 Okay, so thank you to this afternoon session. So it's my pleasure to introduce our capital Nick from Stanford University, and he's going to talk about time reversal symmetry breaking in multi component or the parameter in complex superconductors. Thank you. Like everybody else I want to thank the organizers for the something wrong. I agree. I am. Well, it's maybe not yours. It's made it here. Let's say it's here. Okay. Oh, thank you. So now I need to share it. Okay. Okay. So what is this. I don't know. It's not. So how do I reduce it. Yeah. It's gone. Okay. Thank you for the invitation to come and tell you a little bit about our work on time reversal symmetry breaking of unconventional superconductors. If you read it. You read or you will read the abstract I attempted to focus today on uranium to know you do which is a kind of material of interest, but I want to walk you first through the whole story and in particular. And what does it, what does it mean? Partially because they have been recent papers on other materials where it was ambiguous and sometimes even wrong. Good. So this is a cast of characters that that were involved in this work. And how do I How do I Yeah, I think I do. I click. What do you think Maybe you will hear It works in this way. No, let's do something. Try now. Okay. Now I will Yes. It doesn't I'm fine. I know what to press, but It's not changing. No. You want to try with my I don't know it was working. I mean, I can do you right back. Okay. I'm going to start with my No, I have, I have mine, but mine does not show on the screen for the zoom people. Oh, you have. Okay. Otherwise, I will just use the one that. Yeah. Okay. Something probably wrong with this. Okay, I'll do it. The zoom people will guess where the pointer is. This one, I think This one does work. And, and this is bright. Okay, so I'm going to start the clock now. Okay, so I want to I want to tell you about Some results as I said on your interview too but before I get there I want to review a little bit what we are doing here. So Let's first talk about superconductivity and time was a symmetry breaking which is going to be the subject of the talk today. So if I write the pair wave function as a product of the orbital and the spin part, which, of course, will be also proportional to the gap function which will be our other parameter, then I have two possibilities one for spin singlet. And one for spin triplet where the order parameter is a vector and therefore the most general function for the gap that includes both possibilities is written here where we will focus on on on the gap functions either for a singlet or a triplet case. So if we I have this more general order parameter and I use that and I use that time reversal operator operating on this gap function, then it's easy to see as you operate and you can check me that when time reversal symmetry is preserved, then delta for the spin singlet case is simply equal to the complex conjugate and similarly for the triplet case. Okay, so if I take, therefore, a situation in which the gap function does not equal to complex conjugate obviously time reversal symmetry is broken. And I'll have therefore a real and imaginary part, similarly for the triplet case, and an example is the celebrated P wave superconductor, the first attempt to describe superconductivity in strontium to the new for where the V vector had a P plus IP in the, in the plane, multiplied by the Z component. And, and, as you can see, this is a complex order parameter that describes Cooper pair going one way or another in this orbital motion. Okay, now, I want to talk about multi component order parameter in a more general case. In fact, I decided to take an example, which bring us back about 40 years when people discovered to transitions in uranium platinum three and we're debating what is the cause for it assuming that this is genuine and not in homogeneities or something like that. Even after the specific heat came other measurements such as sound sound attenuation and three different phases were identified. Now, the, the issue is that even at zero magnetic field, one sees two different phases. And that was a puzzle because, in principle, for that, if you start with one possibility, which is one order parameter that belongs to a two dimensional representation, then you need a symmetry breaking field that that will split these, these two blocks for those that followed stones and within a this was one of the big puzzles why it doesn't split, for example, in stone so within it when you apply magnetic field. Okay, so here it was split. And then soon after an idea for a symmetry breaking came along and and and eventually it turns that there was a particular to the representation for the order parameter in UP t three, but at that time, as this was not clear people said well maybe there is another possibility, which you have to primary order parameters. And they are from different irreducible representation. There may be either spin singlet or spin triplet each one of them. And then there is accidental degeneracy there. But since for that you need fine tuning, then maybe there is something else that stab like, so you see that in either possibility, you need something you need something that will play the role of symmetry breaking in the first or something that will do the fine tuning for this second scenario. So I'll come to these two issues. So, I'm going to use light to detect