[00:00:05] >> It's a pleasure to introduce Professor Peter Hirschfeld was going to be or could look me speaker today. Let me see if you was about Peter P's. A very well known. Physicists in the area of contest metaphysics is a distinguished professor at the in the worst of Florida and he's now spend some time in Denmark. [00:00:30] He's well known for his work on how to see superconductors and I read the tides you know which involve a very unconventional kind of system so with the way free for the supercomputers he superconductors and and multiband characteristics for the irony that it's well he's been working in this area for some quite some time and he's very well known. [00:00:59] In if you would over all of many Particle Physics Physics with emphasis in super going to t.v. it was a pleasure to have you here today. And he told me that you know he would welcome questions if you would like to ask directly doing his presentation but Peter welcome and you're free to start to talk Ok Carlos thank you very much for that nice introduction I'm very happy to quote unquote be here. [00:01:32] I would love to visit in person and I hope to do so in the future but I applaud your efforts to keep your colloquium going and I must say I had some very interesting conversations this afternoon per bluejeans and so it's been a worthwhile. Visit for me as well you know let me go ahead and share a look works. [00:02:00] What you should think of looking. Toward later director I do I do thank you pretty radical meeting there. Thank you very much I thank everybody. So my title is a super connotatively there's plenty of cream at the bottom. Let you know what the cat is for later in the talk and explain the title I'm going to be starting out with a very elementary historical introduction to superconductivity. [00:02:31] And a lot of you who have been around the condensed matter physics field for a long time have heard this a lot and I apologize for that but this is also very much for students because I have a message I want to get across and that is that this is an exciting field that students should learn something about and maybe even go into so I have a lot of collaborators over the years worked in various projects here are some of the recent people whom I've worked with on the left of that vertical and white line are people who have passed through the University of Florida at one time or another and I won't read their names because there are too many of them but you may recognize a few of them and on the right side of the line are some. [00:03:16] Quote unquote xterm collaborators and some of the research I'm not really telling you too much about my research today but I think it's fun to show collaborators because this is what really makes physics fun and exciting is to work with so many nice and delaying people. Ok so let's go to the history a little bit 1911 this gentleman is hiker commonly known as from the Netherlands he's interested in the problem of what happens to the resist a video of metals when you go to low temperatures there were 3 theories available at the time or classes of theories one class said the resistivity should go to 01 class that it should diverged and the other class said it was going to some constant value nobody really understood why it should do one of these things or not but he figured he'd just do it experimentally and what he found was something unexpected namely that in mercury when he got down to 4.2 Kelvin the resistance disappeared overnight now when I was a graduate student I learned a story. [00:04:36] Which I found amusing which was that in fact it wasn't discovered by him it was discovered by a high school student called the Blue Boy who monitored the apparatus in the middle of the night and he was at home sleeping in his bed when the actual discovery was made this turns out not to be true on the anniversary of the 100th year of the discovery of superconductivity. [00:05:02] His notebooks were discovered in the back of a lab in in Leiden and it turns out that he was in fact on the case I don't know whether it was exactly the middle of the night but it was evening and he he saw the disappearance of the resistivity of mercury and self so I'm going to skip over a lot of ground here but basically from a theoretical standpoint this was recognised as a very important problem that something so dramatic would happen to the electrical resistance of a metal and in the 50 years until 957 superconductivity had its origins was definitely regarded as one of the most important problems in theoretical physics. [00:05:53] And. My Something has gone wrong here I can't advance there we go Ok. So if anybody has some time and is interested in the history of physics I recommend strongly an article by Yorkshire Molly on which was published in an volume. Celebrating the 50 years of the b.c.s. theory which I'm going to tell you about in a 2nd but the point is that there are awful lot of really interesting ideas about how you can get the reasons to disappear. [00:06:33] All most all of which were totally wrong but some of them were very very creative and they're worth reading about but it was Fineman who said no one is brilliant enough to figure out this problem and that tells you what level this problem was perceived was really one of the challenges that had to be solved to make further progress and here's a. [00:06:56] List of people who worked very hard on this problem Borland our Fineman Einstein and Heisenberg art and they all failed us Ok. This problem was solved eventually by these 3 gentlemen John Bardeen Leon Cooper and Robert Schriefer who identified that superconductivity was a. Quantum mechanical. Macroscopic quantum mechanical effects and they received the Nobel Prize in 1972 for their theory theories based on the notion that electrons bind into pairs and that these pairs acquire a common uniform quantum mechanical phase. [00:07:48] And so here is the famous B.C.'s wave function written in many body language and basically that represents an order characterized by an order parameter which is this anomalous average of c. minus k. down c. k. up I'll tell you what that is in the 2nd and it's effectively a complex scalar with the quantum mechanical overall phase for all of those pairs. [00:08:19] Why are you having I don't like blue jeans Carlos. So. The phenomenon is basically a pairing phenomenon a switch said you start with a normal middle aged let's say it's equals 0 in which case I have a. Isotropic system then the electrons are confined to the so called fer me sphere all of the states inside those fears are occupied with one spin up and once in down electron and outside they're all unoccupied