 on the remote audience in advance that I'm giving this from the local computer and we've been having some problems with it freezing so if it freezes it's not even my computer there's just nothing I can do okay yeah exactly well you'll do that anyway I'm supposed to repeat that comment Andre from the audience said we will just start asking questions I know exactly so right so I'm going to tell you about elastic effect and some things that yeah really surprise me in a very nice way eventually once we've understood them so I've worked on strontium ruthonate for many years what I'm going to talk to the work I'm telling you about today has involved the the collaborators listed there I'll try to cite individual papers and pieces of work so you'll see who's done what the main thing to say is that most of my collaborators are at the Max Blank institutes in Dresden although there are a couple of guys like Andreas Ross and Brad Ramshaw and Sayat Ghosh who are now based elsewhere who are based elsewhere it's been a lot of fun having theory collaborations on this project particularly with Jörg and Marcus and as you'll hear at the end of the talk Bongjai and Igor joined the collaboration actually after seeing this talk a couple of weeks ago at M-square S so you know it's again demonstrating how useful it can be to go and give talks so what I'm going to try and do is to tell you about how we can tune through the lysis transition I say reliably in strontium ruthonate then I'm going to tell you about two well certainly one new technique the AC elasto caloric effect which has been a big uh uh yeah something of a surprise and something that I think is is really significant and as an experimental technique and I'll explain to you why then I'll talk that stuff has just been published what I'll tell you about in the main bulk of the talk are stress strain measurements that have not yet been published we're just in the process the long process of writing them up then I'll draw some conclusions and then people always ask me about superconductivity of strontium ruthonate I can understand why if I haven't been uh used up all my time after 40 minutes I can give you a quick short appendix on the superconductivity but I'm not having seen the conference and how lively it is I'm not so optimistic that we'll get to that so uh based on the desire to study the superconductivity of strontium ruthonate about 10 years ago now Cliff Hicks proposed in our group then in St Andrews that we might want to apply uniaxial pressure using a completely different approach to what had been done previously so previously you would have clamps on a screw basically uh and you it would be like almost a pressure cell without the medium where you're making direct contact between the anvils of the pressure cell and polished faces of a sample one of the things you absolutely can't do then is to apply tension and one of the things we wanted to do to investigate thing the issue of two component order parameters in strontium ruthonate was to tension that caused Cliff to propose this way of doing uniaxial pressure which was you know these things I'm going to give this talk quite experimentally even though it's mainly a theory workshop I think it's useful for people to hear how things really happen Cliff was very used to uh the control and operation of ph o stacks because he'd done as I always tease him about an eight or nine year phd at stanford building um uh scanning probe instruments controlled by phos so he was pretty aware that it might be possible to do something like this and what he said is let's instead of putting the the sample in a pressure cell let's glue it across the jaws of a vice as it turns out the properties of stye cast in high hindsight are absolutely vital to this experiment actually working but you know you make your own luck sometimes so you're going to glue the sample across the jaws of the device and we're going to have a bridge device such that if we lengthen the central stack and leave the other two untouched we'll compress the sample but in this bridge if we lengthen the outer two stacks while leaving the inner stack untouched we will tension the sample and uh and one of the tricks of it was that the sample was going to have to be very small because uh what uh phos stacks are limited by is the force that they can apply right and so what you're wanting to do is to make the sample very small so that a small force controllably is giving you a very large pressure right now and and the reason you might think that that isn't going to work and we had a lot of debates about it is if you take a single crystal you make it very thin and small cross section it's always quite a fragile thing so you would intuitively think that you would break it as you tried to do this and that's where the stye cast comes in just from magic it turns out that it's exactly the right softness if it was much softer it wouldn't transmit enough of the force uh well it wouldn't trans it would deform itself so you would be deforming the stye cast rather than the sample if it was much harder you would break the sample and it's just in the sweet spot so the technique has worked very well so uh in terms of our study of the superconductivity as i might go on to we see absolutely no evidence for two component order parameter in the experiments that we do uh even though we set out to find it and i guess it was pretty disappointing for some of the students who uh who were looking for it but there was very big compensation because we discovered that we could uh increase tc by over a factor of 2.4 and so you could take this traditionally 1.5 kelvin superconductor and create a big maximum in its tc where it went up to 3.5 these are small numbers but the factor is very big right many people many experimentalists including us would love to find other superconductors where we could do the same so so that was really nice okay first glitch with the local equipment yeah even if i touch