time reversal symmetry breaking. So, this is actually quite simple. Light beam of light pointing that say going in the z direction and you apply the time reversal operator. Then for that the only thing that matters is the part of the time reversal operator that that complex conjugate it. And therefore, as you can see the time reversal operator behaves like a mirror. It reflects back into the minus z direction. That's important. It's important for understanding experiments that test for time reversal symmetry breaking. Well, if you have a material that breaks time reversal symmetry breaking it turns that the eigen states of the electric field in in such a material are going to be not linear polarization which sometimes people use in order to detect time reversal symmetry breaking but rather the two circular polarizations written here is e x plus minus i y and then the indices of refraction for right and left polarized light will be maybe different as time reversal symmetry is working. So, again, this is indeed an indication for time reversal symmetry breaking that the index of refraction for right and left circularly polarized light are different. Okay. Now, this leads then to to most common measurements for that which is the father effect which is in in transmission where the father angle that is by how much a linear polarization rotates and remember linear polarization is a superposition of the two circular parallelization by how much it rotates and it's simply proportional to the difference between these two indices of refraction and in polar care effect and I will emphasize the polar care effect a few times in this talk. Then it's this combination that's the imaginary part of this combination of the index of refraction so you see that still there is this difference between the index of refraction refraction for right and left circularly polarized light. So, the issue is that there is another property of materials that will rotate polarization and will have a difference between right and left circularly polarized light. I said time reversal symmetry is broken, when the index of refraction for right and left circularly polarized light are not the same. But this is the property of all gyro topic material and gyro topic materials can be either time reversal symmetry breaking or not a solid I mean a crystal of sugar will rotate polarization because sugar molecules are chiral quotes is chiral tellurium is chiral. These materials don't break time reversal symmetry. However, they will rotate polarization because the right and left circularly indices of refraction for a circular polarization are different. So, really, the whole idea of using optics to search for time reversal symmetry, but breaking hinges on on scrutinizing all these different different possibilities. Okay, so I want to talk about the polar care effect. And as you will see, this is really the asset test for time reversal symmetry breaking every other method. This does not take does not test for it directly. So, when you take light, and you, and you scatter it from a surface of a solid, then, and, and let's talk about circular polarization, then there are two possibilities. Okay, I can. Let's say that that I use one direction and I measure the circular polarization with respect to the direction of propagation. K will be the direction of propagation and plus, let's say will be right circularly polarized light minus is left circularly polarized light. So I can have an index of refraction for going in the direction of K for right circularly polarized light or for left. Exactly for coming back for right or left. They don't need to be the same. In fact, all four can be can be different depending on on the material. So, if you do these calculation using the transition amplitude. If you do this as a scattering problem, then you will find that reflection coefficient for right circularly polarized light is basically the difference in indices of refraction for for right and and for for left going in the opposite direction. And, and similarly, for, for left, for left and right going in this direction if I look at left circularly polarized like that. Yes. Yes. So, so they're okay. So, let's have a good point. Yeah, what happens, what happens if you, if you do this experiment for materials that like anti ferromagnetic that there is no net magnetization in a particular direction. So, there are some unique cases in which you will have a signal, but in general, if it's if you just take a pure anti ferromagnetic, the signal will be zero, unless you do it on atomic scale like like measurement that. Of course, but note, once again, note that I'm talking about. If you see a signal is it or not, if you don't see a signal. Okay, there will be lots of possibilities when you don't see a signal. If I do see a signal in a polar care effect time reversal symmetry is broken. That's it. It could be broken because of anti ferromagnetic type, it could be broken because I don't have enough sensitivity. I'll show you our sensitivity in a minute. You wanted to ask something because that's exactly what I'm telling you that that in a, I mean, if you then now calculate if I have right and left circularly polarized like the care angle. In fact, if you use scattering theory can be represented as the difference in argument between going right coming back right versus going left coming back left, which can be translated into this combination of