you turn on an attractive interaction somehow between opposite momenta electrons going up instant down and you make a pair and then those pairs are collectively condensed into the superconducting ground state which is thought of as I gas of these pairs. [00:09:19] Now why does it want to pair. I'm on. The. Naive dancer in it is works actually for the picture that's on the screen right now is that. Pairs are fermions statistically both arms of a can undergo with normal and we know of this pose condensation and that makes a pair superfluid. [00:09:48] Is this really the right picture of a real superconductor B.C.'s superconductor and the answer is no. Superconductivity in the ground state is really a system of interpenetrating pairs not molecules of electrons but interpenetrating pairs whose size is much larger than the typical enter particle spacing though the size is the fermion the loss of the the speed of electrons at the Fermi surface divided by this gap energy that I showed you before and it's typically much larger than the inner particle spacing in a simple metal at least Ok. [00:10:32] Now all of these pairs this looks like a big jumble but you have to remember that every single parents quantum mechanical many body state has exactly the same phase and therefore these pairs are face coherent they make beautiful music together like they Matthews passion choir in Oxford this is that picture there I got from Steve Blundell who likes to use this analogy. [00:10:59] It's important to know one other thing which is how do you make an extra Taishan above this superconducting condensates ground state well you break a pair you take unbind the pair and you have the 2 electrons go in different directions those are both for us but when you both political exits Haitians and if you look at the spectrum of these acts attentions you see that there is in fact an energy gap in this spectrum and that that's equal to twice this number which we call Delta Ok so a typical superconductor is characterized by Delta in an elemental superconductor this is going to be on the order of a few Kelvin. [00:11:45] Now the big question of course is the origin of the interaction that binds the electrons together because they have like charge and that's not supposed to happen if they're sitting together for a space so if you look at popular accounts of superconductivity what you'll see is a lot of rather hokey explanations. [00:12:12] The one you encounter most frequently is the dance analogy you have a lot of people dancing randomly on the dance floor and then the slow music comes on and they kind of pair up and continue to dance in a semi-coherent way I really hate this analogy I don't think it has any physics in it whatsoever but even somebody as smart and knowledgeable as Bob Schieffer used it in some of his talks and he used to say that the reason pairs form is that by dancing these people lower their energy or make themselves happy or. [00:12:54] If you're a graduate student in physics you really should not be satisfied with that explanation. Schriefer himself. Who was. A member of the faculty of all of the universities in Florida or of the latter part of his career because he was state university system professor although he was based in Tallahassee and the chief scientist at the mag lab he used to use other analogies as well one of which particularly when there were no parents of students present was the law tell bed analogy if you go to a motel and she looks you will have never been to the national tell that has a mattress like the one in the picture and you know that if you live with your part. [00:13:45] Her next to each other the mattress tends to pull you together and that's actually a much more accurate analogy than the dance analogy because it explains that the electrons when they are present they deform the medium around them and it's the defamation of the medium that leads to the attraction. [00:14:06] Ok so. The slightly more sophisticated picture is that a solid consists of look at us of positive ions and there they are in space and an electron which is negatively charged can come along and because it moves at the fair me velocity which is very fast. It's pretty much long gone by the time that the ions contract around the where the electron was and so a 2nd electron can come again come through and go and be attracted to this concentration this excess of positive charge and that leads to a net lowering of the energy now if you do this calculations for an elastic continuum of positive charge in the background of an electron gas what you find is that the electron falling on attraction is dynamical that's where the Omega is in this 2nd term in the expression comes from. [00:15:14] And that just means that electron phone interaction is retarded reflecting the heaviness of the ions and the lightness of the electrons that's very important to make an attraction for this electron phone term this is the result that you get you can see that it can have a negative sign provided Omega is small but you also see in this result however which is also interesting I think I have to tell you what the 1st term as the 1st term is the. [00:15:49] The just the ordinary screens cool interaction of 2 electrons in a metal repelling each other screen however by the other electrons in the intervening gas Ok if you were to set Omega equal to 0 of this formula you see that the 2nd term would exactly cancel the 1st term and you would get 0 and that itself is enough to understand. [00:16:15] In a crude sense why superconductivity exist sometimes but not always so if you do this calculation for a realistic system you basically get the same answer but there's a pretty factor in front of each term which depends on the details of the system. And I've already mentioned that this is the retarded in time interaction but here is the periodic table of the elements and they are indicated as different colors according to whether or not they actually superconductors at some low temperature and you can see that many of the elements are in fact superconducting at ambient pressure many of the others are superconducting when you apply. [00:17:03] Pressure above ambient pressure and some of them are not superconducting at all and that is again due to this slight imbalance of the details of the repulsive Kuhlmann or action which is competing with the attractive electron pulling on interaction ponens being the quantized ionic fibrilation is that we looked at before Ok so. [00:17:30] Maybe I'll stop and see if the students have any questions about any of this. Ok not hearing anything and you guys still hear me I never know whether there's anybody really out