the keyboard this is not happening so if marco could come in and stand stand near the computer needs to be the local guy who stands near yeah good thanks actually not working from this oh yes it is yeah so yeah yeah good good all right excellent very good let's just see marco stay i may need you to stay yeah because it's not you moved you moved just too far away um so the pressures we can now reach are uniaxial pressures of about three gpa but you've got to be very careful in doing that comparison because uh if you uh in in uniaxial pressure you the sample has the ability through Poisson's effect to relax in the transverse directions as used pressure in one direction so for a given change in physical properties more or less there's a factor of 10 you should be thinking about is now reaching uniaxial pressures which have the same effects on a solid what also symmetry breaking effects but they have the same ability to tune the properties as about 30 gpa would in a uniaxial in a hydrostatic cell of course the great thing is that both go together they're both uh you know so now with uniaxial you'll probably have the three principal axes of most samples plus hydrostatic pressure and uh you know the the answers you get from those experiments should be related thermodynamically and you should be able to do those consistency checks and we do and they work out actually very well it's almost surprising great so the the next thing again just to try and get the superconductivity out of the way quickly before the appendix it turns out that when Stuart Brown at UCLA saw this pressure cell he became very interested in in uh studying the NMR night shift through TC in the pressured samples uh he did that he discovered he got very different results to a famous paper from 20 years ago on unpressured samples so over a course of a year he tuned the pressure off thinking he was going to see some superconducting state transition he never did and the net result was that he discovered a key systematic error in that famous 20 year old paper which he corrected and the Japanese group that published the original paper also corrected under you know this sort of recipe he gave them and that's had a huge effect on strontium ruthonite superconductivity because if you take seriously the data you would be able to see in these two papers it's extremely difficult to imagine that it could be an odd parity spin triplet order parameter so strontium ruthonite um particularly this paper in the follow-up paper in the national academy of sciences if that result is correct strontium ruthonite more or less has to be a spin single it's superconductive and so certainly that's the way that many people in the strontium ruthonite field are now thinking and it's a real revision of how you want to think about that superconductivity okay but that isn't what I came to talk about what I wanted to tell you about uh is our interesting normal state physics properties that come on tuning through a lift ships transition so uh you can draw cartoons about what you're doing and we certainly thought that when we maximized the tc at three and a half kelvin that was when we were uh forcing ourselves to reach a lift ships transition but kind of spectroscopically seeing is believing so here's a beautiful experiment from Veronica Suncoe and Cliff and Phil King's group where on the left you're seeing the original topology of the gamma sheet of strontium ruthonite it's nearly a circle on this graph and that's uncontroversial every photo emission group when they study the bulk states gets this and then they developed a way of putting on enough uniaxial pressure so here's a strain where we've gone beyond the liscius transition so the gamma sheet is now seen to be a strongly dispersing open 1d sheet with a different topology to the closed topology of the circle so that's you know textbook liscius transition you're you're only doing it with uh one of the uh two liscius points you know a symmetry uh distinct liscius points in the zone because what you're doing is you are you are going you're as you tune if you notice the high pressure the gamma sheet has become first of all it becomes elliptical and then it opens part of that opening you can see that in the unpressured sample it's sitting closer to what is now the m one point that it is after the strain has been the uniaxial pressure has been applied so it's moved away from one of the van hove points towards the other one and now we've even gone through that and changed the topology yeah oh yeah so this is a this is angle resolved photo emission um and oh sorry yeah yeah yeah what are we seeing here this is an angle resolved photo emission experiment and uh there's always an issue in strontium ruthenate you have both uh bulk states and surface states but you this this is actually so the the data here look a little bit fuzzy compared to the best photo emission but that's because they worked on very simple techniques to suppress the surface states all together so these are the bulk states of strontium ruthenate andre yeah so if you if you went to dft so yeah so in energy units uh which uh this is just k x k y in energy units how much energy is that than that right that's the question yeah yeah so so from dft it would be about uh 70 millivolts but from experiment the whole band is hugely renormalized so it's about 13 millivolts right but okay now i won't go into the bug so i want to finish the talk okay that's there's the answer right so and we could uh show ourselves from this spectroscopy that within our experimental errors that sheet was touching the lift shift's point when the superconductivity was maximized okay so so that was interesting now what we wanted to do was to do thermodynamic measurements i'm strongly of the opinion that we're only going to solve the issues of the superconductivity in strontium ruthenate if we can understand the thermodynamics another question at the back there yeah so could could i tell you what's