1 00:00:10,630 --> 00:00:15,460 Okay. Thanks very much, Steve. Thank you all for coming. Well, I've had a wonderful week. 2 00:00:16,300 --> 00:00:22,580 Too much hospitality, but everything else was perfect. Okay. 3 00:00:22,700 --> 00:00:28,520 Now. All right. So I'm not sure which one of these things to look at. 4 00:00:28,530 --> 00:00:35,260 Let me look at this one. I want to talk about kind of two things. 5 00:00:35,280 --> 00:00:40,980 One thing is techniques and approaches for visualising electronic quantum matter. 6 00:00:41,730 --> 00:00:46,260 Whichever kind of quantum matter you like, that's that's one side of the coin. 7 00:00:46,290 --> 00:00:55,920 The other side of the coin is my own specific interest has been in working on the problem of high temperature superconductivity. 8 00:00:56,580 --> 00:00:57,389 So in fact, 9 00:00:57,390 --> 00:01:05,150 many of the examples that I'll show you of how we develop and use these different techniques are focussed on solving the problem of high tech. 10 00:01:05,730 --> 00:01:13,350 So those are two different sides of the coin. If you couldn't care less about high temperature superconductivity, of course that's hard to imagine. 11 00:01:13,350 --> 00:01:15,540 But if it were possible, 12 00:01:15,990 --> 00:01:23,219 then just concentrate on thinking about how you could address some problem of interest to you by using these these techniques. 13 00:01:23,220 --> 00:01:27,420 Many of them are still quite new. They haven't spread out into the world yet. 14 00:01:27,990 --> 00:01:28,260 However, 15 00:01:28,260 --> 00:01:36,450 I can tell by looking at your beautiful new building under construction across the way that these techniques will be in use in Oxford quite soon. 16 00:01:36,540 --> 00:01:40,620 So this is a wonderful opportunity for me to introduce them to you. 17 00:01:41,670 --> 00:01:45,330 Okay. Here's my present affiliation. Cornell University. 18 00:01:45,870 --> 00:01:52,510 For the students, post-docs in the audience. If you're interested in a stint in the U.S., please consider Cornell. 19 00:01:52,530 --> 00:01:56,669 It's a wonderful university. It's about 250 miles from New York. 20 00:01:56,670 --> 00:02:02,670 So you have to like living in the country, but probably anybody who can survive Oxford can survive Ithaca. 21 00:02:03,270 --> 00:02:14,399 And and we have we have very large physics operation for departments, about 150 active faculty, about 500 graduate students and postdocs. 22 00:02:14,400 --> 00:02:17,610 So it's really a wonderful and very active place. Okay. 23 00:02:18,300 --> 00:02:21,420 All right. So let's define our terms a little bit. 24 00:02:21,420 --> 00:02:29,990 So conventional electronic matter is the stuff that we are all familiar with and have been familiar with in some cases for millennia, 25 00:02:30,010 --> 00:02:38,910 in some cases only for 100 years. And it's the basis of our technology set at present and also of our so-called civilisation. 26 00:02:40,620 --> 00:02:44,330 And we understand it rather well. Conductors. 27 00:02:45,680 --> 00:02:49,630 That's Shawshank Farrow, Shawshank Signet Ring. 28 00:02:49,640 --> 00:02:52,940 It was found outside Jerusalem. So that's a pretty old piece of metal. 29 00:02:52,940 --> 00:03:01,700 So conductors, insulators, magnets, semiconductors, we've known about those for about 140 years, many. 30 00:03:04,830 --> 00:03:10,739 Active electric materials are a key part of our technology set and I regard conventional 31 00:03:10,740 --> 00:03:16,320 superconductivity 100 year old superconductivity in the same light as these well understood questions. 32 00:03:16,890 --> 00:03:21,930 So how do they work? Well, we all know how they work. You have elementary particles, they're called electrons, 33 00:03:22,500 --> 00:03:29,040 and they have a momentum which is related to their wave vector or one over their wavelength via the de broglie relation. 34 00:03:29,580 --> 00:03:36,510 And we're dealing with non relativistic particles usually. So energy goes as a wave vector squared, p squared. 35 00:03:37,200 --> 00:03:43,350 So that's the dispersion relation. If you put these objects in a crystal which has a periodic boundary, 36 00:03:44,370 --> 00:03:53,099 so that defines a new wave vector pi over the distance between the atoms in the crystal and the interaction between these electrons and the nuclei. 37 00:03:53,100 --> 00:04:01,200 And the crystal opens the famous band gaps. Then, depending on how many free electrons you put per unit cells, 38 00:04:01,200 --> 00:04:07,770 you fill up these states because electrons are fermions, as you know, and you fill them up to the Fermi energy. 39 00:04:07,860 --> 00:04:14,720 That's the energy separating the empty from the filled states. And also you fill them up from zero with vector out to the Fermi wave. 40 00:04:15,830 --> 00:04:18,490 In real space. You have to think a little bit. 41 00:04:18,500 --> 00:04:24,890 You have to think in both spaces now because this thing is a very tiny web vector, but it's an enormous wave length. 42 00:04:25,280 --> 00:04:29,870 Okay. And this thing is a large wave vector, but it's a very tiny wavelength. 43 00:04:29,870 --> 00:04:40,430 And you have to consider both things. Okay. So now, you know, it's based on our control of this set of ideas and the material science which uses it, 44 00:04:40,850 --> 00:04:46,979 that we know that a very large fraction of our economy and society is based on. 45 00:04:46,980 --> 00:04:55,940 Now we can for many types of materials, we can find out whether the elements will go together stably to make the materials. 46 00:04:56,240 --> 00:05:03,050 We can predict using band structure or quantum mechanics what the bands will be in the material and where the gaps are. 47 00:05:03,380 --> 00:05:11,320 And then by chemical or electrostatic doping, we can alter the number of carriers and then we can get those things and make active devices. 48 00:05:11,330 --> 00:05:18,290 Transistor being the most famous. So this is based on using Schrodinger equation and independent electrons. 49 00:05:20,000 --> 00:05:25,760 It's often said that we're going to reach some limits of that technology base quite soon. 50 00:05:26,630 --> 00:05:32,120 And, you know, as a matter of fact, when it comes to shrinking devices, that statement is trivially obvious. 51 00:05:32,420 --> 00:05:35,540 And in fact, the truth is, we already reached it quite a while ago. 52 00:05:37,280 --> 00:05:44,840 The device frequency stopped changing. Device performance stopped changing all around or four or five. 53 00:05:45,650 --> 00:05:52,340 Your new computers now are not based on devices which are somewhat which are smaller than they were ten or 12 years ago. 54 00:05:52,820 --> 00:05:55,910 What they're based on is having more and more cores. 55 00:05:55,940 --> 00:06:01,250 That's more and more chips are CPU's onboard each computer. 56 00:06:01,490 --> 00:06:06,860 The next generation of computer that you buy now will have like 18 core sorry, 16 cores it. 57 00:06:07,700 --> 00:06:13,000 So the device size barrier has already been reached or we're very, very close to it. 58 00:06:13,010 --> 00:06:18,410 There's no point in pretending that it isn't there. All that's happening now is we're just putting more chips in each box. 59 00:06:19,730 --> 00:06:24,650 We need new we need some way to get out of this trap. And one of the things we need are new materials. 60 00:06:24,660 --> 00:06:28,130 We also need new ideas like quantum computing. But I'm not going to address that. 61 00:06:28,490 --> 00:06:35,330 But we do need new materials. So what other possible states of electronic matter could exist? 62 00:06:37,000 --> 00:06:46,390 Usually when you read a classic textbook on solid state physics, let's say Steve's textbook or Ashcroft or Merman or something like that. 63 00:06:47,230 --> 00:06:52,120 You're you're taught about these states and it's implied that there are no other states. 64 00:06:52,120 --> 00:06:58,150 What other states could there be? But of course, there is no barrier against having other exotic kinds of electronic matter. 65 00:06:58,450 --> 00:07:04,980 There could be all kinds. And how can that happen? Well, many different ways, but one way is correlations. 