indices of reflection you see all four different indices of reflection appear here in a in a optically active material, for example, then each one of these is zero. And the reason is simply because for a carol material, a right hand screw is a right hand screw whether you look at it from here or from here. You can take you can take a not you can put it on a right hand screw from this direction or this direction is going to be the same. And that's why it doesn't matter on the direction. This is going to be zero for a normal optically active material or carol material, but if kind of a symmetry is broken. Then if I go one way, there will be one index of reflection coming back the other way it's not which for those that want to use father effect. And the way to do it. If you have a transparent material put a mirror. We talked about a mirror for life, right, you put a mirror, and now you go back and forth. You go back and forth if time if time reversal symmetry is not broken you come back to where you started from, if time reversal see reversal symmetry is broken, you get twice the father angle. Okay, that's a way to do it. That's that's what that's what I said. Yes. I have a, I have a circular spring. Yes, spring with a handedness. Yes, in which current is beginning to flow. Yes. So it was not carol before. Let's say I have a situation in which it's not carol before. Okay, wait. I mean, I have a limited time but I can answer you in, in, in show if the quality polarizes the spins. Then you will see a care effect because time reversal symmetry from that point of view that I said, following premise, there is going to be a net result. If the quality does not polarizes the spin, then I will see zero. Okay, let me continue. We'll get the goal. Now. So, if so, by the way, what I showed you so far, I use time reversal symmetry breaking, but actually it's a much more general concept. It's the concept of reciprocity, which means that this this expression for the care effect is the expression where whether reciprocity is preserved or not. And non reciprocity can come out before because of non equilibrium because of in homogeneity is as a function of time temperature, whatever, but if reciprocity is preserved, then this is absolutely true. And if reciprocity is not preserved, then you get a finite, a finite character. And as I wanted to say, this is true only for polar care effect. If you take light and you now shine it at an angle and you measure the care effect, this is no longer true. And a chiral material of any type is going to give you a finite effect. Only the polar care effect gives you an absolutely unambiguous result. Faraday circular dichroism, etc. They, you can view them as going only one direction, and therefore they cannot really distinguish the four different indices of refraction. Okay. Okay, so I want to talk about superconductors and primers running. So, and I want to use light. Okay, and we use near infrared light, which is, which is relatively high frequency. It's at 1550 nanometers, it's point eight. And you can therefore calculate what is going to be the response care response of some unconventional superconductor. I'm not going to go through the theory of that there are lots of papers written. It turns that you really need a multi band superconductor to exhibit a finite care effect. If you do, and you go through the estimate, then it turns that besides the fact suppose you have an estimate of order one for the, for the care effect which for a typical for magnet you get something of order 1020 milli radians that's very typical for iron for cobalt etc. And then you need to multiply it by the ratio of the gap over the frequency of the light square to know how much you're going to measure. It's very easy to see that if you do that exercise, then within these theories, you get something of the order of 50 to 100 nano radians. So, a back of the envelope and relatively small envelope estimate. The question, what is motivation for care effect. So, what he's saying it's, he has said the polar care effect is an optical phenomenon which arises in a stage with broken time perversal symmetry. The question, what is motivation for care effect. I think I said it. Four times that this is, if I want to use optics, this is the unambiguous test for a time reversal symmetry breaking state. So that's the motivation. Andres and Chandra and others tell me is it or not and then I go to the lab and, and I want to do something and the measurement that I think we should do is this measurement. So, so you see that this is this is really very small 50 to 100 nano radians when normal for magnet gives you a hundred. Let's say 50, 20, 50, etc. a million radians. So, I'm talking about a million times smaller than what people usually measure when they measure magnetic materials. Okay, so a typical measurement and for that I am going to show you a magnetic material stones in within him or three is a fellow magnet below 150 Kelvin. And if you measure it. You take a film of sponsor mutinium or three and you measure you see that's that's PC, and it gives you a result of six micro radian I told you that the fellow magnet is much higher. Well, the reason is that the material breaks into domains. Okay, so if I do the measurement many times, and it's just warming it up above the transition and then cooling each time it's a different result. Sometimes positive sometimes negative, I can then do a histogram