 Good morning, I'm so glad to see you. My name is Mariette DiCristina and I'm the Editor-in-Chief of Scientific American, also the Director of Editorial and Publishing for Nature Research Group. I'm just delighted, absolutely delighted to say that today we're going to have a discussion, an idea and insight with Duncan Haldane who is this past year's winner of the Nobel Prize in Physics with David Thouless and J. Michael Kosterlitz and we're going to talk a little bit about that, we're going to talk a little bit about science, about inspiration and I'm going to have a little fun while we're doing it I think. So Professor Haldane, let's start back a little bit because not everybody's maybe quite as familiar with physics as you are. I don't think many people are familiar with physics. I think you're probably right, but let's start with, you know, why science for you, you know, think about, go back to think about when you were when you were younger and what drew you to the physics in the first place? Well, I guess I always had my parents were medical people and they had a kind of great belief and science was the answer to the world's problems and the future. So it was a kind of propaganda for science in my house, but I didn't end up going into medicine like my brother and I was at school, I guess I liked science, geology and rocks and things chemistry. I didn't particularly like physics until it was only the there was a well, the physics teacher also doubled as the sports teacher in in the early part. But the last year I had a very good physics teacher and before that, I'd I'd loved chemistry and doing all the kind of things in in school labs that are completely ruled out by health and safety officers today. You cooked all these things and interesting orange chemicals came turned into green ash and came out of tubes and things. But my kind of chemistry. Yeah, but actually, there's something about physics. So it's got a simplicity in it and underlying it. And it's I guess I probably it was the enthusiasm of a teacher that communicated it to me, which I hadn't really even thought about physics before then. I actually remember having a physics teacher who really got me interested in the topic as well. So I can I can see how that would get you started. But then you you from there decided that that was interesting thing to pursue. So how did you? And then I went to college and did it was a Cambridge and did a general science called natural sciences. So I did a bit of physics, chemistry, biology, math. But then I had to go in the lab and the biology lab. I remember having an experience where I were having to put some nasty chemicals on some nice, nice looking mold to mutate it. And you did it in those days with a mouth pipette. Oh, so I sucked this stuff up and swallowed it. I decided I'm quite clumsy. So I decided maybe I don't want to be involved in any kind of experiments with with chemicals or anything with radioactive materials, because I get contaminated. So I went into nice, clean theoretical physics after. So I like the idea that since you had a lot of medical people in the family and you want to avoid chemistry, that you you almost chose physics as a star as almost a rebellion in a certain way. Did you did you always know that it would be science? Probably some years probably there was a general kind of encouragement that science was really a great future for mankind. We solve all the world's problems. I don't know if that's true, but it's doing it's both creating problems and solving problems. Yeah. Yeah, I think that's an interesting, interesting nature of science in general, isn't it? So so physics and then a particular branch of physics. Can you tell us how you you study quantum mechanics, which is a couple of pretty powerful sounding words. Let's tell people what what does it what does it mean? Quantum mechanics in the area. So physics is a fundamental science and you're in theoretical, which is described with the maths and so on. Quantum mechanics is the real I mean, it seems to be very different. It describes the world in a very different way from the way we understood, with the way you experience it. But because generally it works, it completely control things on the atomic scale of things. But it's the fundamental. It's actually the correct description of the world around us. You would say that. And but it's something we've known the laws of quantum mechanics for nearly 90 years now. It's all found around 1928, 30. And it's just because we've known the laws of quantum mechanics for so long doesn't actually mean we really understand it, right? Many people have tried to come up with experiments to invalidate quantum mechanics, and it's always triumphed. And but it's it's it's something that we understand formally by we know the equations are there. But it's it's been coming up with tremendous surprises in the last few years. So you've mentioned a couple of things here that I just want to pick apart for the audience. So mechanics, obviously, we can think about generically as how things work. And quantum is a very, very small scales. Yes. And there's been a difference in in in science brought by quantum physics, you know, quantum mechanics, because in the past, we'd studied things at larger scales. And the reason I'm introducing this concept is we're going to talk a little bit about the the interfaces. So the way the physics works or looks like it works at larger scales and at smaller scales, sometimes looks a little different. Yeah, the you don't look well, if you can't understand atoms or molecules or chemistry without quantum mechanics, that's why it was it was the big problem of the time at the beginning of the last century to and that's what and basically, we don't we don't experience it because we don't see it the atomic scale. But you can't understand you can't understand why you quantum mechanics is explains why you don't fall through the floor when you stand on it, even though the atoms are made of ninety nine point nine nine percent empty space. And, you know, the but of course, we think we don't fall through the floor because the floor is solid and it exerts a force on our shoe. But that force comes from the fact that the electrons don't to electrons don't like to be in the same place for an important quantum mechanical principle, the Pauli exclusion principle. And that's what really stabilizes. So we can't really