happening along the gamma x line yeah uh what's happening is poor experimental resolution i mean i can show afterwards if people would like or privately laser photoemission data uh it's better seen here these are three distinct sheets right and there are some spin orbit coupling effects that give a little bit of distortion from the shape she might have expected but these are most definitely three sheets and some fantastic laser photoemission data which is extremely high resolution which completely establishes that so does the dachshund alpha effect actually okay right good so i'm of the view that if we're going to solve the uh superconducting state problem of strontium ruthenate we really need thermodynamics to check the results of other measurements so we were setting up to do some thermodynamics particularly heat capacity in the stress cells that isn't a trivial thing because you have very on a you have very unusual high thermal coupling inevitably to your rig because you've got to glue your sample hard to your rig and then you have something which in the sense is even worth which is that the way we apply the the strain obviously we go for a strain field which is uniform about five to ten percent strain and homogeneity in the middle of our samples that's where we cut long bars but what you actually have in a real sample is you have the uniformly strained region a partially strained region and then because we put contacts on to measure some other things we have the sample sticking out into a hole beyond the glue and that bit of the sample is completely unstrained so if you just look at the heat capacity which i always call the unspecific heat because it normally samples everything then you would be sampling all of that yeah the guy who spent years setting this up doesn't like that joke very much and and so so what he did was to use a very high frequency by our standards ac technique so you're at several kilohertz when you're doing this and if you're at several kilohertz you pay some cost experimentally but you restrict your heat to the uniformly strained part of the sample but more the way things really work in order for him to get even respectable data from the heat capacity he had it turns out that the high frequency gives you a very small signal so he needed extremely high set up extremely high precision temperature measurement of the order of micro kelvin per root hertz right and so we'll come on to his results in a minute but that knowledge was extremely important to me because i then heard from uh metia cicada who just won a prize for this l t i think deservedly last week he and ian fischer's group thought about uh taking the elastocaloric effect to correlated electron systems so conceptually the elastocaloric effect is very closely analogous to the magnetocaloric effect that many many more of you will have heard of and so it says that if you can measure the strain derivative of the temperature as you're straining a sample then you're getting information about one over its heat capacity as a function of strain multiplied by the strain derivative of its entropy so that's uh these these this is nice information to have now the problem is that uh you know people have used the elastocaloric effect in samples with huge elastic responses right that gives you a signal you can measure but if you just try to do that dc you have no chance of picking up the signal size right and what matias realized was that we were in some senses underusing the capability of these pho stacks because he said okay we're applying a dc voltage and we're squeezing the sample with the dc by by length in the stacks we can turn this into an ac technique by applying an ac ripple voltage to the stacks themselves so as well as the dc voltage we're wiggling the stacks to and fro that then gets us into all the signal to noise improvements of an ac measurement and he had a very nice rev science just demonstrating exactly how this technique technique was going to work he's been applying it to personally to penicillin superconductors so i knew that because we had sensitivity to burn on our delta t we would probably have a very nice signal from strontium rousinate in the setup that we had and indeed uh i don't think it does anybody any harm to look at raw data sometimes so we have a ppm pat per million applied strain amplitude here that is giving us a total signal uh as we vary the strain which is varying over the range of about one and a half milli k and you know the meaning of a micro kelvin per root hertz noise level is that you don't see any noise on that signal at all to what your naked eye that's all signal okay so and you know this this was very rewarding because we didn't have to set this all up we'd even done it already so it was very nice indeed so what you can do is to oops sorry here's a couple of sweeps of uh sweeps at a couple of temperatures this is the result of 73 sweeps at a whole series of temperatures constant temperatures between eight kelvin and one kelvin and all we've done so far it's uncalibrated we're just plotting the measured delta t uh for the very small wiggle strain we're plotting against temperature and strain it's a little bit blurred out on the on the the projector here but i think you can see there's a huge information content in this graph right so first of all if you plot it like this with zeros in white then what you're finding are the zeros and the zeros in the elastocaloric effect are coming because of extrema in the entropy right so dsd epsilon is going to zero where you get that zero so that that white line there is the extremum in the entropy coming as i'll show you in a minute from the peak in the entropy that you see when you go into when you're going through the van hove point you notice that that peak in the entropy is turning into a dip in the entropy in the superconducting state the superconductor is very good at stealing the van hove entropy and then you also see the white lines tracing