of all these and find that there is a histogram and in fact you know from the standard deviation. What is the actual domain size and when you compare it with a Lawrence picture of the domains, it really fits the ratio with the like like a Gaussian statistics of the domains versus the size of the deal. So it really works very well. But of course, once I realized that there are domains, then I know that if I cool now the material with a field that orient the domain such as magnetic field of course, then I have a single domain, and here the same by the time I am at 90 degrees, it's already two milli radians you see that's 1800 that's two milli radians, and by the time it gets the low temperature is going to be a few milli radians slightly lower than iron at this wavelength. Okay. All right. So, again, this is busy because it is telling you if you do apply magnetic field what are typical numbers for optical rotation, but I want you to look here because this is going to be important very soon that if you look at the normal state of of simple metals. And from that point of view, you pity three is a simple metal there is no magnetism hidden there. Then, a typical care effect should be when you apply a magnetic field of course it is non magnetic. At any, at any temperature, then you can estimate it to be about 10 to the minus 10 radians per Earth's. So, suppose I'm, I want to go through a particular transition, which I will of a super of a superconducting state, and I will apply let's say 50 cows, 100 cows. Then it's going to be 10 nano radians 15 nano radians. Okay, so, therefore, it's a very small number. Okay, so I should be able to do this experiment without getting ambiguity and you'll see what ambiguity one can get. Okay, so I want to talk now about the consequences of what I said so far. First of all, if I want to have an apparatus that will measure the care effect, and we'll have all the properties I talked about. I want it to be an apparatus that reject all reciprocal effects. I want it to be able to measure the absolute value of the of the care effect. I don't want to. If I want to measure the weight of a captain of a ship. I don't want to measure the ship with the captain and subtracted from the ship without a captain to find the weight of the captain. And, and I want high sensitivity because I already estimated for you that it's 100 nano radians that what we are, what we are searching for. So for that, we invented an apparatus in my lab in 2006, which is based on the sonic effect, except that there is no loop for those that remember what's a sonic effect you have to counter propagating beings that interfere at the detector they go through the exact same optical path. And therefore, if time reversal symmetry is not broken because of something, then it's a constructive interference with no effect. But if anything on the way breaks time reversal symmetry, then you get a face sheet and it's used as a sonic effect is used, for example, for fiber optic gyroscopes. We are not using a loop. We are using a single fiber. It's actually an optical communication fiber, which if you didn't know optical communication communication fiber is a polarization maintaining fiber. Because it's a birefringent fiber and optical communication only uses if I'm not mistaken, the slow axis. But there are two axis, and we are using now these two axis as going in and coming back type of axis for constructing a loop. So if I take one example, if into the fiber that's a segment of the fiber. And if I take a linearly polarized light going in the in one of the axis, let's say the fast axis. Then it goes down to a quarter way plate, coming to the sample is circularly polarized light let's say right, going back is left. And because of that going to the same optical. At the same quarter way plate, it will go 90 degrees back on the slow axis. So coming in on the fast going back on the slow coming into the slow going back on the fast. I have to counter propagating beams going in a loop of zero area. And that is really good, because it's extremely stable apparatus, because every point on the beam feels the same temperature the same gradients of whatever environment you have. So it's a very stable apparatus, which allow us to get results. The good thing concerning the properties that I discussed before is that by symmetry of the apparatus. It is fully reciprocal. So only if there is something which is non reciprocal only then we will see a signal. There are a few other properties I want to show you very briefly that to make you know what's an interferometer right it's an interferometer, but interferometer has usually two legs in this case if the two counter propagating beans. Now it becomes an interferometer where when you modulate one leg versus the other and you look at the interference. And the change in the interference. Well in this case we are using a electro optic modulator it's here in the circuit for those that know. And because of that I can measure at the frequency of the modulation at the twice the frequency three times etc etc. Well, this actually have some some it has some very important results one is that where and there is a DC. So if I want to measure the care effect which is fine on reciprocal is actually twice the care angle. Then it comes from the ratio of these two components, the component of the first harmonic over the component of the second harmonic. These days are usually zero for