66 00:07:04,990 --> 00:07:10,470 So I wanted to talk about correlations. Since you live here in the south of England, you know what this is? 67 00:07:10,480 --> 00:07:17,620 It's a traffic jam. And the reason why eventually the traffic comes to a halt if there's no accident, 68 00:07:17,770 --> 00:07:23,620 is the correlations that are being enforced by the drivers and the position of each vehicle. 69 00:07:24,460 --> 00:07:30,160 So, you know, your insurance company certainly wants digital or no double occupancy and your. 70 00:07:30,880 --> 00:07:39,160 And for your own safety, so do you. So. So so you have a two dimensional plane with identical particles in it, but no double occupancy. 71 00:07:39,160 --> 00:07:41,320 And that produces a traffic jam, as you know. 72 00:07:42,010 --> 00:07:49,090 And in fact, if you put a small number of vacancies into a traffic jam, as you all know as well, it can suddenly free up. 73 00:07:50,300 --> 00:07:50,610 Okay. 74 00:07:50,750 --> 00:07:59,360 So the number of vacancies you have to put into a traffic jam to suddenly get it to move is actually a very tiny fraction of the particle density. 75 00:07:59,870 --> 00:08:04,280 And the other thing, you know, is it's virtually impossible to predict and control these things. 76 00:08:04,550 --> 00:08:07,490 And this is a piece of classic classical physics. 77 00:08:07,940 --> 00:08:16,400 Just well-defined square boxes on a two dimensional play, but very difficult to understand and control because of the correlations. 78 00:08:17,300 --> 00:08:19,200 Now, in quantum mechanics, you face the same thing. 79 00:08:19,220 --> 00:08:27,110 So, for example, in several high tech superconductors, you can have a material, let's say, which has one active electron that's a vehicle per site. 80 00:08:27,950 --> 00:08:34,850 And if there's no double occupancy, they get frozen in position in the Mott, the famous Mott insulating state. 81 00:08:36,530 --> 00:08:42,530 So that's a complete quantum mechanical traffic jam. And we do understand the quantum mechanics of this object reasonably well. 82 00:08:44,110 --> 00:08:47,710 So electron no double occupancy produces this traffic jam. 83 00:08:48,040 --> 00:08:51,820 But if you put a small number of vacancies into this system, 84 00:08:52,810 --> 00:09:00,760 suddenly the electronic fluid starts to flow in many materials in a way which has proven extremely difficult to understand. 85 00:09:00,760 --> 00:09:04,990 Actually, decades of work have gone into understanding this situation. 86 00:09:05,440 --> 00:09:10,450 And of course, the reason is that you're trying to solve a correlated quantum mechanical problem. 87 00:09:11,170 --> 00:09:16,749 The state of every electron depends on the state of every other electron and their interactions and the 88 00:09:16,750 --> 00:09:23,799 solution of all those simultaneous Schrödinger equations the diagonal ization of an enormous Hilbert space. 89 00:09:23,800 --> 00:09:27,640 Even for this tiny little patch of material, that's an unsolved problem. 90 00:09:28,720 --> 00:09:34,570 One thing we do know about this situation, though, is that when you make materials that have these properties, 91 00:09:34,570 --> 00:09:38,410 you get astonishing surprises about what can happen. 92 00:09:39,190 --> 00:09:47,620 So you have some very complex interplay locally between charge and spin and also orbital and indeed sometimes the lattice. 93 00:09:48,040 --> 00:09:55,690 And from this situation emerges high temperature superconductivity and colossal magneto resistance and thermal electricity. 94 00:09:55,990 --> 00:10:01,030 Multi ferro x very strange superconductors, very strange electronic states, 95 00:10:01,390 --> 00:10:08,680 new order states that I'm going to talk about and new ways to address the fundamentals of quantum mechanics. 96 00:10:09,550 --> 00:10:18,670 These this set of ideas, this motivation has tremendous potential in many fields of solid state physics and materials science. 97 00:10:18,940 --> 00:10:27,940 But the truth is, it's still poorly understood. And one of the reasons why it's poorly understood is that that experimental technology set, 98 00:10:28,240 --> 00:10:34,060 which had been used to understand metals and semiconductors up into the 1970s and 1980s, 99 00:10:34,480 --> 00:10:37,870 is completely mismatched to the question being addressed here. 100 00:10:38,200 --> 00:10:46,180 And what has happened over the last ten, 15, 20 years is the invention of many new tools, which are what's necessary to solve this problem. 101 00:10:47,660 --> 00:10:52,700 The other thing impression you get from a Ashcroft Merryman style book is that, 102 00:10:52,700 --> 00:10:57,379 you know, virtually the materials we can work with are already established. 103 00:10:57,380 --> 00:11:07,760 And that fact is also around. There's an enormous number of materials that can be made either thermodynamically or nowadays by 104 00:11:07,970 --> 00:11:14,360 molecular beam epitaxy artificial materials which can't exist thermodynamically but can still be made. 105 00:11:15,020 --> 00:11:22,670 And they obviously there's untold possibilities for new materials with exotic new electronic properties. 106 00:11:22,970 --> 00:11:28,280 What we'd really like to have is a predictive theory of correlated electronic material. 107 00:11:28,280 --> 00:11:32,930 Then we could probably design and build many new types of materials and devices. 108 00:11:33,470 --> 00:11:36,950 Okay, now here's the specific example I want to tell you about. 109 00:11:37,490 --> 00:11:42,830 Of new electronic states of matter. These are called electronic liquid crystals. 110 00:11:43,460 --> 00:11:47,000 So you all know, I think what this is, it's a vapour, it's called steam. 111 00:11:47,120 --> 00:11:52,610 And it's made of H2O molecules and it's translational the rotational invariant. 112 00:11:52,620 --> 00:11:55,580 It's isotropic. It has no stranger our internal properties. 113 00:11:55,970 --> 00:12:01,280 If you increase the interactions between the molecules, you get this very mysterious state. 114 00:12:01,790 --> 00:12:07,310 Some of you are familiar with this. It's called water, and it's one of the most difficult to understand states. 115 00:12:07,320 --> 00:12:12,000 It's really a difficult problem to understand water because the interactions are strong. 116 00:12:12,650 --> 00:12:16,730 If you increase the interactions a little bit more and if you live in Ithaca, you get ice. 117 00:12:17,720 --> 00:12:23,570 But that's not the state that I want to talk about, because there's an intermediate state, which is the liquid crystal state. 118 00:12:24,020 --> 00:12:30,800 It's a state which simultaneously is a fluid but brings some special breaks, some of the available symmetries. 119 00:12:31,670 --> 00:12:37,430 So we understand this very well. Of course, it's now the basis of our it's it's how this projector works. 120 00:12:37,790 --> 00:12:41,600 It's how you get your information everyday on your laptop and on your telephone. 121 00:12:42,380 --> 00:12:50,959 Our ability to understand these phases and to control them has indeed revolutionised information technology in a most spectacular way. 122 00:12:50,960 --> 00:12:56,570 And also, it's very good for business. Okay, now there's two types of liquid crystals. 123 00:12:56,720 --> 00:13:03,650 So one is and the magic and the magic liquid crystal is where all the molecules are aligned in the same direction, 124 00:13:03,950 --> 00:13:07,430 but they don't make any pattern in space. They don't break any symmetry. 125 00:13:08,660 --> 00:13:15,530 A liquid crystal is a one where all the molecules are aligned in space and then they get patterned in space as well. 126 00:13:15,860 --> 00:13:19,070 Their periodic density is changing along this direction. 127 00:13:19,400 --> 00:13:25,340 So we say this smectite liquid crystal has a way vector to pi over the wavelength 128 00:13:25,730 --> 00:13:30,350 and pointing in this direction it breaks both rotational and translational symmetry. 129 00:13:31,610 --> 00:13:40,610 It was Piers Illusion who figured this out from the physics point of view in the early 1970s and for which he received the Nobel Prize subsequently. 130 00:13:41,270 --> 00:13:48,079 And one of the key thing I mean, of course, the key thing he used to solve the liquid crystal problem is genius. 131 00:13:48,080 --> 00:13:56,840 Okay. But the other thing he used is that in the early 1970s, visualisation of in phase contrast microscopy became possible. 