understand matter at all without quantum mechanics. So when I put my hand on this table, the tables, electrons don't want my hand in their business. They they exclude they exclude you. They say they've got they've they've taken the space over and too bad for your bad for you. Can't put too bad for the other electrons in your hand. They can't come in. So you study a particular area of quantum mechanics, and I want to I want to talk a little bit about the topological areas and what led you to your Nobel Prize. So how how did that adventure begin in theoretical physics? Well, I think these things always come about through accidents, basically. I think there's lots of things, as we said, we haven't really fully understood what quantum mechanics allows to happen. And initially, I was investigating a very kind of toy model system in the late in the in fact, even as far back as the 30s, people started trying to make models for for matter, for solid matter and things like magnetism. And initially, they started making very sort of toy models quite complicated to understand a full magnetic structure. So they looked at just a little little line of atoms along one direction, one dimension. And this was spot to be in that period. These were kind of toy models. You did homework problems before you went up to the the full the full problem of three dimensional crystals and things. And but it turns out that the quantum mechanics effects actually much become much more important in in in things which are confined either to two dimensional surfaces or lines. So in fact, these these low dimensional systems are kind of even in some sense, more more interesting because. So in two dimensions, let's let's look back at some. So if I think of it like a sheet of paper in two dimensions, we're able to see effects a little differently than we are when you're looking at it in other ways. Yeah, because the fluctuations due to quantum mechanics are stronger and so in the seventies, people started to actually look at organic chain molecules and they started to make materials which could be described by these kind of things which had been regarded purely as mathematical exercises. So so they started to be much more interested in this in this problem. And basically what I was in looking at a different a slightly different language to to look at these problems in that gave you a different perspective from the standard one and found out just by by a tremendous surprise that what people had sort of concluded about these systems was basically wrong. So there's the insight, right? So you take a different perspective on a problem everybody is working on around this single plane and use a single line in the first one. Yeah, and yeah, basically it was an interesting kind of sociological thing. There was a long, a very old mathematical solution of one of these toy models had been around, but it was actually no one really understood it. It was actually a guest by Hans Bethe who was who went on after that to do tremendous things in nuclear physics and explain why the sun shines. But he actually started off with these kind of toy models and Bethe's solution took about 60 or 70 years to be understood because it was a kind of luck that he lucked onto this thing too. And it is superficially confirmed. It the answers from his mathematical solution looked like the looked like the kind of more more hand waving and but understandable kind of theory that people had applied before. So they they had an incorrect theory and there was that there was apparent evidence that looked as if it supported it and it turned out to be a complete accident. Just just so people's opinions can be. I'm sure there's plenty of things that we know about that we assume that we understand and, you know, then we may have quite the wrong idea. And so it's quite but it's a very great surprise when you when you find that what everyone believes just isn't correct, right? Yeah, that is a surprise. So let's talk just a little bit more about this is an area eventually became known as have I got this right? Topological phase transition. Well, where does that where does that topological matter? I guess topological matter. So can we can we explain to people what topological matter is and maybe give them an example or two? I think you brought a couple of things here to share. Well, topology is a branch of pure mathematics, OK? And it hadn't had any role in quantum mechanics before this thing. Before you were. Yeah. So topology is I mean, like here are the examples. There's a there's a famous thing in topology, which is tells you that a that a coffee cup and I guess a bagel. Now, I've got a better bagel here because this is very small. But the big example in topology is that that this object and the bagel with both the same topologically because they basically have a kind of hole in the middle. The hole in the middle of the bagel is now the handle of the cup here. And there's a famous film that everyone takes off YouTube or the people working in topological materials now. And they they show a coffee cup continuously changing into a bagel and back again. So it's like that. But the bagel has a hole in it. And the interesting thing about this is that holes are kind of they come in units. You can have one hole, two holes, no holes, but you can't have one point two holes or six holes. And it turns out that there's some properties which just depend on on on on whether you have a hole or not, or two holes. OK, up till then, most most things in physics required things to be very perfect. You know, if Intel makes a computer chip on a silicon wafer, the a speck of dust on the wafer will kind of ruin it. Right. Well, it turned out some measurements showed up in the in around 1980 that something called the fractional in the integer quantum Hall effect where you measured some resistance and it was exactly a fundamental number, which turned out to be 25,000 ohms, which is a ratio of the charge of the electron squared and Planck's constant times a whole number. And it was unprecedented that some measurement was always the same number to about six or seven digits. And it turned out to be a topological property. The quantum state can be classified in a similar way to the shape of these cups. It's not really, of course, it's not the physical surface. The big breakthrough in topology in mathematics comes from Carl Friedrich Gauss, who who