there you know you could have Yeah Ok Martin so. The c.s. theory is $957.00 Hello Ok b.c.s. there is a $957.00 there were a few bugs that had to be worked out like gauge invariance of the theory that was a lot of intensive effort over the next few years but pretty much all the main problems that people had identified were worked out by 196061 to the extent that a great pioneer in superconductivity physics Bryant depart from Cambridge gave a speech at i.b.m. Thomas Watson I think Center in New York and 1961 which he entitled The cat and the cream and the idea of the speech was. [00:18:37] While superconductivity was fascinating superfluid helium which was another low temperature problem was fascinating but it looks like everything's solved now. And so here's Bryant Park he said I think I might remark that in low temperature physics but this appearance of liquid helium superconductivity and Magni to resistance from the list of major unsolved problems as left this branch of research looking pretty sick from the point of view of any young innocent who thinks he's going to break into the ground cream had all been laughed off by the cat and there was nothing left for the young researchers coming into the field that was his point of view and the next few of the next decade and a half kind of bore out his conclusion. [00:19:27] Until 979 basically if you read the abstract in my talking you know that the basic point I'm trying to make is that this is a field which is driven by experiments we don't understand everything there is to know about materials and they're constantly new discoveries in this field that renew it the 1979 was the 1st. [00:19:48] Well I'm leaving out superfluid helium 3 but that's a superfluid not a superconductor so $979.00 is the 1st. Big discovery that shakes everybody up the discovery of superconductivity and heavy electron systems by Frank stagnation and his collaborators and dumps that. So remember I showed you this picture a picture of superconductivity which relied on the notion that electrons were fast and the ions were slow so that the electrons could get out of the way and create this effective time dependent retarded interaction attraction between between electrons Well that wouldn't work of course if the electrons weighed as much as the $100.00 and these particular materials were super chronic Timothy was indeed discovered that had effective masses as measured by specific heat and susceptibility which were behaving as though their mass were $100.00 or even a 1000 times larger than the bear a lecture on mouse and so. [00:20:58] Why should these things be superconducting How can that possibly work but this is the 1st time that people start proposing that in a superconductor it might be that there's a different source of attractive interaction besides the. Electron phone attraction that I showed you before and then 1986 is the big revolution. [00:21:24] The sky every of the Sr connectivity by these gentleman Alex Miller and bed notes in this oxide system with Barry of lanthanum and copper they were at i.b.m. silly answers I always like to explain that I came very close to this Nobel Prize personally myself. And you can see why because here is just a side show physic table of contents from 1986 and here's my article about heavy for me on superconductor that I was working on as a post doc and here's the Nobel Prize winning article by bad notes and middle and I'm very close to it Ok nobody's laughing over over blue jeans but. [00:22:19] That usually gets a chuckle or 2 in Ok. This is sort of the state of the system of the field excuse me after. The middle of the cooper revolution let's say 1990 or so. Cooper rates were discovered to have higher and higher critical temperatures the vents move us just them was $35.00 Kelvin which was already referred to as high temperature superconductivity at the time because the others the conventional superconductors had only gotten up to about $23.00 Kelvin before that they added g.c. rapidly jumped up to. [00:23:07] Something like a $150.00 which is this mercury material under pressure. And then a few years later sorry on work will come back to this picture in a 2nd though it so that was a lot of excitement during the late eighties about the prospects for superconductivity made superconductivity made the cover of Time magazine all of the technological applications that we were going to have tomorrow were in everybody's minds on the everybody's lips. [00:23:41] So it was an exciting time to be working in the field. The promises of superconductivity I'm not going to go into in great detail but I will mention them on the slide namely that of course if you have a superconductor it has no electrical resistance therefore you can transport power over long distances in an electrical grid without losing energy that is a huge savings of energy. [00:24:10] You can make. Power electrical power density greater in cities you can transmit from renewable sources to the grid using these power lines you can make lights efficiency. Engines motors for ships or for women. Light and you can generate power you can do Joseph in electronics to make quantum and to make quantum mechanically based computers their classical computers but they are based on super conducting electronics in principle you can make large magnets and large magnets are useful for many things including high energy physics. [00:24:55] Including. M.r.i. magnets medic medical technology infused knowledge Ok so I'm just flashing this at you we can talk about it later if anybody's interested in applications so where are we with these Cooper rates that were so exciting in the mid eighty's it's a long time ago now and the t.c. is still stuck at around $135.00 an ambient pressure $150.00 under applied pressure there is something interesting however which is that the superconductivity turns out with many interesting things the superconductivity turns out not to be of the s. wave type meaning that the Cooper pairs exist in the relative angular momentum of l. equals 0 but rather l. equals 2 that means in momentum space this is money fer me so. [00:25:45] See this yellow circle down here than the pear wavefunction. It is a function whose relative Corden it is negative along the x. axis and positive 0 on the y. axis that's a like an atomic d. wave function and in momentum space this is caused k. x. minus course on q. why. [00:26:11] What we don't know yet there's no consensus is what holds these pairs together the electron flow interaction is too weak by consensus to work in this case in this particular case I should say so we don't know what holds the pairs together what's the glue. That binds them into