132 00:13:57,200 --> 00:14:05,179 And you could look at the liquid crystals and see what kinds of topological defects were occurring and what happened when phase transitions occurred, 133 00:14:05,180 --> 00:14:12,050 etc. So actually the visualisation was a key part of the understanding of how the liquid crystals work. 134 00:14:12,650 --> 00:14:15,920 Okay, so this is the classic liquid crystal. 135 00:14:17,240 --> 00:14:21,350 Now in this state. This is a piece of copper wire. No doubt you're all familiar with it. 136 00:14:21,350 --> 00:14:27,499 And inside it, there is a more or less isotropic fluid with weak interactions between the particles. 137 00:14:27,500 --> 00:14:34,670 It's a fluid of electrons. If you increase the interactions between the electrons, you can get a heavy electron fluid, 138 00:14:34,670 --> 00:14:40,249 which is a very exotic state of electronic matter that I don't have time to talk about today. 139 00:14:40,250 --> 00:14:46,790 But it's where the electrons have really become strong and intimately interacting with each other. 140 00:14:47,210 --> 00:14:53,120 And if you increase the interactions a little bit more, probably you would think we should get an insulator or a mat insulator. 141 00:14:53,930 --> 00:15:00,500 But there's another possibility and you know what it is from analogy, it's that there are electronic liquid crystals. 142 00:15:01,400 --> 00:15:10,490 So this idea was put forward by Vicki Emery, Eduardo Fradkin and Steve Gibson in the late 1990s. 143 00:15:10,490 --> 00:15:15,649 And it was at this point that I got interested in this subject. I had been working well, of course, 144 00:15:15,650 --> 00:15:22,340 I had been working on quantum mechanical liquid crystals because Superfluid Helium three is a very elegant quantum crystal. 145 00:15:23,180 --> 00:15:28,880 But I suddenly realised there could be electronic versions of this exotic situation. 146 00:15:29,660 --> 00:15:34,460 Now you see these cartoons here. Those are the actual figures in the nature paper. 147 00:15:34,550 --> 00:15:38,660 It isn't larded with exotic mathematical theoretical statements. 148 00:15:38,930 --> 00:15:46,430 This is the prediction that if you put electrons strongly interacting with each other into a correlated insulator, 149 00:15:47,360 --> 00:15:49,819 they will first break rotational symmetry, 150 00:15:49,820 --> 00:15:56,330 making a pneumatic phase, and secondly, they will break rotational and translational symmetry, making a symmetric phase. 151 00:15:56,780 --> 00:16:01,339 That's the basic, you know, it's just well, I shouldn't say just intuition. 152 00:16:01,340 --> 00:16:05,030 These colleagues have won a number of major prizes for making this proposal. 153 00:16:05,420 --> 00:16:07,010 But but that's the basic idea. 154 00:16:07,610 --> 00:16:14,540 If there can be strong interactions of particles making classical liquid crystals, why not quantum mechanics of liquid crystals? 155 00:16:15,200 --> 00:16:20,180 Okay, now, kibbutzim. At that time I had I was visiting him in UCLA. 156 00:16:20,450 --> 00:16:27,919 I was at a helium three meeting, but I, I took the opportunity to talk to Steve Wilson just when he had published this. 157 00:16:27,920 --> 00:16:32,059 And he really he kind of he radicalised me, as they say now. 158 00:16:32,060 --> 00:16:36,020 He just captured my attention to this problem and we started working on it. 159 00:16:36,440 --> 00:16:42,020 Okay. So how do you visualise electronic matter? You take a scanning tunnelling microscope. 160 00:16:42,050 --> 00:16:44,780 These are very common devices now. They work beautifully. 161 00:16:45,260 --> 00:16:51,319 They have a sharp metal tip with one atom on the end, you scan over the surface, let's say about one angstrom. 162 00:16:51,320 --> 00:16:56,299 From the surface, you apply a voltage between the conducting surface and the conducting tip. 163 00:16:56,300 --> 00:17:01,220 And you and then you measure the current, the tunnel current, which goes through this tunnel junction. 164 00:17:01,910 --> 00:17:10,010 Then by feeding back on that current to keep it constant, you can make an image of the feedback signal and that's called an image of the atoms. 165 00:17:10,580 --> 00:17:14,660 Each dot here is a selenium atom in this complex. This is niobium diselenide. 166 00:17:16,040 --> 00:17:20,210 Now. This is cool. It's very lovely. You can win the Nobel Prize for inventing this machine. 167 00:17:20,630 --> 00:17:24,410 But this machine does not tell you where the electronic wave functions are. 168 00:17:24,890 --> 00:17:33,170 It just tells you where the atoms are. Okay. And in fact, in this compound, this compound, this come this compound. 169 00:17:33,790 --> 00:17:39,049 There there is there's a pneumatic, electronic phase in this one. 170 00:17:39,050 --> 00:17:43,880 And that one there is this metallic electronic face. In this one, there's believed to be a pneumatic, electronic phase. 171 00:17:44,300 --> 00:17:51,230 Conventional ASTM will not allow you to see that, because the thing which breaks the symmetries is not the atoms. 172 00:17:51,590 --> 00:17:57,490 It's the wave functions of the electrons. So the way to visualise the way it functions is the following. 173 00:17:58,630 --> 00:18:02,980 And this is a generalisation of tunnelling spectroscopy introduced by Javor 174 00:18:03,010 --> 00:18:06,580 to for the study of superconductivity and for which he got the Nobel Prize. 175 00:18:06,820 --> 00:18:12,700 In the early 1970s. But now you use SDM tip, so you park your tip at this location. 176 00:18:14,270 --> 00:18:19,999 And now turn off the feedback system so it's passively stable at this location and now change this bias voltage 177 00:18:20,000 --> 00:18:25,100 that's this voltage here and measure the total current as a function of voltage and take the derivative. 178 00:18:25,520 --> 00:18:29,780 That's the differential conductance as a function of voltage of this junction. 179 00:18:30,290 --> 00:18:39,980 Now we know from theory that that function is proportional to the sum overall of the wave functions at that energy at this location. 180 00:18:40,550 --> 00:18:45,980 So you're measuring something proportional to upside squared of the electronic wave functions at this location. 181 00:18:47,510 --> 00:18:51,830 So now here's how you do it. You build one of these machines, put your system, tip over here, 182 00:18:52,340 --> 00:18:59,380 measure the differential conductance spectrum at the first atom, at the second atom, at the third, at etc., etc., etc., etc. 183 00:19:00,220 --> 00:19:04,600 The end of that process, you have a map of the differential conductance. 184 00:19:04,600 --> 00:19:09,820 So if conductance is high, I use a light colour and if the conductance is very low, I use a dark colour. 185 00:19:10,180 --> 00:19:13,810 And this tells me that this image is in this field of view. 186 00:19:13,960 --> 00:19:20,140 The wave functions at that energy. But you have you have a map at all the energies where you measure it. 187 00:19:21,760 --> 00:19:31,000 You can zoom through the energies of the electronic eigen states, and at each energy you visualise the spatial arrangement of the wave functions. 188 00:19:31,600 --> 00:19:33,430 That's the great power of this technique. 189 00:19:34,520 --> 00:19:40,759 And you can all see just by looking at this movie that a tremendous amount of information is contained in each one. 190 00:19:40,760 --> 00:19:44,960 And that's true. It took us many years to discover how to extract the information. 191 00:19:45,410 --> 00:19:52,460 And another thing, which is that many real correlated materials are very, very complicated in terms of their way functions. 192 00:19:52,910 --> 00:19:59,720 So what you get is atomic resolution, energy resolved image of the electronic wave functions in the material of interest. 193 00:20:00,700 --> 00:20:05,780 And this is hard to do. This was very hard to figure out how to do. 194 00:20:06,570 --> 00:20:13,680 And here's the reason. So if you take five, 12 by five, 12 pixels and 200 data points, so that's 250,000. 195 00:20:13,680 --> 00:20:17,969 So that's 50 million measurements to make this movie 50 million. 196 00:20:17,970 --> 00:20:21,120 And there are serial measurements. We have to do them one after the other. 