what turn out to be tc and we know that's tc from susceptibility but also we were actually doing this experiment in a way that we were measuring the heat capacity and the elastocaloric effect on the same sample so there's the heat capacity tc and so obviously the elastocaloric effect is very well traced the superconducting dome if you like of strontium ruthenate now there's a star up here yellow star and what it's showing is that is the single point that we knew from our musr colleagues to be the tc of the entry into some form of magnetic phase it's a phase in which they see musr oscillations right and they their interpretation is that it's some form of a density wave phase it may be but i just want to say it's some form of a magnetic phase what's nice here is that we have again maybe a little bit blurred on this view graph but here we don't have zeros we have a dark line which seems to be the line tracing probably a set of first order transitions that correspond to that magnetic phase yeah Andy so i put in the past people did neutron scattering inelastic neutrons and found you know some peaks in this incommensurate spectrum but not quite evidence for long range that's that's correct and so and now i heard m squared s that kymer's group are doing so we've collaborated a lot with kymer on taking uniaxial pressure into say x-ray scattering so they now have ricks data showing that the inelastic peak is softening a lot they're not at these temperatures yet they're they're there for their they're scanning at temperatures above this phase but as they scan through those ranges of strain it's softening a lot so it looks like it's going to be a density wave of static order at that queue or close to that queue yeah so you know one of the things which is interesting from this just raw data analysis right is that strontium ruthenate plotted against these tuning parameters is seen to have a phase diagram pretty similar into those of other unconventional superconductors it's going to be very interesting to see how exactly the superconductivity and the magnetism exist below one kelvin uh that's going to be harder to calibrate so we do have some data but we're going to be working on that and publishing something over the next year i hope that there is data i'm going to show you right now what the data is of the entropy at this transition right so all of that's uncalibrated right but i insisted that before we publish this we need to find a calibration that was an involved affair took us a couple of years to be convinced andreus rost really solved it so then we were able to calibrate our data so now we're seeing raw elasto caloric data in blue but it's not raw really raw anymore because that's the grunizen parameter in proper units i mean it's a dimensionless quantity but it's in proper numbers as far as we can get it then it's a numerical issue in order to extract simultaneously the heat capacity and the entropy from that raw signal and the entropy that you're seeing is shown in black right so there's the peak in the entropy above tc in the van hove uh because of the van hove singularity you see it sharpening here you see that if you just model the background over that range of strain with some you know simple polynomial or some simple function uh there's no deviations from that background if you do it below at the temperatures below which we begin to see that peak in the grunizen parameter the entropy signal corresponding to that peak is a drop in the entropy of about by four kelvin about three millijoules per mole kelvin squared uh below what the entropy was going to do if you had just continued the elasto caloric effect smoothly the way you did there okay now that looks rather broad but we do have some strain in homogeneity and within the strain homogeneity that we can model that is the breadth you would expect for something that was sharp now i'm i'm uh i'm adherent to the idea this is the first order transition as is urg cliff doesn't necessarily agree so let's just leave it as saying it is a thermodynamically traceable effect which causes the loss of about three millijoules per mole kelvin squared of entropy okay so it is i i would be much better off of now what have i lost that uh i'll be much better off showing you this afterwards i'll be very glad to yeah andrey's asking about how the line looks it needs to be at higher resolution and the actual figure is much higher resolution than that and then you can examine that we can talk about it so yeah no it's different because the line is going down like this so the line if it intersects the superconductivity at all it's intersecting it very near the edge of the superconducting dolma we don't quite know how it intersects that's the take-home message here right and uh um yeah there's a lot i could say but we'll do it later hopefully okay good how much time do i actually have because you had to adjust for the uh lost 16 minutes okay good right but let's speed up a bit so the elastic caloric effect is great and in principle you could use it to combine any spectroscopy that you're doing from the top side of that sample if you've got a thermometer on the back side of your sample you can in principle get spectroscopic and thermodynamic data simultaneously hasn't been done yet but it will be done because i'm determined that we do it and that would be very nice okay now on to what i really wanted to talk about he's a recent unpublished work and this is uh on the stress strain uh characteristics of strontium ruthenate as you go through this lisciz point so this is a big technical development that cliff had been working on for a long time in our original strain cell we had a displacement sensor so we were seeing roughly what the strain of the sample was now he's designed something where we have two sensors of displacement and a force sensor so we can simultaneously measure the stress and the strain and so therefore look at things like elastic moduli very important thing is