pairs. [00:26:32] Ok We're going to jump forward to 2008. This is because discovery of iron based superconductors by it a whole host on all in Japan. And probably too much data on this slide but what you saw was that initial discovery was a superconductor in a material based on iron which had a critical temperature of 26 Kelman and iron was surprising nobody looked there before because the whole theory of super coming to be that led up to this point. [00:27:11] Was based on the idea that if you had a a magnetic moment inside your sample it was going to break Cooper pairs and thereby lower the critical temperature pretty much kill superconductivity the iron was expected to have a magnetic moment in most materials and therefore shouldn't be very good for superconductivity but it was and. [00:27:37] It was found that you could get a dull almost superconductivity by doping chemically with chlorine this is a little bit like this doping phase diagram of the coupe rates where you your dope chemically and introduce holes into the copper oxygen plane and c.c. goes up and comes back down that's the superconducting dome I didn't go through the rest of this phase diagram there's an anti for a magnetic insulator at hold open 0 It's a so-called pseudo gap phase which is very mysterious and there are various competing theories and what might be a fairly liquid on the far right side of the dome. [00:28:17] Anyway back to to see what happens if you continue this plot as t.c. vs time is that you can add these. Iron based systems and you see this was another mini revolution with a lot of activity discovering a series of materials over time but at the moment the highest sort of verified critical temperature in this family is about 70000 Ok so not as high as the Cooper it's I'll just mention a little bit more about them because this is a more recent field it's still going on and something I've worked on so there are several families I'm listing only a few of them here. [00:29:01] The original family was the so-called fossil when we named the materials by their. By by that sometimes it's called lanthanum 1111 because there's one. Of each of these elements in the chemical formula this is barium once or 2 lithium iron arsenide 111 iron so in the $11.00 you see what they have in common are square loudest as of irons and. [00:29:33] Arsenic so or in the case of r. and selenium selenium it's either chemically challenged in or nic to gin Sorry Nick to gin and challenge and over here in the selenium Adams above and below the iron plain and then there are various reservoir layers that provide charge in the plains and between the in the spacing between the iron plates Ok so all. [00:30:04] That c.r. and sell into it. One of the new interesting developments in this field was the. Electronic structure the band structure of these materials was a little more complicated than the Cooper hits where there was just one d. band at the firm and getting an mpeg ship with question before you Will Forte's you might look for you sure this iron cell an eye on that reaches you graph which has up until a critical temperature of 8 Kelvin that's correct in the previous one you said that the modeling of that has about 70 killing Well so what are the steps we as you who tools this probably a buck the picture when you go through smaller the biggest things fluctuation become more important Whitey Siegel's up. [00:31:01] Carl this is this is an excellent question I Ansel and I had in the bulk bulk crystals are 8 or 9 Kelvin superconductors if you do almost anything to them they turn into 40506070 Kelvin superconductors. There is at present big argument in the field about what the right answer to your question is in the case of the monolayer which I said was the highest critical temperature about 70 kill and it's believed that. [00:31:37] 2 things happen 1st it has to be made on the substrate the substrate is strong tightly made and that puts a little bit of strain on the. Iron selenite and removes. What's called electronic pneumatic order that allows t.c. to rise to about 40 Kelvin we think and then in addition the follow Non's in the substrate may help the electronic acceptation. [00:32:07] Through creates a higher temperature let me come back to your question a little bit later if I may say but that's the basic answer and I can I also interrupt quickly Absolutely yeah. Are that the superconductors which are basically seem to be 2 dimensional either on the layered ones are they all the weight. [00:32:32] These are 2 dimensional the ones we're looking at right now and most of them are probably not the way that I'm going to tell you about that Ok so is that Ok can I continue thank you if I don't answer your question then then come back to me Ok. [00:32:49] First I just wanted to say that these materials have. A number of. Ends at the firm surface of the surface is quite striking it tends to be consist of very small pockets around the high symmetry points of the 1st 3 ones and on in addition to that the orbital character of the d. character of the states at the fairly level changes as you go around each pocket so that makes for quite an isotropic pairing interactions in these systems. [00:33:25] As a result you can get a bunch of different kinds of superconducting States when I have is a cartoon here plotted as a sort of a polar style plot on a cartoon fairly surface consisting of these small pockets the center pocket is a whole pocket around what's called the gamma point at cable 0 and the 4 pockets around the outside are the so-called electron pockets because they disperse upwards and the color represents the sign of the superconducting gap function or if you prefer order parameter or if you prefer pair wave function though the ordinary superconductors that I introduced at the beginning on this particular Fermi surface would all have the same sign the function if I rotated this picture by 45 degrees would go into itself that's therefore called an s. wave superconductor there are other ways to make an s. wave superconductor by symmetry you could have the function change sign for example between the inner pockets and the outer electron pockets. [00:34:41] You could also even have no woods where the gap goes to 0 at various points on the Fermi service and still preserve this overall as. Sway of symmetry in group theory language this is called Transforming according to the a one gene representation you can also have a d. way of State like the group rates where if you rotate the state by 45 degrees the gap changes sign but. [00:35:04] The electron phone interaction is again to weaken these materials to account for the heights we see by 2008 we had very good