197 00:20:21,120 --> 00:20:26,610 So 50 million serial measurements in 24 hours gives you about 2 milliseconds per measurement. 198 00:20:27,120 --> 00:20:31,290 So you have to get a high signal to noise measurement of the current in a millisecond. 199 00:20:31,440 --> 00:20:32,730 That's basically where we're at. 200 00:20:33,330 --> 00:20:41,520 And that was really hard to figure out because when you look at the equations, it requires you to move the STM to the right location, 201 00:20:41,790 --> 00:20:48,150 turn off the feedback, and then have the tip vibrate no more than a few centimetres. 202 00:20:48,330 --> 00:20:48,720 Okay. 203 00:20:49,350 --> 00:20:56,730 So the constraint is not to improve the spatial resolution, it's because the current noise is a function of where the tip is relative to the surface. 204 00:20:57,240 --> 00:21:00,570 So to suppress the current noise and do the experiment quickly, 205 00:21:00,690 --> 00:21:06,360 you have to clamp the tip in the right location with our mass motion of only a few centimetres. 206 00:21:06,810 --> 00:21:12,930 And that was that's hard to do. So we introduced a way to do that, which is the so-called ultra low vibration lab. 207 00:21:14,010 --> 00:21:19,800 You take an underground concrete vault, you put acoustic isolation inside the external vault, 208 00:21:20,280 --> 00:21:25,380 and then inside you put your experimental chamber on a separate, massive slab. 209 00:21:25,410 --> 00:21:30,030 First ones were around 30 tons. Second generation, my lab is about 100 tons. 210 00:21:30,300 --> 00:21:34,560 It looks to me like some of the new ones in your building will be in the 100 ton range as well. 211 00:21:35,310 --> 00:21:38,459 And then on this lab, you put an inner acoustic chamber, 212 00:21:38,460 --> 00:21:44,790 and inside there you put an ultra low vibration refrigerator so that you're cooled down to a fraction of a kelvin. 213 00:21:45,210 --> 00:21:49,110 So here so the arms motions on the floor here are in the micron range. 214 00:21:49,860 --> 00:21:54,150 So in your lab, in your basement lab down here, they'll be in the few nanometre range. 215 00:21:54,600 --> 00:22:00,450 When these isolators are working, the motion of this whole room will be in the few angstrom arm's range. 216 00:22:01,020 --> 00:22:08,040 This isolator of the motion up here is a few peak metres and down inside the crash that we get rid of as well. 217 00:22:08,130 --> 00:22:11,880 The motion goes down to a few centimetres if you don't make any mistakes. 218 00:22:12,990 --> 00:22:18,350 Okay. Well, so. So that's cool, right? 219 00:22:18,930 --> 00:22:22,559 So. Okay, so now this seems like an obvious idea. 220 00:22:22,560 --> 00:22:26,160 And if you want to see one of these amazing things go over and take a tour of your 221 00:22:26,160 --> 00:22:29,280 new building as soon as they're available because they're really impressive. 222 00:22:30,030 --> 00:22:37,079 But when we first came up with this idea, you know, I went to see the dean at the institution where I was then working, 223 00:22:37,080 --> 00:22:41,909 and I said, look, this is a really good idea, right? We'd be able to visualise electronic metal. 224 00:22:41,910 --> 00:22:45,920 All we need is some of these labs. There is no precedent for it. 225 00:22:45,930 --> 00:22:52,350 So the dean just laughed and said, You know, it's too expensive and we just can't take the risk. 226 00:22:52,350 --> 00:22:59,250 You know, we're not going to invest in this. So it was at that stage I moved to Cornell because the Cornell audience were willing to take the risk. 227 00:22:59,790 --> 00:23:04,440 They demolished one of their underground stores of charcoal, their famous low temperature building, 228 00:23:04,980 --> 00:23:09,180 and into that demolished corridor, they dug down another story. 229 00:23:09,180 --> 00:23:14,400 So they ended up two floors high and the whole length of the building, more or less like the design of your building. 230 00:23:14,910 --> 00:23:25,979 And then into this space built for ultralow vibration labs, three of which are in use today for spectroscopic ASTM This one is online right now. 231 00:23:25,980 --> 00:23:30,600 This one is is just gone offline and this one is under repair. 232 00:23:30,600 --> 00:23:37,560 So one is working today, but typically they're all working and we have visitors working on these projects coming from all over the world. 233 00:23:38,530 --> 00:23:42,570 Okay. And of course, the design does work. 234 00:23:43,860 --> 00:23:44,790 That's the good part. 235 00:23:45,300 --> 00:23:51,930 So one of the powerful techniques you can bring to bear now with this facility is the following thing crossing particle interference, imaging. 236 00:23:52,440 --> 00:23:55,800 Every material has it has impurity atoms in it. 237 00:23:56,730 --> 00:24:01,709 An incoming electron is in a fluid of electrons and incoming electron with this wave 238 00:24:01,710 --> 00:24:05,550 vector will scatter from the impurity atom and make an outgoing wave function. 239 00:24:06,000 --> 00:24:13,440 If you add these two wave functions together to get the interference pattern and then square to get the probability density of the electrons, 240 00:24:14,070 --> 00:24:19,650 the q vector of this modulation, the wave length is half because you added and squared. 241 00:24:19,980 --> 00:24:23,880 So that means the Q is twice the Q of the original electronic state. 242 00:24:24,660 --> 00:24:30,620 So you can take the for your transform of that image. And measure the Q vector of all these oscillations. 243 00:24:30,890 --> 00:24:34,320 Super. This is reasonably easy to do, of course. 244 00:24:34,590 --> 00:24:42,950 It wasn't easy to think of, but it's easy to do. So now you know the Q vector is related to the vector by a factor of two. 245 00:24:42,960 --> 00:24:48,750 So you can just divide and that's plus minus K, it's plus K scattering to minus K. 246 00:24:49,080 --> 00:24:54,330 So you get two pieces of information about the energy, momentum relationship of the electrons here. 247 00:24:55,140 --> 00:25:01,500 But now if you have an energy resolved movie of this process, you can do that as a function of energy. 248 00:25:04,480 --> 00:25:12,430 This is called QPR. If you look up QPR on Google now, you'll find hundreds and hundreds of papers about it because it is a very powerful technique. 249 00:25:13,000 --> 00:25:16,120 You can image the empty states as well as the failed states. 250 00:25:16,630 --> 00:25:23,200 You can do this. And ultra low temperatures, we do it down to about 50 milli kelvin and you can do it in very high magnetic fields. 251 00:25:23,590 --> 00:25:27,400 The record is not in my lab. It's in Japan. It's about 18 Tesla. 252 00:25:27,700 --> 00:25:31,750 But we hope to recover the record again next year by going to about 20 Tesla. 253 00:25:32,350 --> 00:25:33,660 Very powerful technique. 254 00:25:33,670 --> 00:25:41,110 So with this technique, we were able to make the first visualisation of the electronic structure of many classes of materials. 255 00:25:41,800 --> 00:25:47,340 So this one I already showed you, it's the copper based high temperature superconductor. 256 00:25:47,390 --> 00:25:52,060 It's a bit of a mess, of course, but before you transform of that mess. 257 00:25:52,660 --> 00:26:03,470 Oh. Is. Very ordered because there's only a small number of island states which are undergoing this scattering interference. 258 00:26:03,890 --> 00:26:09,350 We can undo this Fourier transform movie to determine a very complicated band structure. 259 00:26:09,470 --> 00:26:18,290 Let's start again. So these are the cue vectors of the scattering interference related to all the momentum space states. 260 00:26:18,920 --> 00:26:23,300 So we were also able to reveal the equivalent thing for the arm superconductors. 261 00:26:25,780 --> 00:26:31,230 Horrible. It's interesting. I discovered that in real space, you know, wave functions don't look beautiful. 262 00:26:31,240 --> 00:26:34,479 I suppose Mother Nature is in charge of that. 263 00:26:34,480 --> 00:26:40,780 God is in charge of that. But in momentum space, in reciprocal space, they're beautifully ordered. 264 00:26:40,780 --> 00:26:47,560 You can see three bands and three energy gaps. We were able to unscramble the electronic structure of our own superconductors. 