1 00:00:00,300 --> 00:00:04,814 In this lecture we're going to discuss a very interesting anybody quantum effect 2 00:00:04,814 --> 00:00:08,491 namely the phenomenon of super conductivity. 3 00:00:08,491 --> 00:00:13,516 which is rather amazing field, because superconductors have a number of 4 00:00:13,516 --> 00:00:18,541 remarkable properties, such as for instance so shown here the phenomenon of 5 00:00:18,541 --> 00:00:24,703 levitation, I'm showing. A, a high-temperature superconductor, 6 00:00:24,703 --> 00:00:30,158 wrapped up in a tissue to avoid heating, levitating on top of the magnet. 7 00:00:30,158 --> 00:00:34,44 So, and this phenomenon is actually unique in this forum to superconductors 8 00:00:34,44 --> 00:00:38,110 based on expulsion of magnetic flux or Meissner effect. 9 00:00:38,110 --> 00:00:43,536 So here I'm actually showing you a movie. Of the same effect which was recorded by 10 00:00:43,536 --> 00:00:48,260 my experimental colleague Johnpierre Paglione in the Joint Quantum Institute. 11 00:00:48,260 --> 00:00:50,120 So and you here see a superconductor moving around on top of a magnet. 12 00:00:50,120 --> 00:00:51,914 So this phenomenon of levitation is indeed, well, quite remarkable, and is 13 00:00:51,914 --> 00:00:54,260 oftentimes used to to impress visitors at various science shows. 14 00:00:54,260 --> 00:01:04,200 but it's just one of many exciting phenomena that appear in relation to 15 00:01:04,200 --> 00:01:16,356 superconductor, and some of them we're going to discuss later today. 16 00:01:16,356 --> 00:01:20,955 But let me just mention that superconductivity is an extremely rich 17 00:01:20,955 --> 00:01:28,235 field, so suffices to say that it has so far resulted in about ten Nobel Prizes. 18 00:01:28,235 --> 00:01:32,582 This that have been awarded for various discoveries of superconductivity and 19 00:01:32,582 --> 00:01:37,118 furthermore there are definitely a lot of major mysteries that still remain in the 20 00:01:37,118 --> 00:01:41,72 field. And obviously we can not discuss 21 00:01:41,72 --> 00:01:45,350 everything in one lecture so I'm going to focus on the of the lecture on a key 22 00:01:45,350 --> 00:01:50,660 theoretical concept that sort of underlies. 23 00:01:50,660 --> 00:01:55,160 The theory so-called Bardeen Cooper Schrieffer Theory of Superconductivity. 24 00:01:55,160 --> 00:02:00,818 And this is the phenomenon of Cooper pairing, which is responsible for to a, 25 00:02:00,818 --> 00:02:06,480 to a large degree for the appearance of the theory . 26 00:02:06,480 --> 00:02:11,920 But let me start with discussing the main property of superconductor, namely the 27 00:02:11,920 --> 00:02:17,12 state of zero resistance. Which, is the reason why super conductors 28 00:02:17,12 --> 00:02:21,830 is actually called super conductors. And so let me go back in time about a 29 00:02:21,830 --> 00:02:26,950 hundred a little more than a hundred years ago to 1911, when this happy 30 00:02:26,950 --> 00:02:35,716 looking guy, Heike Kamerlingh Onnes. was performing various low temperature 31 00:02:35,716 --> 00:02:41,266 experiments to liquefy helium. And during these experiments he noticed 32 00:02:41,266 --> 00:02:46,570 that the resistivity of mercury dropped exactly to zero below a certain critical 33 00:02:46,570 --> 00:02:51,540 temperature of 4.2 Kelvin. So, this was very surprising. 34 00:02:51,540 --> 00:02:55,50 And actually, it is very surprising, and also it should surprise you. 35 00:02:55,50 --> 00:02:59,670 In particular, if you recall what we discussed in the fourth lecture, in the 36 00:02:59,670 --> 00:03:06,200 last lecture last week, where we talked about the resistivity of metals. 37 00:03:06,200 --> 00:03:10,552 And so I mentioned that in all real materials, there always are imperfections 38 00:03:10,552 --> 00:03:14,904 that give rise to disorder, that in turn give rise to scattering and finite 39 00:03:14,904 --> 00:03:19,230 resitance. So, what you would expect in a normal 40 00:03:19,230 --> 00:03:23,10 metal would be that the resistance can, well, it can go down but you would want 41 00:03:23,10 --> 00:03:28,190 it to saturate to a certain final value. [NOISE] If there is no localization. 