Aben issue no methods of calculating t.c. in the electron photon systems and it doesn't work to explain even $26.00 Cal them much less 70. So I'm going to go now backwards a little bit and explain a little bit ideas which. [00:35:30] Arose in the early sixty's and were later applied to both the coop rates and the iron based superconductors and the heavy Firmian superconductors which are called now unconventional superconductors because the pairing is thought to arise from the exchange not of phone Non's but of electronic exits Haitians in the electron liquid so these developments go back to Conan Lawton sure and also roughly speaking that was in the United States and put the ascii in what was then the Soviet Union so. [00:36:07] Here's a statement from the original Conan Ludger paper which sounds very striking if you've never heard it before if you have an electron gas with no phone no and no and degrees of freedom at all only repulsive Coolum their actions between these electrons this can be a superconductor and the reason this can work is that electrons can avoid the repulsive part of the Coolum interaction in space rather than time so how does that work well the basic idea of the cone Ledger interactions. [00:36:44] It is that if you put a charge in a metal the Electra static potential that it creates because of the presence of the screening from the surrounding electron gas is oscillatory in nature so it changes sign and it falls off with something in 3 dimensions of falls off like one of our cubed. [00:37:04] And so this is a plot of what it would feel and so if you would like to experience an attractive interaction with that electron which is nailed down at the origin all you need to do is live on your way function needs to live in one of these rings where the. [00:37:24] Interaction is attractive and so you can see that that core is going to correspond to finite anger moments and pairing though there's more to this than just a cartoon of course Conan Ledger did. A low order diagrammatic calculation in terms of a screen Coolum interaction and they came up with a formula for cheap and it. [00:37:47] Falls off exponentially with a large power of the angular momentum of the cooper pair now in 1965 when they wrote their paper the best guess of best estimate for the channel in which helium 3 atoms which are fermions after all would would pair was the wave and so eloquent too and so Conan not major inserted this l. equal to into their formula and got 10 to the minus 17 Kellen. [00:38:21] So that's pretty small temperature not likely to be discovered anytime soon and so Conan What was your superconductivity when I was a graduate student was a little bit of a joke Ok. But it is interesting to note that the pairing interaction in superfluid Helium 3 is actually in the l a call one channel and if they had known this and just bothered to insert equal one in here they would have gotten 3 c. is a one Millet Kelvin and that's actually the critical temperature of superfluid healing 3 at ambient pressure though there's something to this theory and I would like to just sort of step back for a 2nd and with that mind you I told you about 2 types of superconductivity so far one is the conventional type where the attraction arises because the electron photon interaction is retarded in time and so you can avoid the Coolum repulsion in time when it needs to single sign or s. wave superconductivity on a given chairman surface this unconventional type of pairing comes from repulsive interactions that the rive ultimately just from Coolum forces and can lead to sign changing types of pairing functions on the same theorem a service. [00:39:51] I'm sorry yes yes what the con I love you good thing it gives a p.d. 3 though right it's it's a neutral area so so though how does the the by which would change in that case the terms of the intimate because the couple it wasn't a cool interactions right it was done for 4 screen call interactions but it was also done just for short range Republican around it and that. [00:40:18] You know you know more than anything it's a neglect the momentum dependence it's just a very short range short range for the pulse of interaction and you get the same answer. Factor the prefecture and the exponentials a little different. If you. Ok so there's a slightly more sophisticated version of this due to free for his student Neil Burke 966 they took a Hubbard interaction this is sort of the answer because Carlos this question you just take the q. going to 0 the limit of the screen column interaction which is just a constant and you pair. [00:41:00] Electrons with opposite momentum and opposite spins you look at the the scattering of this pair of the electrons and you add up all of the diagrams which correspond to particular many body approximation which consists of sums of bubbles and these latter diagrams and you what you get is something that's proportional remarkably enough to the susceptibility in the so-called random pays approximation it has this structure 0 is what you would calculate in the absence of the screen cooling interactions it's the dynamical susceptibility that has this denominator one minus a few times cannot and this can get big this expression can get big if if this denominator gets small. [00:41:49] So this is one of the most popular ideas about how you can get pairing and superconductivity in the cool trades for example entirely from the pulse of interactions so here is a plot of the function I'll call it vs of q. here is Q x and Q Why so I'm plotting a function in 2 dimensions and it's positive everywhere I haven't labeled the axis but just trust me it's positive everywhere but it has a peak and at pipe in this 1st brew one zone and so basically what happens is if you try to solve the b.c.s. gap equation which I'm showing you for the 1st time here. [00:42:31] If you put in a result where the gap is function is constant it's a function of momentum on the left and on the right this is a self consistency integral equation and v the interaction is positive everywhere this capital easy is the quasi particle energy it is also positive and so you can't solve this equation because there's a minus sign out front. [00:42:57] You have a problem but if you allow the gap to vary in momentum space to take advantage of this peak and change sign itself then whenever this is big the pairing interaction big gap itself is also big and all the opposite sign and so you solve this equation and that's where the d. wave state in the cook rates comes from because when you shift the momentum by pipe I go into minus itself. [00:43:25] And I remember it's the graduate student saying Well Ok but fine