discovered an amazing formula that you could actually work out the number of holes in an object by doing a complicated integral. So there's so there's a way to calculate. Yeah, you do an integral of the curvature over the surface of the and then you can figure it out. And then this gives you and he was just amazed. This always give you a whole number, which told you how many holes were on the surface. And and an analogous thing, it's not a physical surface that you're integrating a curvature over. And it's not not the not the actual curvature of of of the surface. I mean, this is a surface with has approximately a spherical curvature, but it's a mathematical analogy of Gauss's formula. OK, so let's back up a bit. Yeah. So you got us to wear that mathematically. Yeah. The donut and the cup are the same because well, they have a they both have a hole, right? And they and they're different and they're different from that. That's correct. Because there's no hole in that. And the regular the the normal matter, the non topological matter is basically got no holes in it. Now, the stability of the thing is that if you if I squeeze this a little bit, I'm going to change its shape, but I'm not going to put a hole in it. I have to do a lot of violence to to put a hole in it. Similarly, if I squeeze the bagel, it's not going to remove the hole. So the properties that depend on topology are much, much more stable. They're not affected by dirt, right? Or by by by that. Things are rough. Was affected by a grain of dust. So that turned out to be a remarkable property. So it's a different kind of matter. And it had just different properties, which were why it was unexpected in the first place. So and so you've you spent a bit of time studying these this topological matter. We didn't know it was topological at the time. It turned out it was just different. And the the interesting thing that emerges that the difference the boundary between normal matter and this topological matter has to be kind of interesting stuff happening on the boundary. And no one had noticed that before and this has emerged. And all kinds of strange things can happen. For example, in a two dimensional system, you can have signals that propagate one way around the edge with like one way, one way like light, or certain signals could move in one way only, like a one way street. And that has amazing implications for there's a lot of hope that one can harness that technologically, because if you put a kink in the pathway, the signal can't get reflected backwards. It just finds its way around. So for example, traffic flows in a road nicely because you have the cars moving in one direction on one side and the other direction on the other side. If everyone was moving without a rule of the road, there'd be a big mess. Well, in a usual piece of wire, the electrons can move in both directions. So to actually have something where you physically, where the signal gets separated spatially, which is something that happens in these topological materials is quite amazing. So there's all kinds of extremely unexpected properties that no one would have dreamed of turned up to be manifested by these strange topological matter. So I mean, I can understand, first of all, I know it takes a long time to understand at a fundamental level like what you're looking at. And you said there are a lot of strange properties of these. Is there anything that, I know it takes a long time. I mean, for instance, when Einstein was working on relativity, we didn't know that that would be used in the GPS in our phones 100 years ago, right? So can you speak to us a little bit about, I mean, are we still at the entirely fundamental understanding part of the Nobel work that you've done? Or is there, are we seeing some ways that it can be used in the everyday world yet? Well, this stuff has been growing tremendously. I mean, I just uncovered the tip of an iceberg and of course other people have gone on and covered more of this thing. And it, other ones- I mean, it's just interesting in the first place. Right, but it's really fueled, there was a very interesting proposal. That it could be used for quantum computers. So this is the bill, one of the big problem with a quantum computer is it's very fragile. The information that you try to store in a quantum state is very fragile against being a decoherence, which means it interacts with the environment and the information is kind of lost. But if you can encode the information in this topologically stable way, that it's unaffected by- So let's back up quantum computer. Let's say what it's good at doing or maybe good at doing because of the unique properties at the quantum scale and you just mentioned it can be fragile, which is called decoherence because it can be disturbed easily. But what would it be good at doing, different from- Well, a quantum computer in principle does a whole lot of calculations at the same time. Well, a classical computer just does one calculation then another calculation- So this has been a large area of interest for quite a while. That's right. Of course, one can find and propose this originally as a way to simulate quantum matter, which is a kind of circular argument, but it would be very useful. But if one could get a quantum computer to work, it would, for example, be able to factor large numbers very easily and the NSA, the National Security Agency, is investing in this because they want to know if people can make a quantum computer, it's going to break all the codes, for example. So I'm not sure that's that interesting as a scientific idea. It's why you want to break the codes, but I find it more interesting to simulate- Of course, you want to know- Scientific calculations rather than the acting, but yes, one could do it. It's not really clear what one, what one, all the things one can do with it, but anyway, it's viewed as the future of computing. So understanding now, I'm going to say this incorrectly, but the area that you're studying, that's more stable in certain ways at those interfaces between classical and quantum, have I got that right? Well, the- You explain it. You have interesting extra degrees of freedom at the interfaces, and also you can have little vortices. And in fact, Alexey Kiteyev, who's now at Santa Barbara proposed around 2000, that you could make a stable quantum computer out of topological matter. And then, which is very, still