265 00:26:48,370 --> 00:26:54,010 These were the first heavy fermion wave function movies. They look like crap. 266 00:26:56,140 --> 00:27:02,560 But before your transform looks beautiful, it contains exactly what's predicted for heavy firmly on cue vectors. 267 00:27:04,270 --> 00:27:09,940 These were to diagnose the first measurement of the superconducting energy gap of a heavy Fermi on compound. 268 00:27:10,240 --> 00:27:16,780 Last year we were able to see the wave functions of our gapped topological insulator for the first time. 269 00:27:17,200 --> 00:27:21,420 They are cooled. You see that this is the direct service state. 270 00:27:21,600 --> 00:27:23,310 It's a six Ford symmetric cone. 271 00:27:23,550 --> 00:27:32,010 It's approaching not it's known, but the gap from below you enter the gap surface state is completely gapped, doesn't exist. 272 00:27:32,340 --> 00:27:37,770 Then you exit at the top edge of the gap and the direct surface state reappears and heads off the way. 273 00:27:37,770 --> 00:27:41,400 It's very beautiful. Okay. All right. 274 00:27:41,410 --> 00:27:44,910 Now I want to talk about superconductivity. Let's see. How are we doing for time? 275 00:27:46,360 --> 00:27:51,610 Good. Okay. Great. Superconductivity, my own. 276 00:27:52,920 --> 00:27:59,070 I suppose passion would be a polite word for it. Obsession might be more honest. 277 00:27:59,580 --> 00:28:08,040 So as you all know, you know, superconductivity is the appearance of perfectly dissipation, this electrical transport, 278 00:28:08,220 --> 00:28:14,040 and also would be perfectly dissipation, less electronics if you use the correct the correct devices. 279 00:28:14,880 --> 00:28:20,840 And it's a bit over 100 years old now. It occurs because in a metro these states here. 280 00:28:22,070 --> 00:28:28,970 A plus and minus. Q are susceptible to of forming a new quantum mechanical object, which is a bound pair. 281 00:28:29,690 --> 00:28:33,530 And that pair of plus minus K is called a Cooper pair. 282 00:28:34,940 --> 00:28:43,489 That those Cooper pairs condense into a new quantum mechanical state and they leave behind some single particle excitations, 283 00:28:43,490 --> 00:28:47,900 which are the signature of the existence of the Cooper pair of condensate. 284 00:28:47,990 --> 00:28:53,330 The superfluid of Cooper pairs. So that's our classic understanding of this problem. 285 00:28:54,890 --> 00:28:56,780 The Cooper pair of binding energy. 286 00:28:56,900 --> 00:29:05,240 In the simplest case you can think of this energy gap here at this is an energy scale where a gap opens in the spectrum at the chemical potential. 287 00:29:05,630 --> 00:29:13,160 It's the Cooper pair finding energy per particle. We also have the classic theory of how that works. 288 00:29:13,170 --> 00:29:18,110 If there's some interaction between the electrons and you solve the species gap equation, 289 00:29:18,120 --> 00:29:22,109 if it's solvable, then the gap structure contains the information. 290 00:29:22,110 --> 00:29:25,319 So this is the momentum space structure of this energy gap. 291 00:29:25,320 --> 00:29:31,110 It may be different in different directions, so it contains the information about the mechanism of the parent. 292 00:29:32,870 --> 00:29:38,290 So the critical temperature is the temperature below which the material will superconductor. 293 00:29:38,300 --> 00:29:43,790 And for classic superconductors, of course it's very low below 20 Kelvin, even up to the 1980s. 294 00:29:44,260 --> 00:29:50,180 You know, at this rate it would have taken until the year 3500 to get to room temperature superconductivity. 295 00:29:51,230 --> 00:29:54,380 But we need room temperature superconductivity part of my. 296 00:29:55,630 --> 00:30:07,300 Task when I wear my working for The Daily Hat is to think about, you know, what will be the implications of having room temperature superconductivity. 297 00:30:07,840 --> 00:30:14,850 We need very greatly increased efficiency and capacity and stability in our power network. 298 00:30:14,870 --> 00:30:20,950 Certainly in North America, we need that desperately. And, you know, a superconducting power network could do that. 299 00:30:22,110 --> 00:30:27,600 Here's a problem which is certainly occurring in the UK and it's known to be occurring in the US. 300 00:30:27,630 --> 00:30:32,070 It's that as people move back into the city centres and they are doing so, 301 00:30:32,880 --> 00:30:39,540 the energy density which is being required to be delivered to each major city is going up very rapidly and 302 00:30:39,540 --> 00:30:45,510 there are many big cities in the world where we won't be able to deliver enough energy by around 2050. 303 00:30:47,250 --> 00:30:52,920 One thing you could do, of course, is dig up every city and put in many more copper wires, but nobody wants that. 304 00:30:53,340 --> 00:30:58,710 So an alternative would be to pull out the copper wire network and put in a superconducting network. 305 00:30:59,040 --> 00:31:04,020 Then we could increase the capacity in basically every network by a factor of around 30. 306 00:31:04,680 --> 00:31:13,440 So this is the important thing. We need room temperature superconductivity to accommodate renewables, to make efficient harvesting of energy. 307 00:31:13,930 --> 00:31:17,490 You know, devices that don't waste a lot of the energy they harvest. 308 00:31:17,850 --> 00:31:24,390 We need it desperately for information technology. We're using a huge amount of energy now for our information technology. 309 00:31:24,660 --> 00:31:31,920 And most of it is going to heat or to air conditioning to get rid of the heat so that the CPUs keep working. 310 00:31:32,370 --> 00:31:37,500 But a room temperature, superconducting information technology wouldn't generate any heat like that. 311 00:31:37,680 --> 00:31:42,020 It would be largely non dissipative. We need it for high energy physics. 312 00:31:42,530 --> 00:31:46,250 We need it for high energy physics. We need it for medicine. We need it for transport. 313 00:31:47,610 --> 00:31:58,019 We have two candidate classes of materials, copper oxide and iron arsenide based compounds, and they have a number of characteristics in common. 314 00:31:58,020 --> 00:32:02,670 There are two dimensional, quasi two dimensional, and they are strongly antiferromagnetic. 315 00:32:02,790 --> 00:32:11,540 Those are the basic things. It's these two families which are discovered starting in the eighties and again in the 2000s whose critical 316 00:32:11,540 --> 00:32:17,810 temperatures are rising such that it's not implausible that we could reach room temperature superconductivity. 317 00:32:18,110 --> 00:32:21,140 In fact, there is one other family. There's the famous hydrogen. 318 00:32:24,440 --> 00:32:30,920 It's too easy compound, which doesn't superconductive at ambient pressure, but also its critical temperature is above this line. 319 00:32:31,790 --> 00:32:35,480 Well, it's perfectly plausible that we can reach room temperature superconductivity. 320 00:32:35,540 --> 00:32:38,180 But we need to understand how do these compounds work? 321 00:32:38,960 --> 00:32:45,260 So there are strong two dimensional antiferromagnetic there phase diagrams are somewhat the same when used. 322 00:32:45,740 --> 00:32:51,650 The parent state is an antiferromagnetic antiferromagnetic insulator or antiferromagnetic correlated metal. 323 00:32:51,980 --> 00:32:56,870 You introduce the holes antiferromagnetic and disappear as the superconductivity appears. 324 00:32:56,870 --> 00:32:59,930 And if our magnetism disappears, superconductivity appears. 325 00:33:00,800 --> 00:33:08,270 But in both of these classes of materials, an exotic phase has been more than one exotic phase has been discovered in this part of the phase. 326 00:33:08,270 --> 00:33:13,230 Diamond unexpected. And so here is a cartoon of the situation. 327 00:33:13,290 --> 00:33:19,920 We believe that if we could destroy the long range antiferromagnetic ism but keep the antiferromagnetic spin interactions, 328 00:33:20,250 --> 00:33:26,970 then we could reach the point of having very robust, cool preparing and high temperature superconductivity to go from here to there. 329 00:33:27,540 --> 00:33:35,610 But apparently in real materials, when you're going from here to there, you must pass through some other exotic correlated electronic phase. 