that's a recent paper by Antoine Georgian and company on on this thing so yeah that's basically it Aviska, sorry there is a question in the chat from Pierce Goleman who is asking if the disorder in g prime is also giving a residual scattering rate? Yeah not not within not within this Eliasberg calculation and you know this Eliasberg calculation can also be formally justified by a large n syk type construction which I haven't invoked just to keep things simple but it's there in the papers but within within the scope of this calculation it doesn't generate a residual piece but if you are not using that that large n construction it there it will I mean there will be higher order diagrams which generate some residual contribution I think so you'll always have some some residual residual resistivity plus linear t correction. Well can you hear me I wonder that's a kind of self-serving result though is there any way of measuring the g prime disorder is there any way the experimentalist who improved their sample and brings the residual resistivity down to a tiny amount can can still say that you know I mean it looks to me as if you can always say well you've got the most wonderful sample you've ever made with a tiny residual resistivity but I still declare to you that it's disorder that's driving your resistance linear resistivity how can you test your idea? Yeah I mean there are you know there are different ways of inducing disorder in experimental samples I think the most common way is irradiation and that that creates a lot of residual resistivity but one would have to let me give you an example. Serium Cobalt indium-5 it has a linear resistivity linear rise is probably 100 times maybe even 150 times larger than residual resistivity can one then still boldly go and say well I still think you've got disordered coupling to your critical bosons? Yeah I would I would think that's the case I do when these these two can have they're not they're not the same thing they're they're right so how can I test that hypothesis that it's coming from disordered coupling to critical bosons? I mean one thing that critical bosons do is well they can condense it you could have a phase transition so that will happen even if they're ordered even if the coupling is ordered but I would like to know yes how to quantify the randomness in the boson coupling in an experiment? Yeah so yeah I was just going to say that if you know that you do have the randomness in a coupling that when you do have a phase transition to the ordering phase like all parts of the sample may not order at the same time so you could have some emulsion of of ordered phases and disordered phases if you could see something like that. Is the hypothesis falsifiable? Sorry Pirs to interrupt you but I mean from the formal it's just showing the residual resistivity is the coupling V and the slope is the randomness in the coupling. Thank you Natasha I've understood that perfectly but what I want to know is whether this hypothesis is falsifiable by experiment whether it's always going to be something that you can claim is the case. I don't have a complete answer to that question I was maybe if you use there is absolutely no evidence of any inhomogeneity at all near a phase transition like this it just looked the sample just if you take zoom in with STM or whatever and the sample looks exactly the same you know exactly the same phase at all points in the sample then there's no like you're not having any kind of variation in the order parameter close to a phase transition then yeah then maybe then this then this theory doesn't apply thank you so maybe we can let just a wish card conclude if you'd still want to say something otherwise there are other questions here oh no I think that yeah that was that was okay okay okay okay thanks very much so maybe we thank you first sorry and let me the additional question here in the audience just a second yeah I have quick technical question maybe you can just very quickly answer you have two terms both omega log omega one you explain come from small momentum scattering in other you said doesn't involve small momentum scattering is due to randomness of the interaction yes how you how you get omega log omega which doesn't involve small q scattering it's just maybe you can sketch quickly how you got it right so let me just go back to right you have we have this this diagram you're this self-energy right so if if it's a g prime term there's a additional line for disorder averaging that that you have to add that so what happens is that the momentum being carried by the boson and the internal fermion are different now they're not they're no longer the same because you know it's not you have a small q boson but you also have the disordered line and the the change in the fermion momentum is the boson momentum plus the momentum in the disordered line so it can be quite big so it's not small small q scattering there are other two very quick question please i also want to ask some technical question in the last slide you explain one over tau transport it consists of two terms one is v square and another is related with g prime yes if you take a look at the contributions at the same slide you look at the e sigma g and sigma g prime you can see that g and g prime has different dimensionalities at the same time in your Lagrangian you put them side by side so it is supposed that they have the same dimensionalities so i want to understand what is the dimensionality of g prime because it is not just some technical problem now it has important consequences in one over tau oh yeah g prime and g are the same or different sorry no there i believe that this is misprint but then you see that it gives you v square so if it is proportional to v square so you will have both terms proportional so just in the normalization so i want to understand this yeah i think we did yes so the question is why if you took the self energy the contribution of the boson to the self self energy the terms in g and g prime of different dimension one is divided by v square and the other is not so it's just a misprint or there is they are really different dimension no they are they are they are different and there's this result for the self energy yes so maybe we'll discuss later so some other question was coming from this now okay i'm sorry i have to cut because we're already running out of time so let's thank again i wish that was a nice talk and i'm ready