but I still have to have an attraction somewhere where does the attraction come from well one way to think about it is if I have a function that looks like this I could always write it in terms of a series of harmonics s. wave deal where I've just imagined expanding a an arbitrary function. [00:43:54] In terms of orthonormal functions on the sphere for example then there would be a big repulsive constant term but you might have been a weak attractive the wave term Ok So although. The overall interaction is positive and repulsive there is this attractive piece and the b.c.s. equations project out this attraction and take advantage of it. [00:44:22] This is what it looks like in real space electron number one is at the center and electron Number 2 is on any of these points you can see that the nearest neighbors for this way function have a big attraction for the electron at the center. In the iron based systems the same paradigm was used by eager models and who said look I've got these little circles that around the gamma point and some other little circles around the important these are nearly are quite well nested. [00:44:56] And so I expect the magnetic susceptibility to be peaked excuse me at this wave vector that connects these circles the red circles and the green circles Well if that's true that drive that forces justice in the d. wave case a sign change of this order parameter delta between those 2 pockets where that interaction is peaked and so that leads instead of to the wave through the so-called s. plus minus state which has the full symmetry of the lattice but nevertheless changes sign. [00:45:32] Ok so we did a lot of work over the years trying to do I'm running out of time so I'm going to skip forward here is a little going to skip And yes there's a clock says I should really check the time though let me move forward because I really want to tell you about some new developments these are all things that have been going on for at least 10 years 12 years and me you haven't really used me you have never made good at it. [00:46:02] Did I Ok well then I'll just mention that. The monolayer that Carlos asked about the iron selenite moment monolayer is one of a class of systems called Iron shell Kaja nights which are kind of at the center of the controversy right now and the reason you can understand based on this picture that I showed you. [00:46:25] The s. plus minus state which is sort of the paradigm for superconductivity and these aren't based systems requires that you have. This whole pocket in the center but supposing it disappeared for some reason then this mechanism would go away and yet these 3 systems which are all based on iron cell annoyed. [00:46:50] They're different in Turkle it's a Veyron cell annoyed and there in the one in the middle is the monolayer that I spoke about before they all are missing the the center hole pockets and so question is where the superconductivity come from and why is it so high and that is really one of the big questions in the field right now another question Ok I wanted to go on because in 2004 you know I was giving talks for 20 years saying electron thought interaction it's too weak to make high temperature superconductors and this was not just me this was a standard line in the field and in fact there were calculations which purported to show that there was an upper limit on electron flow on superconductivity of about 40 Kelvin and then in 2014 Michele Yerevan mines. [00:47:53] Showed that. The hydrogen sulfur system sulfur hydride whatever you want to call it he put in h 2 s. and what probably came out under high pressure was h 3 s. they had a little sulfur in the process. And this became a superconductor at $200.00 Kelvin below 50 Kelvin higher than the highest who prayed under pressure. [00:48:18] And something which contains no elements which have any deal like Johns in them are in this any deal lexicons anywhere close to the fair Mr fas so. In fact I think no deal accounts period though there's There goes our all of our lovely ideas about how you need strong electronic correlations to make i.t.c. superconductivity. [00:48:44] Doesn't mean that they go entirely out the window as I'll tell you in a 2nd but it means somehow that there is in fact a way to probably make very high temperature superconductivity with the ordinary electron phone as a mechanism now the catch of course is that this 200 Kelvin superconductor occurred at very high pressure. [00:49:10] At $200.00 gig of Pascals which are $150.00 Gig of Pascals when it went off and that's about $1.00 mega bars which is probably half the pressure in the center of the earth so it's a very high pressure and. This was you know I'll say it well as I'll show you one more thing this is the structure that probably was identified eventually as causing the high high temperature superconductivity under this very high pressure. [00:49:45] A year later 2 years later Russ Hadley and Michelle their mitts again found that lanthanum hydride. It was a superconductor at 260 Calvin's And so this is now getting really serious again you need. Very high pressure unfortunately and so they're not going to be any any applications of these materials so what about room temperature superconductivity So let's give you let's give ourselves a sense of what these temperatures mean so hydrogen sulfide under 2 mega bars of pressure is at a t.c. of 210 Calvin Max That's minus 63 Celsius and if you want to know how cold that is that's the lowest recorded temperature in the UK which in Russia whereas my pictures come on your quit school a month. [00:50:48] There we go there's a call it's Ok on a very very cold day. Let them hydride under 1.5 mega bore pressure that's minus 23 Celsius that's the average low temperature in your eclipse in November so Ok still pretty cold you wouldn't call this room temperature superconductivity yet I'm reminding you that the challenge now is to duplicate the physics of these hydrides and related high pressure superconductors at ambient pressure Ok that's where the applications are at ambient pressure. [00:51:24] And finally I get to tell you maybe some of you haven't heard the sea hunt that. If you mix hydrogen sulfide and methane and hydrogen together under 2.6 mega bars of pressure you get 15 Celsius which I think qualifies as room temperature and that's an average temperature in your quotes in July. [00:51:49] This is the coldest city in the world by the way so this is a really nice sunny day probably doesn't happen that often this is the paper nature of last week Ok this result appeared and here's the data you see that they have beautiful data beautiful sharp transitions up to about 