an isotopic material and finite for a chiral or or birefringent material but we know how to do that, how to to to get these these coefficients. And the, the, there is another issue, which is, if I measure now the ratio between the DC and the second harmonic, I get this these two coefficients a two and a zero a one is typically zero. I get these two and these two are very sensitive to optical to to all kind of optical activity, and to buy refringence. Okay. A teaser for for Android. These are results on cobalt doc. I own nick tied measuring it here. This is this curve that's this idea of of that, that intensity that measures the, the birefringence and indeed you see that a dramatic transition. We can make him that's, and, and, and then we can measure the resistive transition, and that's the actual PC, but care effect only starts at lower temperatures and it's very easy to distinguish where it starts. Okay, so there is time reversal symmetry breaking, but it is distinct from either the pneumatic or the, or the super the onset of superconductivity I'm not going to talk about that one today. The model of interest currently is this Kagome, we call it CVS. And, and it was proposed that it breaks time reversal symmetry below the charge density wave transition. And, as I told you, I can see by the fringes optical activity I cannot distinguish them. That's, you see this is the, that intensity, and the good thing is that it's within the same optical volume that I measure the care effect and the, the birefringence or whatever other pneumatic transition that occurs. So you see, indeed, there is a CDW transition, very abrupt just like it was found in susceptibility or in specific heat. And there is nothing in the care effect to within, if you look at the average to within plus minus 13 nano radians. Okay, yes. Yeah, yeah. Yes, we didn't measure it yet. Yes. So, basically, I just want to show you. And, and, you know, sometimes I heard people behind my back saying, oh, he always sees something. Well, no, here's an example where we don't see anything, despite the fact that there were that there were reports in the literature. If you report so far on care effect of order of 40 micro radians, that's a factor of 1000 larger than what I show you here is nothing. Okay, so I believe that there is nothing. Okay, so I need to get soon to the subject of the talk. And before I get there, I will start with the you. But you note tellurium to you platinum three I mentioned it before, because at the time it was a puzzle whether what kind of multi component order parameter it is. And we get amazing crystals from Bill Halperin at Northwestern with triple hour of 1000 very, very typically extremely high quality and you see they're very big few millimeters. So we can do a lot of measurements. And, well, here it is. So we got people proposed. I told you there was a debate. The debate, calm down with the proposal. I think the theory was was mostly done by by Jim souls. And that is, if you remember how to do it then. The real part is is kz kx square minus k y square, and the imaginary part is k kz k y, which is basically kx plus I k y square times crazy. Okay. So, indeed, there are two components. The A phase, as people call it, has just the real part, the B phase adds the imaginary part and the C phase has just the imaginary part. Okay, now, just to show you the capability of the apparatus. The red is the care effect. This is the susceptibility, you see that we are already way in the superconducting state, when, when the care effect picks up. This is point five five Kelvin. This is point point four six Kelvin where we see the transition, and we can easily distinguish distinguish them. Okay. By the way, it's much easier to measure at these temperatures, then at one and a half Kelvin, because the dilution refrigerator. The helium three systems they are all very stable at lower temperatures and much less stable around above one Kelvin. Okay. So I told you that that you want to do it, you want to do it many times, and then see that the effect is, is changing sign well it is this was done. These are many as your field cooldowns that were done in a low temperature. And so sometimes plus, sometimes minus, and all of them of the same size, which means that it's really within the size of the beam which was about 10 microns. This is a single domain. Okay. We talked about training with the field suppose it was not a single domain. How do we know we call it in magnetic field. And, and here we call it that plus or minus 50 girls. And we see that, first, we see that indeed it's, it's determining the sign of the effect. I call it a plus 50 girls I get, I get that this is just one of the zero field results to show you that it's the same size. You call it in minus 50 girls, it flip sign it flip direction it's the same size, which together with the normal state understanding that a care effect in the normal state is only of order of 10 to the minus 10 radians per gauss means that at 50 Gauss, I will just have a maybe a couple of nano radians. And, and therefore if, even if they're trapped vortices, I will not see them, right, because unless I have magnetism, which will be, which will see within the vortex core. Then, then I will not see it because, in a way, it's like the normal state times H over 82. And this is very small thing. So, yes. You want to ask something. And no, sorry. Okay, so this was, this was up to three and