42 00:03:28,190 --> 00:03:32,411 If there is localization, it actually would shoot up and go to infinity, but 43 00:03:32,411 --> 00:03:36,967 there is no sort of reasonable sort of a priori reason, why it would drop down to 44 00:03:36,967 --> 00:03:41,774 exactly zero. Not to a small value, not to a tiny 45 00:03:41,774 --> 00:03:45,804 value, to exactly as a zero and this is what Kamerlingh Onnes observed and this 46 00:03:45,804 --> 00:03:51,172 was the birth of superconductivity. It was the first time people, so 47 00:03:51,172 --> 00:03:55,76 superconductivity, and it was truly amazing in fact, and in particular, 48 00:03:55,76 --> 00:04:01,844 because of that he was awarded. the 1913 Nobel Prize in physics. 49 00:04:01,844 --> 00:04:07,874 Now another effect which already discussed in relation to this levitation, 50 00:04:07,874 --> 00:04:14,130 was magnetic flux expulsion. This is probably the second very 51 00:04:14,130 --> 00:04:19,956 interesting phenomenon and well. If you if you have metal let's say if you 52 00:04:19,956 --> 00:04:23,201 heat up this material up to room temperature, let's say and the 53 00:04:23,201 --> 00:04:28,618 penetrating with magnetic flux. Well, the flux will, more or less, just 54 00:04:28,618 --> 00:04:32,689 go through the material above the critical temperature and there will be no 55 00:04:32,689 --> 00:04:38,343 significant distortion of the flux. So, it's sort of amazing phenomenon that 56 00:04:38,343 --> 00:04:41,470 happens once you go into the superconducting phase, is that the 57 00:04:41,470 --> 00:04:46,10 magnetic field now tries to avoid the superconductor. 58 00:04:46,10 --> 00:04:50,218 So an, instead of going through it. It goes around it, and so you may say 59 00:04:50,218 --> 00:04:54,124 that it's expelled from the super conductor and this effect is called to 60 00:04:54,124 --> 00:04:58,875 the Meissner effect. So, returning to this picture of a high 61 00:04:58,875 --> 00:05:03,64 temperature super conductor levitating on top of a magnet, what's actually going on 62 00:05:03,64 --> 00:05:07,734 here. Is that the magnetic field lines are sort 63 00:05:07,734 --> 00:05:12,879 of, go around, primarily go around this superconductor. 64 00:05:12,879 --> 00:05:17,551 And you may see that this superconductor is sort of, is sitting on this on this 65 00:05:17,551 --> 00:05:23,20 flux, because it's energetically not favorable for it to go down. 66 00:05:23,20 --> 00:05:26,973 It would increase the energy of this system and therefore, it's supported by 67 00:05:26,973 --> 00:05:30,660 this flux. Well just a short comment here, though, 68 00:05:30,660 --> 00:05:34,248 is that I'm a bit oversimplifying this picture. 69 00:05:34,248 --> 00:05:38,263 so as a matter of fact there is there is indeed this Meissner effect, but apart 70 00:05:38,263 --> 00:05:41,673 from the Meissner effect, there is also a little bit of a penetration of the 71 00:05:41,673 --> 00:05:47,530 superconductor by a magnetic field. But this penetration happens in the form 72 00:05:47,530 --> 00:05:51,806 of so-called vortices. Which are if you look at the, let's say 73 00:05:51,806 --> 00:05:55,818 if you look at the cross section of the super conductor, two dimensional cross 74 00:05:55,818 --> 00:06:00,328 section. And sorry let me just plot it here, so 75 00:06:00,328 --> 00:06:05,320 there will be the super conductor. And most of this cross section is 76 00:06:05,320 --> 00:06:10,61 magnetic field free. But there are certain regions which are 77 00:06:10,61 --> 00:06:14,818 very, narrow regions, very small regions, were you do have a magnetic field, sort 78 00:06:14,818 --> 00:06:21,850 of penetrating through, very thin lines and these lines are called vortices. 79 00:06:21,850 --> 00:06:26,750 So if, in a superconductor these, magnetic field lines are called vortices. 