that we wouldn't be able to get this technique to work experimentally if we weren't able to make use of our focused iron beam machining that we have in our group very fortunately to really prepare the next part of the sample properly that's just a little technical point so hillary node did this experiment and at four kelvin this is what she saw and it surprised the heck out of me at least at first it didn't surprise me because i hadn't thought hard enough and then when i thought hard it started to surprise me right because what she sees is an absolutely huge effect you go through this lisciz transition and the the thing softens by 15 percent at four kelvin right and it also has a very strong temperature dependence to which we'll return but the reason and and we also know that the uh the the the lowest point of the dip within our experimental resolution comes at the lisciz strain so we're pretty confident that this is the strain through the lisciz transition now that's intuitively surprising and why because uh all electrons contribute this is a bonding issue right this is a softening of the overall lattice all electrons contribute to the stiffness of the lattice and you know this that logic about lisciz transition would say the conduction electrons are dominating this huge change in this in the lattice softness so i see martin's in the audience uh he gave this uh elegant uh theater analogy uh yesterday about who's the who's the actor and what's the stage and everything i'm a less erudite person so the way i look at this is to say you know all of these electrons should be contributing to the bonding and in fact the way we physicists think is that here's where we do the physics and here's where they do the chemistry right it's a very direct thing okay and um you know so it's very surprising because this result seems to be telling you that you're in the physics part of the energy landscape and you're making this huge change so you'd say to yourself how can that be at least i said to myself that it's true is proved by i mean yog would say you can prove other ways which is true but seeing again is believing because we knew the entropy from the elastocaloric effect we could look at the entropy relative to the young's modulus i think any sane person would say they're pretty closely linked right and if we go back the none of the chemistry bands can give you any electronic entropy because they don't cross the Fermi level we're at temperatures below the phonon characteristic phonon scales there's very you know the phonons are only contributing five percent of the heat capacity at four kelvin so it's not the phonon term so it seems to be really strong indication that it actually is the conduction electrons that are messing with the chemistry here all right and so then uh you know or even before uh yog had been thinking about these kind of things in marcus and so we had the theory that they had developed to help us interpret the elastocaloric effect which i should have cited was really fantastic in that elastocaloric project all they needed to do then is a bit like our bit of luck with that they had the theory already to start trying to analyze this so and what they see is that the elastic constants of the second strain derivative of the free energy right and so you can you write down a model for the gamma band which we knew for its dispersion constrained experimentally take this write down the free energy take its second derivative and that tells you that this is the elastic constant of the gamma band and it's negative right and there's there's a key point right so you can turn that simple gamma band only model into a much more sophisticated model which incorporates all the chemistry by adding a constant this constant is c lattice right this is the background of all the other chemistry and so what we're actually seeing here is that the conduction band negative term is able to compete with the summed contribution of everything else right and uh yeah so there we go now um and now that's what you can write down or you can write down very easily is about the lattice constant we are measuring the Young's modulus and there's a numerical issue here that you then need to be very careful about non-linear Poisson's ratios as you go close to the Young's to the Lucius transition to get the right Young's modulus out of your calculation and this was so you know you always tells me you can trivialize what I've done too much right and so this was actually uh not the tall trivial um and it's very gratifying because there's what the model does uh and he's tried very hard to constrain the model experimentally to get predictions and absolute units as well so there's the model in absolute units there's the data I mean obviously the data have a bit of broadening the model doesn't have an everything but it's pretty good there's yeah no almost none well the input parameters uh there's almost no free parameters in the theory because the input parameters all come from experiment right and so uh what they're doing is we have the dispersion and we basically know that in the end the dispersion is like it's it's constrained by photo emission right so we we know it under House van Alpen and we know it's very similar a bit like your Malta was saying yesterday it's very similar to just a numerically scaled renormalization of the whole gamma band but we've put that in and then crucially you put in what is the strain at which you see the van the the Lucius transition and that's that is very much concerned with how big is this pre-factor but yeah and the pre-factor yeah you see the logarithm you think it's all going to be the logarithm but the pre-factor is anomalously large and after speaking with Igor Mazin we now understand why the pre-factor is anomalously large if I get time I'll mention that okay but but you know without that extra insight everything was experimental so you know it's not trying to fit to our data no it's just taking experimental