and we understand it very well we made we did lots of measurements on this, on this material. But now you went into the room to, and this is very different now. Okay. So, this is actually results written in these in these two papers. At the beginning, you're going to learn to was proposed to be an end compound of the series of electromagnetic superconductors and compound in the sense that these are for magnet is higher and higher. So, in the query temperature, where you ran into the room to people could not find an order in temperature down to the lowest temperature that they measured. So the idea was well maybe it's a quantum critical point of, of, of a magnet, and, and it was understood at the time that maybe as well is associated with for magnetic fluctuations. And indeed, the, the, here is magnetization measurements that that show that at least down to this temperature show that there is no finite moment. And these are magnetic susceptibility measurements that showed that the axis is the easy axis and, and there is a query. No, kind of, actually, there are some issues. And then a possible for magnetic quantum critical point was was suggested by doing some scaling with a particular exponent. But then, more recently, and this is all I'm talking about. There is, in time, there is BC, DC and AC. So BC is before COVID AC is after COVID and DC is during COVID. So these are, these are all measurements DC. And, well, well, first there were measurements. Peng Cheng dies group, actually finding anti for magnetic fluctuations are more relevant. There was no doubt to the, to the idea of for magnetic fluctuations. Then, then, there were more recent measurements from the, from the group of look at that, that there are other fluctuations, which, which again are for magnetic and in fact, the magnetic fluctuations are weak. So all these put doubt into the idea of for magnetic fluctuations is responsible for that superconductivity. At the same time, STM measurements are in the group of video, but I have an Illinois find that there is some signature of chiral in gap states. The, the spin susceptibility was found not changing or very, very little changing through the, through the superconducting transition which by the way is of order of one and a half Kelvin. But the thing that that started people started to think Oh, magnetism, superconductivity, complex order parameter. What should be then the order parameter, but it's the material is auto rhombic. So you cannot have two dimensional representation. So you need to rely on two components or the order parameter that will, that will be. Okay, so in the superconducting state, there were measurements finding a nice mean field look specific heat but a lot of excitations at low temperatures. The transition was normal spin susceptibility I just showed you. So, oh, here it is. Okay, again, no changing through, through PC peculiarities started to appear when people compared the three different critical fields. And recently people measured as you can see by the date the lower critical field, and the upper critical field was known. And there was a mystery that the upper critical field times the lower critical field which, in fact should be roughly the, the thermodynamic critical field square, did not match at all. Okay, real, real positive there. And then, in the group of John Pierre Paglione, they started to grow samples that have two transitions as I show you. So two transitions. Magnetism around, maybe time of a symmetry is broken. Samples were shipped to us DC that is. And then we started to measure them. Now, I should add that concurrently it was also found that if you apply pressure and not that high pressure. There are even in samples that don't show two transitions, the about point point three giga Pascal transition split. So, there is a reason there, and maybe there is a multi component auto parameter, and pressure is doing something to eat. So that's now specific it as a function of, of magnetic field in the, with the field in the three different direction and you can see the two transitions. Okay, so that that actually led to our collaboration. So that's why we use to do the care effect. Now, I, I, okay, I'm going to, I'm going to zoom now, but I just want to say something about again about measurement of superconductors. Now, when you have a superconductor and you apply, and you apply magnetic field. Okay, then there is very strong susceptibility, you have the magnetic susceptibility it's a very strong susceptibility. But it's an edge effect, which means that if I come with a care effect to the center of the sample, I will not see these currents I will not see the Meissner effect. But that's an advantage. It's really an advantage if you want to study, for example, the vortex state. If you want to study really the, the, the symmetry of the other parameter without being affected by these, these kinds. So for that you really need to, to go to the center of the, of the sample which we did. And these are now many zero field cool. It's a mess. But I think it's very clear to see that, and you see the signal, the, the size okay that's 100 nano radians. That's 200 nano radians. The slope is roughly at 400 plus minus 400 nano radians. So that's already an indication that the flow temperature something is really happening as, as compared to above, above PC, but unlike up to three, which in all our measurements and by the way also in measurements, it's