330 00:33:36,180 --> 00:33:43,440 And one of the proposals for what this phase is is the famous Fradkin and Kim Wilson proposal that it's electronic liquid 331 00:33:43,440 --> 00:33:49,740 crystals that you have to pass through on your way from the correlated insulator to the high temperature superconductor. 332 00:33:50,860 --> 00:33:57,310 They imply in this paper that it's even unavoidable. I don't know if it's unavoidable, but the prediction is pretty clear that it should be there. 333 00:33:58,810 --> 00:34:02,950 All right. So we started to look for those states. 334 00:34:03,430 --> 00:34:10,870 So in the iron based superconductors with two primary questions what is the mechanism of the superconductivity and what is this exotic state? 335 00:34:11,230 --> 00:34:20,300 Is it an electronic liquid crystal? So in those compounds, two calcium ion, two arsenic, two dose with cobalt. 336 00:34:20,900 --> 00:34:23,730 The surface is very clean, stable and nice. 337 00:34:24,350 --> 00:34:30,410 We were able to visualise this was the first visualisation of the wave functions in the non superconducting states 338 00:34:31,520 --> 00:34:37,970 of an iron based materials and the wave functions we immediately saw are all dispersing in only one direction. 339 00:34:38,130 --> 00:34:45,800 Looks a little bit subtle there, but if I show you the Q space version, these are the wave vectors of the scattering, interference versus energy. 340 00:34:46,610 --> 00:34:48,620 They're all just dispersing in one direction. 341 00:34:49,670 --> 00:34:56,750 All the states, which you would imagine should be travelling in the other direction and scattering, interference and so on don't seem to be there. 342 00:34:58,070 --> 00:35:03,860 We were able to visualise the static breaking of rotational symmetry and luckily or in fact 343 00:35:03,860 --> 00:35:10,040 unavoidably we were able to find some twin boundaries because this crystal is our ceramic. 344 00:35:10,640 --> 00:35:18,200 And at those twin boundaries we could see that the static breaking of rotational symmetry and the dynamic making of rotational symmetry rotates. 345 00:35:19,100 --> 00:35:29,090 So actually in 2020 or nine, we first tried to report that the parent phase of the iron based superconductors is an electronic mimetic. 346 00:35:29,720 --> 00:35:34,910 The first paper was difficult to publish. It took until the middle of 2010 to convince the referees. 347 00:35:36,500 --> 00:35:41,030 But but luckily for us, this was the first observation of that state. 348 00:35:42,900 --> 00:35:48,110 Okay. Now, the other thing we can do, equivalent materials, is look at the superconductivity. 349 00:35:48,120 --> 00:35:54,030 How is the superconductivity? What is the interplay of the superconductivity with the electronic pneumatic state? 350 00:35:54,930 --> 00:36:00,300 So this is a different compound. But these this is the superconducting energy gap. 351 00:36:00,690 --> 00:36:04,950 If we image the wave functions here, they're a mess. There's a lot of scattering interference. 352 00:36:05,490 --> 00:36:15,900 But as I said, if we image, if we take the four year transform and do the QPR analysis, we're able to find three bands, a central band here. 353 00:36:16,470 --> 00:36:20,370 So that's the scattering interference signal from one of the primary bands. 354 00:36:20,940 --> 00:36:26,130 And from that, we're able to determine determine the exotic structure of the superconducting energy gap. 355 00:36:26,700 --> 00:36:32,670 So now you don't have to remember all that. I just put the key facts here for you on one slide. 356 00:36:33,650 --> 00:36:37,490 In the army superconductors. You have a fairly simple Fermi surface. 357 00:36:38,270 --> 00:36:41,840 You have an exotic superconducting energy gap there. 358 00:36:42,030 --> 00:36:45,890 There's no density wave phase. There's no spectacle phase as far as we can tell. 359 00:36:46,190 --> 00:36:55,130 But there is a pneumatic phase which now plays a vivid role in the study of those complex OC like this. 360 00:36:55,610 --> 00:36:59,330 So in here there is an electronic pneumatic in the R&B superconductors. 361 00:37:00,350 --> 00:37:04,249 All right. How about copper based? So in the copper based superconductors, same. 362 00:37:04,250 --> 00:37:08,540 Two questions. What's the mechanism? What is this strange face? 363 00:37:08,690 --> 00:37:16,270 Is it an electronic liquid crystal? So here's an image of the crystalline surface of one of the copper superconductors. 364 00:37:17,070 --> 00:37:21,940 Okay, now I'm going to show you an image, a simultaneously take an image of the wave functions. 365 00:37:25,890 --> 00:37:32,220 Oops. You see, the wave function image is very dense and looks quite different. 366 00:37:32,760 --> 00:37:36,720 It's taken us a long time to diagnose it, but it looks quite different. Looks like a bad tweet. 367 00:37:37,080 --> 00:37:40,020 Well, what it is is bad quantum mechanical tweet, I think. 368 00:37:40,920 --> 00:37:45,870 In any case, you can diagnose what broken symmetries are in this image by taking the 40 and transform. 369 00:37:47,250 --> 00:37:50,639 There are two key things in the for your transform. There are the Bragg peaks. 370 00:37:50,640 --> 00:37:52,530 They're the ones periodic with the crystal. 371 00:37:52,980 --> 00:38:01,470 And there are these broad peaks of incommensurate modulations which exist actually throughout the material, but only for a few periods. 372 00:38:02,610 --> 00:38:06,310 So now I have to tell you a little bit about CO2, the unit sell of copper. 373 00:38:06,330 --> 00:38:12,150 So inside each unit, sell of copper. Obviously there's one copper atom and two oxygen atoms. 374 00:38:13,020 --> 00:38:18,970 If you just focussed on the copper atoms and took the for a transform of this pattern, it looks like this. 375 00:38:18,990 --> 00:38:23,280 These are the Bragg peaks, you know, not of the orbital, but just of this periodic pattern. 376 00:38:23,910 --> 00:38:30,020 These are the Bragg peaks and they have the same side. Let's just ignore this one for a moment. 377 00:38:30,040 --> 00:38:36,150 This is what would happen if the two oxygens were equivalent. If the two oxygens are equivalent inside the unit cell. 378 00:38:36,700 --> 00:38:41,260 Then when you take the four, you can transform this peak, and that peak will have opposite side. 379 00:38:42,160 --> 00:38:45,370 The two modulations are opposite sine in the four year transform. 380 00:38:46,300 --> 00:38:49,450 So now in the real material, suppose you have a combination of this, 381 00:38:49,450 --> 00:38:55,030 plus that then you would add this to that this thing and this thing are the same sign. 382 00:38:55,060 --> 00:38:57,040 This thing in this thing are opposite signs. 383 00:38:57,460 --> 00:39:05,770 So the two brand peg should be in equivalent if there's a broken rotational symmetry inside the unit cell, which is what an electronic pneumatic is. 384 00:39:06,670 --> 00:39:11,050 So when we did that experiment, the two Bragg picks are identical in the topographic image, 385 00:39:11,380 --> 00:39:16,720 but they're quite different in the electronic structure image, about 40% different at low doping. 386 00:39:17,380 --> 00:39:24,220 And so this and you can actually demonstrate in real space that the same thing is happening inside each unit. 387 00:39:24,220 --> 00:39:26,920 So there there's a strong breaking of rotational symmetry. 388 00:39:28,140 --> 00:39:36,240 So this constituted the discovery of an electronic pneumatic phase in the copper based superconductors, and people were very surprised about this one. 389 00:39:36,630 --> 00:39:37,710 It's interesting. 390 00:39:38,580 --> 00:39:45,320 Somehow the magic in the arm based superconductor seemed to be more acceptable than the the magic in the copper, evasive or inductive. 391 00:39:47,650 --> 00:39:51,760 Now, the other thing is that the other thing we could look for is these incommensurate peaks. 392 00:39:52,450 --> 00:39:55,719 Now we can look at those things, you know, with high spatial resolution. 393 00:39:55,720 --> 00:40:01,270 So that's one, two, maybe three periods of this strange incommensurate modulation. 394 00:40:01,540 --> 00:40:01,869 Of course, 395 00:40:01,870 --> 00:40:08,050 it's not there in every energy because in quantum mechanics some energies are doing localised states and some energies are localised states. 