data but other things using that in the model to calculate this quantity and getting the right answer yeah you're welcome so everything's well reproduced and the you know for me in a sense this is superfluous but you know the the visual impact of this entropy and Young's modulus graph is so high that it's very nice to see that it's you know almost exactly at least qualitatively reproduced by the theory so the theory has to be right I would say so it's really true that a single conduction band in this case ends up with a negative contribution to compressibility which is overcoming what the rest of the conduction bands are doing and all the valence bands and that to us was very surprising now this temperature dependence I said I'd come back to it so this is what it would be predicted to be in the simple theory because you're at the lift-shift strain and that is a prediction that says that it's got this very strong downward curvature which is also seen in the experiment so there again is just an honest comparison we haven't tried to fit numbers and numbers here that has implications because it turns out that that logarithmic term would be capable of becoming negative and divergent as t went to zero right so what you're saying is that in principle a boring lift-shift transition could give you quantum critical elasticity right and again you know we hadn't thought about this until we started looking at this data and thinking about this problem of course in reality something intervenes we know here that superconductivity intervenes so the question is what does super conductivity do but yeah so here is the the lift-shifts the lift-shifts elasticity as a function of tell the young's modulus as a function of temperature taken in a field of two tesla to suppress the superconductivity going down that's where tc of the sample at this relative lift-shift van hose strain is and here's what you see when you've done the experiment with with the field taken off so now the superconductivity probably has to make a ppm softening of the lattice i think right at tc but the main thing it's doing is it's hardening the lattice so it's stealing the van hose entropy and it's hardening the lattice again so superconductivity is a thing which could intervene to get rid of this kind of effect anyway this was very thought-provoking for us and we start wondering whether avoiding elastic catastrophes can you know it can be quantified as a way of giving superconductivity in systems like this yog also in about a couple of hours started to write down scaling relations for the generalized free energy that you would have for a generalized strain-tuned transition and he realized that it's like i'm told to say this is lacking the pick in physics right that when you've written in that scaling form you have a quantum whatever lacking picking criterion that says that if those indices or in this calculation get to be less than two then you're actually guaranteed to have a finite temperature lattice instability because of that the existence of that physics we have the marginal case and you know we have a very simple system it's a 2d saddle point so you can say you genuinely know and we can quantify how 2d it is and it's you know the dispersion is only of a couple of kelvin so it's so we know these exponents therefore we're at the marginal case where the instability would be a t equals zero instability but you know yog can show that it would be the t equals zero instability so that's the story on this this was very very educational to me as i say wasn't surprised at all when i first saw it because i didn't know anything then i started thinking and we all started thinking and i was incredibly surprised then we kind of taught ourselves the answer and you're a bit less surprised again but i think the middle state is the good state to be in this is a pretty surprising observation that under any circumstances at all conduction electrons can do something like this to the elastic properties of a solid so that was very good how much time do i have do you want to hear okay well i've got five minutes i'll go on and say a couple of things about the superconductivity and our approach oh yeah please yeah absolutely completely correct yeah yeah but but so okay so it's to take it into account by nature to the extent that the experiment and the theory are doing you know the close enough to the same thing that it is taken into account actually the strontium ruthenate is incredibly 2d we've known that the out-of-plane dispersion of the gamma sheet is a couple of kelvin ever since um old dhva days but even stewart brown's work and we have some other work which didn't have time to talk about they're all showing you that the dimensional crossover is just coming it's becoming uh would become relevant only below the superconducting tc so superconductivity is the first thing that intervenes eventually it would like you're not perfectly 2d but you're very very close to 2d so it's this kind of incredible model system for studying this kind of physics okay oh and on the question there in case i didn't repeat the question uh malta's question was about the dimensionality i hope that's clear to the online audience andrey yeah yeah yeah yeah so so from the data no and you wouldn't really expect it to be because i'm giving this a proximal yeah so so you're andre saying are we really seeing a logarithm in that experimental data uh well it honestly speaking uh if you really look at it probably not quite right but then that's not so surprising because we're now getting down to four kelvin uh and our dimensionality scales of the order of two kelvin so it's not killing us in a very visibly obvious way but it's beginning to have an effect is the way that i would i would say so yeah we aren't a perfectly 2d system but we are enough of a 2d system to be able to see very surprising things right and then make you think of other surprising things and now your other question where was