a, the domains are enormous. Here it could be that they are very small domains. In fact, a recent USR paper that just appeared a few weeks ago suggests also very, very small domains. So then we started to do measurements at very low field and not at field, cooling in the field, turning the field to zero and measuring, and you see that 23rd, 2025, 30, they all fall on top of each other, which suggests that, and, and the, and now it's a cleaner 0.4 micro radian. So this could be really the intrinsic time of a succinctly breaking. I'm going to skip the theory part of that. That's the analysis that that Daniel Atterberg did that ended up with this idea of, of this, these two components, which as you can see are from different other parameters, but then you increase the magnetic field that you you cool. Now, do you know, you probably remember if you did some vortex physics, if you take a hard superconductor, and you cool it in magnetic field, then vortices start to go in if it's a hard superconductor, you are in the critical state in the critical state. Okay, then you have a finite critical current and the magnetization, then penetrates in until you get to the point where the magnetization penetrated vortices if you want penetrated to the center of the field. Okay, that's the first time that when you have vortices at the center of the sample. It's, it's, it's called the full penetration field. Okay, and, and, and so what we did is we cooled in magnetic field, but this time, we do see a huge change, depending on the magnetic field that we cool it, which really says that we see vortices. But this is no surprise, because in the normal state, there is enormous effect, it's a killing. It's a paramagnet, a strong paramagnet and pension. Okay, so it turns that that at high field high cooling field. It's, it's indeed I see vortices at low field it saturates to about point four which we claim is, is the, is the intrinsic order parameter time of a symmetry breaking effect. There is a difference between the UPT three or you're going to continue to silicon to and this material that that they show in magnetization. But when you look at the care effect of UPT three, it doesn't show anything. So that's the UPT three but in in two we do see the critical state in care effect where we don't see it. As you can see here, we don't see the critical state in UPT three as expected. And if you calculate the critical current from that critical state that is when you see the first vote is coming with the care effect to the center. So you see the field and you get and you get a critical current, which is very similar to what is found experimentally using using magnetization books. Okay, so it really works. So I'm going to stress the measurement pulse and at all, and we are very close to what they have. Okay, so I'm going to skip the, the infield measurement, because I'm, I run out of time. But I want to say that if you measure susceptibility in magnetic field at some field 240 Gauss as an example. If you measure the care effect of the same field, then there is saturation here. There is, there is actually a turning down of the care effect. As if, as if something fights the vortices that are already in because of the, because of the magnetic field. I want to suggest and that's calculation that that I did, but, but I don't have time to talk about it, that the contribution to the free energy that you need to put due to the magnetization must include a spatial varying magnetization and local magnetic field rather than a global magnetic field, just like you do in the vortex state of any superconductor. And when you do that, actually you do get that that there is strong screening of the magnetization of the union to that fights against the killing. Okay, so I'm, and that's the, I'm going to, that's, I'm going to stop here. Thanks for the talk. There has been already a few questions, but I see people raising hands. I apologize for not being more egos on the magnetic field dependence but it's quite fascinating what you can do when you really sit at the center, and you wait for both of these to come in. Yeah. Now, question about your insight into it's a story as far as I understand against the story about two water parameters belong to different representations and below the lower temperatures are getting done with I fact. Yeah, probably you said that but it was very quickly. Is there any way is to check this by adding pressure or something and splitting the two temperatures are making the two temperature flow that something that will show that they're really two So with the pressure with the pressure idea, I will also assume that a uniaxial effect with hydro study pressure will be a little bit more, more difficult, because I want nice surface access with the beam. So maybe with with diamond one can do it and go through, but uniaxial, and the, you can, you can do this kind of experiments and we have a plan for the stones and wuthnate. Maybe we'll also put a year into Louisville. But I think that that that this, this should do. I mean, right. That's a good question. Being a chair, you get a lot of exercise. You measured it with the beam along C direction, right, you do. Yes. Now, the highest critical field is a long age. Right. So would measurement along gay and be give different results and what could be, we don't have a good sample with good surface along these other directions. We asked from, from JP