396 00:40:09,900 --> 00:40:14,310 And we were able to show that the same strange pattern of breaking of rotational 397 00:40:14,760 --> 00:40:19,360 translational symmetry and rotational symmetry exists in multiple cuprates. 398 00:40:20,070 --> 00:40:22,920 And then if you zoom in and look at this thing carefully, 399 00:40:23,220 --> 00:40:29,100 you'll see that it's made of some very interesting and iconic object, a pattern we're not really familiar with. 400 00:40:29,100 --> 00:40:32,820 It's unique directional. It's four unit cells wide. 401 00:40:33,300 --> 00:40:39,150 Somehow it manages to break rotational symmetry inside every unit cell while still being periodic. 402 00:40:39,540 --> 00:40:49,230 It took a long time to figure out what that pattern is. Specifically, what is this object which appears in the broken symmetry state of the Cuprates? 403 00:40:49,740 --> 00:40:54,320 But now we know it's a D symmetry form factor density width. 404 00:40:54,420 --> 00:40:57,060 So now I get to do my little dance to tell you what that is. 405 00:40:57,750 --> 00:41:03,750 So a conventional density wave is supposed to charge on the two oxygen atoms inside the unit itself, 406 00:41:03,900 --> 00:41:07,050 where modulating in space and their modulating in phase. 407 00:41:07,410 --> 00:41:10,860 And the signal that the two copper sites would do this. 408 00:41:11,770 --> 00:41:15,690 Sorry, the two oxygen sets. Let me do that again. Think of me as the copper. 409 00:41:15,720 --> 00:41:21,090 These are the two oxygens, a conventional density wave, the charge modulation phase. 410 00:41:21,090 --> 00:41:25,260 That's exactly what we all learned to expect. But it's not the only possibility. 411 00:41:25,770 --> 00:41:33,030 The other possibility is that the two oxygens could be equivalent, which they are, and the charge on them can modulate out of phase. 412 00:41:33,510 --> 00:41:39,690 That's a D symmetry density, something predicted since the 1970s on symmetry principles. 413 00:41:39,990 --> 00:41:43,160 Actually I've never seen before, so it's kind of surprising. 414 00:41:43,170 --> 00:41:48,600 But we don't think it's a coincidence that this happens in the copper based superconductors. 415 00:41:50,010 --> 00:41:56,639 We can also visualised superconducting wave functions, as I said before, by using QPR. 416 00:41:56,640 --> 00:42:08,469 I see if this is working. Yeah. But by measuring the energy dependence of the of all these different wave vectors and having a model for their cause, 417 00:42:08,470 --> 00:42:13,720 which is scattering interference due to impurities, we can measure the superconducting energy gap. 418 00:42:13,960 --> 00:42:20,140 Now, this wasn't something new to the study and it had been done by photogrammetry, but nevertheless one can do it. 419 00:42:20,620 --> 00:42:25,510 So here's a summary for what the package of information is in the copper based superconductors. 420 00:42:26,260 --> 00:42:32,260 There's a very simple Fermi surface. It's got a relatively simple body symmetry, superconducting energy gap. 421 00:42:32,830 --> 00:42:40,240 There's a vivid smectite electronic liquid, crystal, four unit cell periodicity. 422 00:42:41,140 --> 00:42:47,470 And the degree of freedom which is modulated in this liquid crystal actually is the same degree of freedom, 423 00:42:48,040 --> 00:42:53,020 which is whose symmetry, whose rotational symmetry is broken in the pneumatic phase. 424 00:42:53,560 --> 00:43:05,120 And that's exactly what you would expect if you would read Macmillan or Daejeon papers about liquid crystals in the 1970s and early 1980s. 425 00:43:05,140 --> 00:43:08,650 This is exactly what you would expect. There are some degree of freedom. 426 00:43:08,890 --> 00:43:12,700 First, it breaks rotational symmetry and then it breaks translation of symmetry. 427 00:43:12,910 --> 00:43:17,250 Well, that's exactly what's happening in the copper based superconductors and the pseudo graphics. 428 00:43:17,830 --> 00:43:27,430 Okay. So there is both the pneumatic and the mechanic in this part of the phase done schematic phase diagram of the copper superconductors. 429 00:43:28,090 --> 00:43:35,799 All right, so now I'll make a few comments about the consequences of that for the fundamental problem we're trying to solve, 430 00:43:35,800 --> 00:43:42,310 which is I haven't forgotten it. It's what is the mechanism of how to see and how can we get to room temperature? 431 00:43:42,670 --> 00:43:46,870 But I'm going to reserve those comments for a few minutes because one other really 432 00:43:46,870 --> 00:43:51,670 interesting thing intervened at this point and really this only about two years. 433 00:43:55,190 --> 00:43:59,120 There's another possible electronic crystal stake that can exist. 434 00:43:59,390 --> 00:44:05,650 It's a cooper pair of crystal. It's a very different state than a density modulation in the charge. 435 00:44:05,660 --> 00:44:15,550 It's a modulation in the Cooper pairing. So it's a it's a mathematically valid statement to say that in Ginsburg, Landau's theory of such a situation, 436 00:44:15,760 --> 00:44:21,309 if you had an electronic liquid crystal like this and if it was coexisting with a superconductor, 437 00:44:21,310 --> 00:44:26,740 let's say here, then a Cooper pair density wave, a cooper pair of crystal would be allowed. 438 00:44:27,520 --> 00:44:36,700 Now that strong and such such cooper pair modulations actually have been predicted for more than 50 years, but never seen in any material. 439 00:44:37,270 --> 00:44:41,980 They were predicted by Fulda Feller and Larkin and of Chillicothe in 1964. 440 00:44:43,300 --> 00:44:46,480 So. And furthermore, there are good. 441 00:44:47,110 --> 00:44:54,220 So the mechanism used in this proposal is different than the one which would exist in a doped instrument or in a correlated material, 442 00:44:54,730 --> 00:44:59,440 but in advance theories of doped model insulators, specifically the cuprates. 443 00:44:59,710 --> 00:45:03,280 There have been predictions that there should be a pair density wave, 444 00:45:03,490 --> 00:45:10,990 a cooper pair of crystal appearing if this same type of broken translational and rotational symmetry occurs. 445 00:45:11,770 --> 00:45:19,600 So. So the question is, could there be a there should be, but could we find if there is a Cooper pair density wave in the cuprates? 446 00:45:20,590 --> 00:45:23,440 All right. So that involved developing a new technique. 447 00:45:24,490 --> 00:45:32,800 The reason is that if you use a conventional SDM, your tip is made of, let's say, a normal metal like tungsten or iridium or something. 448 00:45:33,220 --> 00:45:41,500 And the tunnelling from that normal metal tip is to states which have equivalent iron states, states which are single electron states. 449 00:45:42,220 --> 00:45:50,420 So normal chips here in this cartoon will only detect a signal, you know, where it picks up an individual electron. 450 00:45:50,440 --> 00:45:56,410 But if there are cooper pairs, it'll ignore it. There's no matrix element for a could prepare to tunnel into a regular chip. 451 00:45:57,220 --> 00:46:02,890 However, if you had a superconducting chip, the opposite argument holds the superconducting chip. 452 00:46:02,900 --> 00:46:04,480 If if we're working properly, 453 00:46:04,720 --> 00:46:12,400 it's full of cooper pairs and at low temperature no normal electrons as it scans over the surface that the Josephson current. 454 00:46:13,640 --> 00:46:17,600 Should tell you what the density of Cooper Pairs is as a function of location. 455 00:46:17,990 --> 00:46:22,670 Now, of course, this is an old idea. This idea has been around for many years, 15, 20 years. 456 00:46:23,240 --> 00:46:29,180 But nevertheless, the motivation really to try and implement it was brought forward by the Cooper problem. 457 00:46:29,540 --> 00:46:34,850 So what's required is a scanned Josephson tunnelling microscope with Nanometre resolution. 458 00:46:35,600 --> 00:46:41,480 This distance is 1.6 nanometres. So if you wanted to see this object, you need to have nanometre resolution. 459 00:46:43,300 --> 00:46:48,730 Furthermore, when you look at the equations, you need the superconducting gap in the tip to be as high as possible. 460 00:46:49,090 --> 00:46:52,990 And it turns out you need the Josephson Energy, which couples the tip, 461 00:46:53,440 --> 00:46:58,030 the superconducting tip to the superconducting sample to exceed the thermal fluctuations. 