200. [00:52:10] 60. They have the past 2.6 mega bars and temperature is really very high and this is the variation of t.c. with pressure there's this initial kind of looks like it's going to be a dome and then it jumps up higher and like I said I've barely had a chance to read this paper much less digest it though I don't really know exactly what's going on they don't have a crystal structure yet but it's very exciting again very high pressure no applications. [00:52:46] I'll mention in one minutes that superconductivity shown up in some other places recently boosted by layer graphene is a. A beautiful system which has received a great deal of attention recently you take a layer of graphene you twist it with respect to another layer underneath it by about a degree and there is a magic angle where the. [00:53:12] Band structure is such that you get some very flat bands it is believed that those flat bands lead to very strong effective strong electronic correlations because of. The fact that the bands are are very narrow and therefore even the Coolum interactions on carbon are sufficient to create physics that are not it may not be terribly different from in the Cooper rates this was understood initially and terms of the overlap of these direct cones in graphene by bind Brit's career and McDonald and what else that I want to say about this the wonderful thing about the system is that you can gate it and you can make a face diagram which looks remarkably like the cooperage this is as a function of density that you put on the system with the gates you have regions of super common Timothy not very high temperature but nevertheless compared to the grapheme fairly It's an energy quite high in that sense and then there's a parent mod insulator phase which is very similar to the Cooper 8 empty for a minute it might insulator face which I didn't really talk about though that's really exciting. [00:54:30] There are. Other articles that appear occasionally in literature about room temperature superconductivity and other systems I want to alert you to them we call them us those or an identified superconducting objects. They come up from time to time and they never get verified but nevertheless there are intriguing one of them is. [00:54:59] These aluminum carbon sandwiches. Graphite powder mixed with water Peter fennel that's only a couple of years ago and all have various suggestions of superconductivity but you can never pin down the basic signatures of superconductivity 0 resistance the Meisner effect. And and so on. And the last one is this of silver nanoparticles in the gold matrix where they reported. [00:55:29] 2 years ago and I haven't heard much about that since Ok. Let me finish up my conclusions I showed you that there are actually 2 paradigms for super chronic Timothy one is the one that's been around since 1957 the conventional superconductors electron photon interaction is responsible it's retarded in time and then there's the so-called unconventional superconductors where it's believed that they exchange tronic acceptation. [00:55:58] And they typically exist in high higher anger Manton pairs. It is an open question but generally believed by many of us that a lot of these families of superconductors have a common mechanism these unconventional ones and that sometimes referred to as the common thread a term coined by Doug scallop you know I've shown you about superconductivity and twisted by later graphene showing you about superconductivity and hydrogen sulfide in various hydrogen compounds it appears that from the theoretical point of view. [00:56:34] That there is no limit on an electron phone on t.c. the park on a kitty elsewhere used to believe before that's one of the main points here even though it requires very high pressure and finally I've tried to convince you that super kind of stupidity is strongly driven by experiment and therefore is the fuel bit constantly renews itself. [00:56:56] Thank you. Ok so if people like us some questions to be great if we can hang around the few more minutes right look at Fully I have that adrenaline rush. So all I can ask your question. So is there a. Minute right is there a process to picking the kind of compounds you put into the superconductors before you test them or people just I'm just guessing and checking out looking for the properties that is a great question historically virtually every superconductor has been discovered accidentally or by empirical rules of thumb. [00:57:54] Or by intuition or whatever you want to call it. The hydrogen sulfide that I showed you before it was actually predicted. And so while I don't think there is any quantitative theory in the sense that you can predict the seed within 10 percent of every material. It is a well defined well controlled theory and so module Some technical. [00:58:23] Difficulties about which physical ingredients you include in the in the equations you can get a pretty decent prediction Now one question is and that's something I'm actually working on at the moment is how do you take this vast space of materials. And tried to give the experimentalists some guidance as a theorist where to look and we are working on ways of using machine learning to find out which properties of a material are favorable for electron phone superconductivity. [00:59:05] And it's a little Quixotic at the moment but it's really fun to work on we haven't made any great breakthroughs but we're working on it there's that answer question kiter Yep great answer thank you Ok. Ira But what do you believe we're going to see applications in our everyday life. [00:59:33] Well there are applications already I mean a lot of you are m.r.i. machines. Are are now working on superconducting magnets. There are. Superconducting magnets at Cern at the Large Hadron Collider there are. Some superconducting wind machines in operation. What we don't have yet are long distance power lines because right now the materials need to be refrigerated and that's technology that is just not economical there are test lines on the order of a few kilometers. [01:00:19] That work on the. Second generation who prate i.t.c. wire. But nobody is using it in a large scale way at the moment so I don't have a prediction you know I'm I'm not in a play applications person I'm a theorist. I would love it if we had some applications tomorrow but I just don't know if that is the real answer your question. [01:00:49] I mean I should mention that we all emphasize i.t.c. and it is kind of the Holy Grail of the field but for a lot of applications heights you see is not good enough you need to have a material which is. This is fairly 3 dimensional. In order to avoid having