80 00:06:26,750 --> 00:06:30,692 And these vortices are attempt to appear in the regions where superconductivity is 81 00:06:30,692 --> 00:06:34,202 suppressed due to various kinds of imperfections, a disorder that we already 82 00:06:34,202 --> 00:06:38,286 discussed. And this, in turn leads to the pinning of 83 00:06:38,286 --> 00:06:42,183 this magnetic field line. So, as a matter-of-fact, if you performed 84 00:06:42,183 --> 00:06:45,813 this experiment with a true simple type II superconductor, which allows these 85 00:06:45,813 --> 00:06:49,506 flux, flux lines. You, you not only would be able to see 86 00:06:49,506 --> 00:06:52,916 that it can be levitating on top of a magnet, you can actually turn it anyway 87 00:06:52,916 --> 00:06:56,780 you see fit. You can turn it at any angle and still 88 00:06:56,780 --> 00:07:02,262 going to sort of retain its position. And this actually even more impressive 89 00:07:02,262 --> 00:07:06,550 phenomenon is due to these flux lines and the spin. 90 00:07:06,550 --> 00:07:11,546 But you know, to discuss it further would be, it'd be going too far. 91 00:07:11,546 --> 00:07:15,901 So, let me just stop here and say that all and all so this magnetic field 92 00:07:15,901 --> 00:07:21,220 expulsion is responsible for this phenomenon of levitation. 93 00:07:21,220 --> 00:07:25,844 On a, on a different note, interestingly, the Meissner effect, this expulsion of 94 00:07:25,844 --> 00:07:30,468 the magnetic flux, on the theoretical side is to some degree equivalent to the 95 00:07:30,468 --> 00:07:35,834 Higgs mechanism. That occurs in elementary particle 96 00:07:35,834 --> 00:07:38,569 physics. I'm sure many of you have heard about the 97 00:07:38,569 --> 00:07:42,700 discovery of so-called the God particle or Higgs particle. 98 00:07:42,700 --> 00:07:47,120 Last year, but actually the mathematical theory of this Higgs mechanism, in a 99 00:07:47,120 --> 00:07:52,652 different context of condensed metrics. Physics was put together before Higgs by 100 00:07:52,652 --> 00:07:54,833 Phil Anderson. As speaking, I would call it 101 00:07:54,833 --> 00:07:58,592 Anderson-Higgs mechanism. I'm not going to go into [NOISE] details 102 00:07:58,592 --> 00:08:03,506 of why this expulsion of magnet flux is equal in to Higgs. 103 00:08:03,506 --> 00:08:07,586 But, you may have heard that Higgs really is important to elementary particle 104 00:08:07,586 --> 00:08:11,726 physics because it gives rise, because it gives rise to masses for some elementary 105 00:08:11,726 --> 00:08:16,146 particles. Here you may see that the Higgs mechanism 106 00:08:16,146 --> 00:08:19,854 in this form gives rise to mass of the magnetic field. 107 00:08:19,854 --> 00:08:23,798 So, it becomes energetically unfavorable for the magnetic field to be inside the 108 00:08:23,798 --> 00:08:27,994 superconductor. And well this energy, this energy 109 00:08:27,994 --> 00:08:32,301 apparently for it to be there, is sort of proportional to the so called, 110 00:08:32,301 --> 00:08:39,769 superconductivity order parameter that appears below the critical temperature. 111 00:08:39,769 --> 00:08:44,124 So, I already advertised the fact that superconductors host an amazing variety 112 00:08:44,124 --> 00:08:49,312 of various new phenomena. And the discoveries of this phenomena 113 00:08:49,312 --> 00:08:52,580 have in turn led to these ten Nobel prizes. 114 00:08:52,580 --> 00:08:57,337 And I list here these major discoveries, sort of hallmark discoveries in the 115 00:08:57,337 --> 00:09:01,450 field. And the first one, I've already talked 116 00:09:01,450 --> 00:09:07,705 about, this is Kamerlingh Onnes discovery of the effect itself back in 1911. 117 00:09:07,705 --> 00:09:12,450 Then John Bardeen, Leon Cooper, and Bob Schrieffer, got a 1972 Nobel Prize for 118 00:09:12,450 --> 00:09:18,350 developing a microscopic theory of super connectivity in the 50s. 119 00:09:18,350 --> 00:09:22,970 Brian Josephson and Ivar Giaever, got the 1973 Nobel prize for discovering 120 00:09:22,970 --> 00:09:29,364 tunneling phenomena is a very interesting tunneling event in superconductors. 