it i may have put the wrong yeah one of the things that we did recently with ego and bunjai kim was they were you know dft can investigate this so imagine the our assumption of c lattice being a strain independent wasn't true but i think the entropy kind of rules that are already but they went away and did the full dft first principles calculation and found this about the scale of dip that we find so certainly you know ego is a skeptical guy and a careful guy his conclusion is that yeah this is a believable story from the dft point of view dft also tells you a bit about this pre-factor because so there is something called anderson's theorem but that's early anderson not phil and that's telling you about the the the power law dependence of hopping parameters when the hopping is going between orbitals of different kinds and it's to do with the angle me i don't understand this in detail but the point is it's to do with the angular momentum of the orbitals and here we're doing the hopping is ruthenium oxygen ruthenium so we're doing two hops between a d level and a p level and it actually turns out that that gives you a power law dependence of the distance i function functional form of the distance dependence of the hopping parameter which actually matches a dimensionless number that we had been puzzled about from our analysis very nicely so we think that that's the other key thing is strontium ruthenate is also you know if you were doing sp hopping then we'd be a factor of 10 down in that number that comes in squared to elastic constant so we'd have lost a factor of 100 all right and so we believe we can understand this now now i don't have five minutes anymore negative one but there's four minutes well okay but i mean we don't have to do you want me to go okay i'm being told to go on okay no i won't go on yeah i will so one of the other experiments we've been doing now about the superconductivity was a heroic effort experimentally to build a huge strain rig to allow them usr to be done under strain in strontium ruthenate because we heard from erin about the care effect being interpreted as time reversal symmetry breaking at tc musr also has a signal looking like an internal field at tc and uh you know our musr colleagues insisted on drawing this musr phase diagram for strontium ruthenate uh i particularly enjoyed that by the way but anyway um uh so let's look at what the elastocaloric effect tells you actually tells you that all qualitative features of that kind of educated guess of a phase diagram are obeyed except that there is absolutely no sign thermodynamically of this line for time reversal symmetry breaking now they are predicting a very very weak strain dependence of that so the elastocaloric signal would be small what we can also do is the heat capacity coming down in temperature at different strains that should pick things up perfectly well i'm showing you the heat capacity transitions that we see there they show no convincing sign of splitting at all just a little bit of broadening musr tells us exactly the temperature range we should be looking at in every strain to see a second transition that is circled there and within probably five percent criterion we do not resolve any thermodynamic signature of a second transition there so uh to me what that tells you is that you've got to be very careful uh when we use the term phase diagram when we draw diagrams like this the assumption that everybody has either implicitly or explicitly is that these are the boundaries of bulk equilibrium thermodynamic phases that's why i think it's extremely important to investigate that kind of stuff uh with thermodynamics and we're getting a negative answer and you know and so it's really important that we see what the care effect does under strain in future and as Aaron said we have the aspiration to do that but certainly the musr doesn't tie in with what we're doing thermodynamically now there's very final slide uh yeah okay the other thing by the way that our entropy inversion tells us from the elastocaloric is that the gap function of strontium ruthenate just has to be fully gapped at the van hoog point right so it rules out any order parameter which is put nodes there and Jurgen Marcus did a nice calculation illustrative calculation proving that i think that's in the supplementary information of the elastocaloric paper now we have something else about strontium ruthenate which is very suggestive which is that ultrasound which is normally a thermodynamic probe as well it shows jumps in elastic constants that should not jump unless you have a two component order parameter right and so that's a very interesting result indeed however where they found the jumps are in the c66 parameter everything i've showed you so far has been straining along the bond the zone edge in k space and that has nothing to say about a c66 anomaly with uniaxial pressure we can also pressure along the one one direction which we're doing in some depth at the moment and you know that's a that's great it's purportedly a thermodynamic measurement there should be thermodynamic consequences and the the the message at the moment is that there are again big discrepancies between what we get with the bulk measurements and the numbers that are coming out here you also noticed by the way there's a factor of 35 in jump height difference between these two different ways of doing ultrasound and you know if this jump is supposed to be unfest related to the jump in in the heat capacity so that also should worry us i would say so you know my now we get from fact to fiction my my personal bias at the moment is that it's going to wash out in the end the strontum ruthenate is a single component even parity order parameter that's probably where we're headed but we know we need to really really nail that down over the next few years before we can be certain about okay thanks very much for your attention thank you questions from the audience i'll jump on the