strong to protect and fluctuations which will cause you problems if you try to run a magnet on a 2 dimensional material and then you have fluctuations which quench your magnet in the middle of its operation though that's the kind of question practical questions are limiting applications at the moment as well though one should search in material space for not only heights you see but also 3 dimensionality and other figures of merit which are good for applications as of a lot of work to be done there but IP our comps are very. [01:01:50] Hi Peter on a car here I know that let me ask you. About so for these very high pressure superconductors has there been any effort to sort of come up with a compound. Early strange so or. In charcoal 8 in some ways didn't that it existed ambient pressure even if it was as well as or anything like that I think that that's a question that a lot of people are asking I have not heard about any any. [01:02:26] Idea that really implements your your notion right you want to come up with this centrally chemical pressure some structure where. The pressure at which all this magic happens gets lowered substantially I mean we would be very happy if we had 200 Kelvin transition temperature. I don't know 20 Giga Pascals that would still not be great for applications but it would tell us that there's a principle where you can actually. [01:02:58] Do the Right. Electronics structure in a. Weaker pressure environment and then I think we'd all be very encouraged to look for something similar at ambient pressure so far I don't know of any great steps in that direction thanks now. I have a question though you said that you were using machine learning approaches to the 2 sold abroad and superconductive would be my question is are you using machine learning as in the we'd like to look for patterns. [01:03:39] Be existing get out experimental results or are you doing a period because of pollution using what he learned that that's a really good question to the answer is we're doing both but what's been most interesting so far is. Erratic old can I share my screen again Carlos yakkers Ok let me see if I can go back here Ok so yeah let me let me show you this thing. [01:04:10] We tried to learn a formula for t c analogous to that invented in the seventy's by Phil Allen and Bob Diamond's So there's the formula right there. What you what you should have. Bore the so-called theory of superconductivity is this function which is called the l.-e. aspart function which is the electron flow in coupling constant squared times the density of phone States this is a picture for real materials that's the input to the alley Ashford theory but it's complicated and hard to calculate but if you knew various moments of that distribution for example the dimensionless coupling constant lambda or the Coolum pseudo potential music star you could come up with a formula which describes the predicted g c. [01:05:09] Sorry the t.c. from experiment relatively well and that's what Alan Dines did now there is a a method developed I can't remember where it was developed but it's called Cisco and it has this acronym sure independent screening and sparse the flying operator maybe a Cornell and it is a way of the sheen learning analytical equations. [01:05:35] So this was just perfectly suited for our problem because. Not only were we looking for formula but also we had a very pitifully small data base easily do material space machine learning on on databases with tens or hundreds of thousands of materials let's say tens tens of thousands and we had we had 29 material from the Allen and Don's paper and yet we could with the machine learning equation which fit the data better then the Allen and. [01:06:09] Equation with fewer parameters and so we are pursuing that method a little bit to try to figure out what types of let's go back to this function what types of Alpha squared f. it's called this alley aspart function how do you maximize t c imagining that you could play with these peaks and their positions and their weights. [01:06:32] And having the machine learn that kind of thing so I don't have time to talk about that but that is something that we're we're thinking about at the moment. That's about that's a lot of money because I didn't think much about electron phone superconductivity because I thought it was passe my entire career and now and I turned out I was very much alone. [01:06:55] But Peter the only back yard here and I very. Probably the last weekend at that angle gave up the beautiful call aku I'm here to tell you all. The land if. I go over there could be a vault talk of the hype epic that couldn't bear to be thought of ever mentioning that name I'm just curious if you have any relation to the subject. [01:07:22] He absolutely did. He was one of the high priests of high temperature superconductivity if you like. And I use that religious analogy advisedly because he referred always to his dog and as for high temperature superconductivity know if a fill. Was of course active in virtually every area of superconductivity he's the one who proved that the theory was Cajun variant back in the late fifties and then when she came along and then the superfluid helium 3 was very very important and then. [01:08:03] You see he was the one who wrote the 1st paper pointing out that the materials the copper oxygen planes that were common to the coop rates could be described by a Harvard model and that was definitely the source of inspiration for many of us including myself. Learning how to solve the 2 dimensional Hubbard model and its variants became. [01:08:35] Not the only Holy Grail but one of the subgraph and its people are still working on that I just talked to 2 blend this afternoon and we're talking about the Hubbard model again so that all comes from Phil. Phil's ideas were always interesting in my opinion they were not always right and sometimes he insisted on them so vociferously that I think he didn't always do the field a. [01:09:06] A favor but that's my private opinion and this but as far as I want to cooperate. It's not being courted here. I'm sorry. The fact. We're going to have architect I don't see anything like. My 3rd person talk yeah I actually heard that expression it. Hasn't done Yes Ok. [01:09:35] Ok let me run you know else you have questions or we shall we go to they Ok so it's not sort of like think Peter for the very nice thought coming I I think people west lots of question is in Probably there are a lot of other questions at least I have lots of other questions too. [01:09:56] But we have another time later can chat about this I would like to thank you very much for being. So thank you again.