and so far we don't have. Can it be polished. So, by the way, attempts that we had in the past to polish other crystals failed to get because of strain. I, well, I don't know if it's just strain I think that that polishing also reduce reflectivity for us. And it means I need more power, more power, more local heating and things like that. We never succeeded with polishing. Other questions here or we go to the questions. Yeah, so first I, Leonid has was rising the hand. So Leonid, can you talk. Yeah, you hear me. Yeah. Yeah. Hi, Aaron. Very nice talk. Had a quick question. If your system, I mean you talked about it briefly, what happens if you have disorder at the mains, etc. But what if the mains are correlated, what if it's something like what Elie, Elie Zelda is measuring and maybe also talked about that earlier today. I was asleep at the time, but if it's a checkerboard checkerboard pattern of organization correlated throughout the signal. To be to be greater or smaller. Okay, so I think, I think that that it depends on the, on the size of, of these older domains versus the size of the beam, because it's, it's basically an effect that will have to do the conference of the beam right because inside. Exactly. And all I have, I mean in a random fashion, it just square root of the, of the two areas, the area of the beam versus the area of the domain. But if it's ordered I think that it will have to do with how. It's, it's going to be more of a, of a circumference than a full area, I think, but I think that that that for proper relative dimensions that we should be able to see an effect. And the same for density waves for spin density waves. I don't know. I think for simple spin density wave. I don't think we will see anything. Thank you. Yeah, thank you. Thank you for a lovely talk, Aaron. I only wish I was downstairs with you guys. And infect everybody right. So the question is, you're in your early met in the early measurements, there was a split transition the specific heat but you alluded to the fact that with subsequent crystals, the you need to apply a finite pressure to see the specific heat split apart. So what kind of contradict the idea to accidentally degenerate representations coming together that that is, I mean I could go to that. So, okay, so right now, there are still two types of crystals. There are those that that have two transitions. And there are those that that have a single transition those with a single transition typically will have a higher TC of order of two Kelvin 1.8 to two Kelvin. Those with the two transitions, which are made regularly. There are two transitions, by the way, the split of the two transitions in the in the Maryland crystals is is very small, but they can resolve it. We cannot resolve it with care effect so I cannot say anything about it. We just got a couple of months ago crystals of a single transition. A single specific heat transition to measure but we did not measure them yet. So I don't think the story is is is ending. We need to measure those and see whether we see an effect or not. I would say that Jeff Sonier measured us are for both types of crystals and didn't see any difference, both appear to show some inhomogeneous magnetism in them in a very similar fashion. But we did not measure yet the single, the single transition one. Thanks very much great. Okay, so I'm going to read there are some questions here in the trap. I think that one of them, maybe you have already answered that because when you were answering Leonid so there is one question which is whether you can measure polar graphite in after magnetic metals and whether you will see in that case. So there is another. One of the questions one is how much a strong electric field is requiring case of care effect so how is strong as to be the electric field. I'm, I don't understand I mean the electric field is the light. Okay, that's the, that's. If, if the person wants to know the, the, the intensity. We measure it at around 50 micro watt on a beam of 1010 micrometer at very low temperatures and smaller beans at higher temperatures. This is way below any heating or anything that one should be worried about. Thank you for your nice presentation what the signification of the presence of two peaks in the heat and the specific heat. Thank you. Maybe the first response to the real orientation disorder and the second correspond to the new temperature transition, whether you can. I just answered when I answered peers. I mean, there are two types of crystals that are those that ambient pressure show two transitions and they are those that don't. And, and I think that that we need to measure those that don't in order to see whether, whether time was whether there is a care effect there or not which we didn't do it yet we just got crystals. So this is another one is why is the critical temperature is lower compared to resistivity and industry results for the cobalt arsenide data and why. Yeah, is that I think that somehow probably there is. There is some resistivity data going. I don't know if you want to show it. Yeah, and that the PC is supposed to be lower to the one I don't know the one that you're showing. It's not a matter of supposed to be I mean this is a result. Yeah, I think that I think that I showed it as a teaser to to Andre I don't think that this is expected. Okay, so this is this are all the questions and so now, thanks again. And so we move now to Leonid.