121 00:09:29,364 --> 00:09:32,484 In particular quantum, right here, Josephson if he acts simple, Josephson if 122 00:09:32,484 --> 00:09:36,372 you act other than you are talking about it, but's very interesting. 123 00:09:36,372 --> 00:09:41,547 So, this guys made a major breakthrough in the field, I'm going to mention it in 124 00:09:41,547 --> 00:09:47,322 the next slide, by discovering so-called, the family of high temperature copper 125 00:09:47,322 --> 00:09:54,360 superconductors And finally just ten years ago Alexei A 126 00:09:54,360 --> 00:10:02,31 Abriskosov and Vitaly L Ginzburg, along with Tony Leggett, got a Nobel prize 127 00:10:02,31 --> 00:10:07,287 In particular, these two gentlemen have a put together a theory of vortices 128 00:10:07,287 --> 00:10:13,870 topological excitations, that appear in these quantum fluids. 129 00:10:13,870 --> 00:10:18,280 And I'm also including here a future Nobel prize, which almost guaranteed to 130 00:10:18,280 --> 00:10:21,934 be awarded sometime in the future for a theory, of this high numbers of 131 00:10:21,934 --> 00:10:28,22 superconductors, that I just mentioned. We don't really know yet the nature of 132 00:10:28,22 --> 00:10:30,604 these guys/g. We know they exist and know a lot of 133 00:10:30,604 --> 00:10:33,784 their properties, very unusual properties, but what's really going on 134 00:10:33,784 --> 00:10:37,200 there, we don't know. So, maybe it's going to be you. 135 00:10:37,200 --> 00:10:40,854 Who knows? But you should hurry because I think the 136 00:10:40,854 --> 00:10:45,879 new experiments are getting us closer and closer to the to understanding the, sort 137 00:10:45,879 --> 00:10:51,670 of uncovering the mystery of this high-temperature coppers. 138 00:10:51,670 --> 00:10:55,757 In any case I want, what I want to emphasize here on this slide, is a very 139 00:10:55,757 --> 00:11:00,45 large time gap between the discovery and the corresponding prize for, of the 140 00:11:00,45 --> 00:11:07,133 different superconductor in the microscopic theory of superconductivity. 141 00:11:07,133 --> 00:11:12,430 Which was put together about 40-50 years later, it's not for a lack of trying. 142 00:11:12,430 --> 00:11:16,966 People have tried very hard, and couldn't succeed so it turned out to be very 143 00:11:16,966 --> 00:11:22,533 difficult to explain the basic nature of superconductors. 144 00:11:22,533 --> 00:11:27,351 Even though it took a while for the theories to provide an explanation of 145 00:11:27,351 --> 00:11:32,15 superconductivity. The experimental work on this in fact 146 00:11:32,15 --> 00:11:38,102 never really stopped since 1911 since the discovery by Kamerlingh Onnes. 147 00:11:38,102 --> 00:11:43,360 And, the motivation for these experiments is really easy to understand. 148 00:11:43,360 --> 00:11:46,816 So, as I mentioned of course a super conductor is are special in that, they 149 00:11:46,816 --> 00:11:51,850 have exactly zero resistance. So they have no losses whatsoever. 150 00:11:51,850 --> 00:11:57,264 And they are able to conduct electricity with no heating. 151 00:11:57,264 --> 00:12:01,46 So, if we were able to have a superconductor at room temperature, such 152 00:12:01,46 --> 00:12:05,262 a room temperature superconducting wires, would have been able to transport 153 00:12:05,262 --> 00:12:11,190 electricity over large distances with, with no losses. 154 00:12:11,190 --> 00:12:15,474 And this of course would have been great, especially now in the view of this 155 00:12:15,474 --> 00:12:20,338 looming energy crisis. Of course now we transport electricity 156 00:12:20,338 --> 00:12:24,43 from where we produce it, to where we use it, using well normal wires, metallic 157 00:12:24,43 --> 00:12:27,825 wires. And those involve wide resistance and 158 00:12:27,825 --> 00:12:30,252 heating. And so this heat, which is loss, so this 159 00:12:30,252 --> 00:12:33,325 goes nowhere. So to have a room temperature 160 00:12:33,325 --> 00:12:38,518 superconductor would be great. Unfortunately, we don't really know 161 00:12:38,518 --> 00:12:44,600 whether