462 00:46:58,330 --> 00:47:00,880 And that means you need to be at a miller Kelvin temperature. 463 00:47:01,780 --> 00:47:08,560 So what we had to make is a milli Kelvin dilution fringe based a scan Josephson tunnelling microscope which we did. 464 00:47:10,100 --> 00:47:17,900 And we can tell that the chip has sufficient resolution because we can use conventional imaging to see objects in real space. 465 00:47:18,230 --> 00:47:27,290 Superconducting tape does have reasonably good resolution, and we can also tell that it's a high gap, high tech superconducting chip. 466 00:47:27,290 --> 00:47:33,880 We know that because we made it by picking up a piece of material, but also we can measure the spectrum and that tells us the gap in the tip. 467 00:47:35,440 --> 00:47:42,549 So finally you put all this together. Nick Miller Kelvin Hijab, Nanometre Resolution Low Junction Resistance Scan. 468 00:47:42,550 --> 00:47:46,270 Josephson Tunnelling Microscope. I won't tell you about the engineering. 469 00:47:46,660 --> 00:47:49,720 Here is the critical current. Here's the Josephson critical current. 470 00:47:51,640 --> 00:48:00,150 Measured on such a tip on a high tech compound. So now we want to image not the single electrons but the cooper pairs. 471 00:48:00,150 --> 00:48:07,799 Where are the Cooper pairs? So this is a topographic image with such a tip, and this is a scanned Josephson image. 472 00:48:07,800 --> 00:48:18,600 Actually, it's the first scan Josephson image with atomic resolution, and it already contains a tremendous amount of information. 473 00:48:18,600 --> 00:48:27,090 But there's some scepticism that actually we were visualising the condensate, the Cooper pairs, the density of Cooper pairs. 474 00:48:27,210 --> 00:48:30,750 There is no precedent and you know, there are always sceptics. 475 00:48:31,590 --> 00:48:35,280 So we were motivated to do one more thing, which is the following. 476 00:48:35,850 --> 00:48:41,640 It's known it has been known for many decades that if you put zinc atoms on the Cooper site in Cuprates. 477 00:48:42,880 --> 00:48:46,120 A hole appears in the superconducting order parameter. 478 00:48:46,150 --> 00:48:53,770 The superfluid diminishes to zero for a small radius about two nanometres surrounding each zinc atom. 479 00:48:54,280 --> 00:48:56,290 So, you know, obvious for obvious reasons. 480 00:48:56,290 --> 00:49:02,620 This is called a Swiss cheese model of zinc doping of the Cuprates, and it's known from the US arm that this happens. 481 00:49:03,040 --> 00:49:07,120 So we wanted to use this to validate the contrast in our imaging. 482 00:49:07,810 --> 00:49:11,650 So we had zinc atoms substituted in one of these crystals. 483 00:49:11,830 --> 00:49:15,100 I mean, new crystals made with zinc atoms substituted. 484 00:49:15,790 --> 00:49:21,399 And we can find where each zinc atom is with rather high spatial resolution, 485 00:49:21,400 --> 00:49:26,860 a fraction of a nanometre from the normal tunnelling spectrum, nothing to do with the superconductivity. 486 00:49:27,340 --> 00:49:31,200 And then simultaneously, we can look at the Josephson image everywhere. 487 00:49:31,210 --> 00:49:34,810 There's a zinc atom, the Josephson current dimensions close to zero. 488 00:49:36,060 --> 00:49:42,000 You can see that for yourself. Every place where there is income and justice, power diminishes to a very low value. 489 00:49:42,780 --> 00:49:48,900 So this allowed us to quantify the contrast of San Jose sin and pretty good the city that is around 90%. 490 00:49:48,930 --> 00:49:55,590 We're sure that the things we're seeing here are real spatial variations in the superconducting condensate. 491 00:49:56,460 --> 00:50:00,570 Okay, last but not least, what you should do with this is now the obvious thing. 492 00:50:00,600 --> 00:50:06,390 Take the for you and transform and before you transform shows for peaks there at. 493 00:50:08,120 --> 00:50:14,150 Zero comma a quarter or quarter a sorry, a quarter comma zero. 494 00:50:14,240 --> 00:50:21,380 That means there are four units out. Periodic modulation in the density of Cooper pairs along the two axes in this compound. 495 00:50:23,740 --> 00:50:24,400 This is great. 496 00:50:24,580 --> 00:50:33,310 This really gives us a new handle on the situation, and it also constrains them a variety of theoretical approaches you can take to the cuprates. 497 00:50:33,580 --> 00:50:39,610 Because now we know a great deal about the pseudo gap physics. We know two broken symmetries. 498 00:50:39,610 --> 00:50:42,940 We know how they impact the superconductivity in the density wave. 499 00:50:43,330 --> 00:50:49,180 And so at the empirical level, these are have been rapid advances also. 500 00:50:49,270 --> 00:50:52,620 And this is cool. So suppose you hate the cuprates. 501 00:50:52,630 --> 00:51:00,430 I know that that's not possible, but suppose it's true. There are many other problems theoretical predictions, 502 00:51:00,430 --> 00:51:08,380 proposals for the properties of condensates which have never been validated because there was no way of visualising or condensate. 503 00:51:08,680 --> 00:51:12,600 Well, now, with this technique, we can think about pursuing those new. 504 00:51:12,610 --> 00:51:16,950 Or maybe you guys can think about pursuing those new avenues. All right. 505 00:51:17,320 --> 00:51:21,470 No good. Conclusions and the future. 506 00:51:22,190 --> 00:51:30,440 So one conclusion I can tell you immediately is that these two guys are very happy so that I know them both very well. 507 00:51:30,440 --> 00:51:34,700 Of course, the basic pieces of their theory are right. 508 00:51:34,730 --> 00:51:40,730 Even their phase diagram, which is in another, which is in another frame from this paper, 509 00:51:41,120 --> 00:51:46,340 appears to be right when you don't feel correlated insulator enough to make it metallic. 510 00:51:47,360 --> 00:51:53,239 First it breaks rotational symmetry inside the unit itself, and if the susceptibility is there, 511 00:51:53,240 --> 00:51:59,390 then it breaks translational symmetry in the same degree of freedom the way a molecular liquid crystal would. 512 00:52:00,230 --> 00:52:09,170 So that part of their theory is right. And now the difficulty is that we don't have a quantitative theory for understanding the 513 00:52:09,170 --> 00:52:14,180 relationship between the electronic liquid crystal phase and the high tech superconductivity. 514 00:52:14,240 --> 00:52:17,990 I mean, we have a number of theories. We just don't know which one is right. 515 00:52:19,400 --> 00:52:23,090 But this is the key practical question now, if you have this stuff. 516 00:52:23,720 --> 00:52:27,260 Okay. Is it beneficial to the high tech? 517 00:52:27,280 --> 00:52:31,290 Do you need more of it or do you need less of it? Is the new magic beneficial? 518 00:52:31,470 --> 00:52:38,550 You would guess the new magic is beneficial because there are two families of high tech superconductors that have pneumatic electronic states. 519 00:52:39,000 --> 00:52:43,890 But that's just a logical guess rather than a theory. So the frontier, now it's back. 520 00:52:44,160 --> 00:52:52,770 The ball is back in the court of theorists to understand if doped correlated insulators contain electronic liquid crystals. 521 00:52:53,100 --> 00:52:58,370 What is the the Zen style theory which explains the interplay between the two auditoriums? 522 00:52:58,740 --> 00:53:06,309 If we could find that, then we understand these materials. Also, this technique is very powerful. 523 00:53:06,310 --> 00:53:09,580 You can do all kinds of other things that I haven't had time to talk about. 524 00:53:10,090 --> 00:53:13,790 You can see nanoscale domains and electronic disorder. 525 00:53:13,840 --> 00:53:17,800 This is the scattering interference. You can see individual impurity atoms. 526 00:53:18,220 --> 00:53:24,070 You can see heavy fermions. This is an this is the pseudo gapped fluid whose properties we don't understand. 527 00:53:24,100 --> 00:53:32,180 You can see electronic liquid crystals. You can see where every doping is in the material and what the doping atoms due to the electronic structure. 528 00:53:32,210 --> 00:53:36,550 You don't have to guess. You can just make a movie and find out, etc. 529 00:53:37,940 --> 00:53:38,630 Thanks very much.