very last phrase that you pronounced even parity single component even parity order parameter uh two questions yeah one very specific is it d-wave in your opinion or or not in my opinion yes it's d-wave in my opinion it's dx squared minus y squared let me ask my opinion right but let's just see let me ask a little bit could i could i say one thing very quickly there the thing which survives completely is the disorder dependence of the tc of strontum ruthenate so it has to be a sign changing order parameter because every single way you disorder these crystals you destroy the superconductivity completely and second it's the last day of conference i'll ask some semi-philosophical question which is mostly for theories but you know you qualify as theories as well so question is that uh you know cooperate and we know there is one whole point in the cooperants yeah and there was number of theory papers saying that at one whole point is the best case for both magnetism and super in d-wave superconductivity yet tc is almost zero at one whole point it's a very end point of all this wonderful superconducting phase diagram why is there one hope is nothing for superconductivity and here it's everything okay so uh if you listen to your colleague your theory colleague Peter Hirschfeldt and another honorary theorist Dave Brun they would say that that's because it's very highly disordered by the time you've driven it to the Lucius point yeah so that's the first point uh the second thing is it's i've been tearing my hair out for nearly 10 years that we should be working on cuprates and i'm really motivating people now to go to the lanthan strontium system uh what we can at least do is to start at slightly cleaner lower order levels of disorder and drive it the rest of the way by strain and then end up studying the disorder dependence of what happens in some kind of a controlled way that would be really interesting the other point about the cuprates though is that you always have this diamond square issue right the the the diamond fermi surfaces are very go very close to the van hoek point the square ones are very far from the van hoek point and you know you get just as good superconductivity in the cuprate families where the family surface is square as you do when it's that when it's uh diamond shaped again though we should just be going to investigate that i mean the other thing i believe is that in strain terms i didn't mention this we've been talking today about about up to 0.8 lattice parameter changes but the yield strain of most materials is way higher than that so that's the other thing i'm trying to motivate the people doing the hard work to do we can probably put three or four percent strain into these materials in eventually so i would love to take some square family surface to cuprate superconductors and see what happens to them under high enough strain ending let me ask one question about this ultrasound evidence yeah so if you had a scenario in which by accident one superconducting a single component superconducting state and a non superconducting state happened to have condensing at the same point would you see an anomaly in c66 and a non superconducting state yes so that might be okay good um i don't know my guru on this is yog who might be on the call i'm gonna say i doubt it but is yog are you on the call i told him not to because it would be boring okay it took me seriously yes i am yeah yeah so did you hear shri's question yog yes i did i don't think it would work because you need two order parameters that that have to be gaussian variant in their combination so if it's non-magnetic here for psi star and something else that doesn't have a face that couples to strain so they are i mean i receive wisdom is that it needs to be two superconducting auto parameters yeah okay so there's a question in the i don't see any questions from well okay then i'll get back to the online participant thanks for the nice talk i have a very naive question which is related to the fact that if you have a two component order parameter and they're two different symmetry irreducible representations when both of them have condensed you expect to be in a different symmetry group we expect to be in a lower symmetry group now is that not something that would show up if you did some very simple experiment like brag diffraction the crystal lattice constants would not change so one of the things that's taken me far too long to really appreciate is that symmetry is useful but there's always got to be an energy scale associated with any symmetric effect and it's the energy scale which is going to tell you whether you have observables associated with it right and and so that's that's the key point you need to really be careful that it's uh and this is why it's you know you do some incredibly sensitive experiment uh that can find you like what david shea is doing right he's finding symmetry anomalies in many things right but until he knows or we all know the energy scale associated with those observations we just don't know whether they're significant or not so so that's my answer there so there's one question from john cooper uh would you like to speak up john or shall i read your question read it please read it he said okay so he said so towards the end you showed specific heat jumps at tc versus negative strain how do they vary with positive strain uh so um i i don't have the graph with me john i'm sorry um uh the the strain dependence of tc measured um magnetically is nearly even right so it's flat bottoms uh and it goes up almost quadratically uh both under tension and compression we have a we've followed it a slight way under tension but the thing about tension is the samples break much more easily under tension so uh we're always a bit if we're not particularly interested in tension we tend to avoid it because we want to then do a long experiment instead of a short one okay thank you great okay let's thank andy for a beautiful talk