such a material may exist, or whether it is possible at all. 162 00:12:44,600 --> 00:12:47,736 There has been a lot of progress, growing materials, which have a much higher 163 00:12:47,736 --> 00:12:53,221 transition temperatures. Then the first 4.2 kelvin superconductors 164 00:12:53,221 --> 00:12:56,409 back here. So, this is the discovery of 165 00:12:56,409 --> 00:13:01,887 superconductors, and this plot here is really a diagram, so here is the year 166 00:13:01,887 --> 00:13:08,337 from the early 1900s. Up to almost now, and the points are the 167 00:13:08,337 --> 00:13:13,670 correspond to compounds, with the various transition temperatures. 168 00:13:13,670 --> 00:13:19,110 And so it, you see that for the first let's say 70 or so years the progress has 169 00:13:19,110 --> 00:13:24,602 been really slow. But then in the, in the 80s, there is a 170 00:13:24,602 --> 00:13:32,10 huge jump up to here, and this class of materials are what I already mentioned. 171 00:13:32,10 --> 00:13:35,829 The high temperature superconductors, so-called Copper Superconductors 172 00:13:35,829 --> 00:13:39,876 conductors, which are getting, which is, is somehow dangerously enclosed, close to 173 00:13:39,876 --> 00:13:43,936 room temperature but we are not, they are not yet. 174 00:13:43,936 --> 00:13:49,110 So, they're close, but you know, we still have about 100 kelvin to go. 175 00:13:49,110 --> 00:13:53,334 Now and also very recently, there was a discovery of a new class of a material 176 00:13:53,334 --> 00:14:00,140 so-called iron based superconductors, and it does also look promising. 177 00:14:00,140 --> 00:14:04,471 but so far, although this phrase to increase the transition temperatures is, 178 00:14:04,471 --> 00:14:09,150 in superconductors hasn't really involved much theories,. 179 00:14:09,150 --> 00:14:13,907 It's mostly about experimental magic of growing materials and trying out 180 00:14:13,907 --> 00:14:20,278 different compounds. To emphasize this fact let me actually, 181 00:14:20,278 --> 00:14:25,218 in the last slide in this segment, let's actually mention a guy who was really, 182 00:14:25,218 --> 00:14:30,350 really good at finding new super conductors. 183 00:14:30,350 --> 00:14:33,650 He was an experimentalist working at Bell Labs. 184 00:14:33,650 --> 00:14:40,10 His name was Bernd Matthias. and he was a legend in in this business. 185 00:14:40,10 --> 00:14:44,978 And he, back in the 50s and 60s, he came up with a set of rules to help others 186 00:14:44,978 --> 00:14:51,310 discover new super conductors and here I just list those rules. 187 00:14:51,310 --> 00:14:54,576 I don't expect you to understand their significance of actually, they're not, to 188 00:14:54,576 --> 00:14:57,796 be taken too, too seriously, because, in these high-temperature superconductors 189 00:14:57,796 --> 00:15:00,840 most of these rules are actually violated. 190 00:15:00,840 --> 00:15:04,674 But let me go over them, so he said that high symmetry is good, cubic symmetry is 191 00:15:04,674 --> 00:15:09,629 best, wants you stay away from oxygen. Stay away from magnetism, stay away from 192 00:15:09,629 --> 00:15:14,200 insulator, by the way, this is all we find in high-t superconductors. 193 00:15:14,200 --> 00:15:20,200 And impose the most important rule due to Matthias was to stay away from theories. 194 00:15:20,200 --> 00:15:25,888 And this was really bad we know because it was deserved, because again for many 195 00:15:25,888 --> 00:15:31,112 years there was no theory of super conducting. 196 00:15:31,112 --> 00:15:37,590 But fortunately the situation has changed in, in the 1950s, when Leon Cooper and 197 00:15:37,590 --> 00:15:42,330 then John Bardeen and Bob Schrieffer, came up with the, a very, clear 198 00:15:42,330 --> 00:15:49,510 explanation of the effect. And in the remaining three segments we're 199 00:15:49,510 --> 00:15:54,134 going to go over, this explanation but in the next video I'm going to mostly talk 200 00:15:54,134 --> 00:15:59,894 about the preliminary materials we need to know to get there.