it was at a theoretical level then, but a lot of topological matter suddenly got discovered around 2007, 2008. So some of these old toy models that I and others had worked on, they'd been very theoretically interesting, but and some examples have been found in extremely high magnetic fields that weren't practical for much, but suddenly it was realized that extensions of the art of my ideas by others to three-dimensional systems also worked, and then people realized, my gosh, there's all these materials around that we never looked at closely enough, and they turned out to be topological matter. And once you've got fancy mathematics, you've got little kind of toy models that you can do calculations with and actually show that something's possible, and then real materials, those things come together, it's fueled a huge explosion of this. And in fact, Microsoft are now putting quite a lot of effort into funding. I think it's called Myerana Wires, which is a proposal for topological properties of some little indium and Timonite whiskers, which kind of grow little crystals that grow like a hair. And you can make, and there's a very interesting proposal for that you can do this quantum stuff with it. So let's get us, I mean, I'm always interested in how long it takes. I mean, obviously, even if, like me, we're not all quantum physicists here, we're getting the sense of how complicated it is to tease out the different properties. When did you begin the work that led to your Nobel Prize? So how long has the arc so far? And you said it was the tip of an iceberg and it's begun to explode. There were only two pieces of work which I didn't understand were connected in any way, in fact. They're just two different kinds of topological matter, one in one dimension in around 1980 and the other one around 1988. And I didn't even see the connection. It's just that later, people have realized, brought this to a, realized as a whole general kind of framework for thinking about it. It's just like the blind men with the elephant, you're getting different pieces of how the... Well, just so that it takes time to see the generality of the principle, right? And it's just really changed the way, it's actually changed completely the way we tend to look at quantum effects in matter and there's been a huge extra impetus coming from people with ideas in so-called quantum information. So there's been coming together of different strands which have led to rather a very exciting way. It's difficult to explain how excited people have become. I mean, it's obviously quantum mechanics is something incredibly difficult to explain to people because it doesn't seem to agree with the way we see the world around it, right? But it's just amazing how excited young people have become and it's just such a thing that's become big. I'd like to spend the last few minutes talking just a little bit about that. So obviously a complicated problem, set of problems, a long journey to find things out. How do you know, so for people in the audience, how did you think about what would be an interesting problem to solve? You found something and you pursued it, how did you know? Well, I think you come across something, if you see you can understand something in some simpler way then, see some underlying principle to understand it, then some blinkers come down from your eyes and you actually see that you can understand things before you were just describing something, right? And the more one gets to a, physicists believe that the true explanation of the world is simple. At least if you could, of course, if you could reduce it down to something that looks beautiful mathematically and simple, you feel that's most likely the right answer, right? And so what's happened with this is that a whole lot of apparently unrelated and different sorts of things have got, one could now see a common framework that you understand these all as different examples of a general principle. And so that's what's really excited people about this topological matter is, it's got a, it's conceptually very simple in some sense, because mathematics of course is simple, in the end looks for simplicity, right? And to actually understand you can understand some physical reality and see that mathematics, topology is a very well-developed subject mathematically, right? So suddenly it was a surprise that you could take a piece of mathematics which was developed for completely other reasons and apply it to understanding basic properties of quantum matter basically. So I'd like to also ask you about this insight. You mentioned that you found one kind of properties at one time in the 80s and then another. You didn't realize they were connected until later. How did you come to understand that? Probably other people understood that. They understand that there were the general, that these both were systems which had interesting things going on at the edge, right? And there were some topological ideas were floating around in both of these two things. And it was probably only when the three-dimensional extensions happened, when it was generalized and a lot more topological matter was found that then people started making a systematic classification. And it turns out what I found in 1980 is somehow the simplest, something like the hydrogen atom of topological matter. It's the simplest, the most basic example. And then the later thing turns out to be a generalization of something called the quantum Hall effect which is a system which has signals that go around one way around the edge. Right, like we were talking about before. And this is now being demonstrated. Similar, it's been done first with electrons, but then there was the same principle applied to some materials used for light, so-called photonic crystals. People have been trying to manipulate the flow of light using kind of periodic structures like electrons in crystals. And so it's surprising how the same basic kind of principle gets extended to very different things. It's been seen in gases of cold atoms. It's been seen in light. So if I could generalize a little, if you don't mind, just for the people who are listening. So it sounds like you found something interesting. You followed that interest. You shared your findings, the way people in science do. Other people built on that eventually found the framework. So it sounds to me like, I mean, on the one hand, you have to be kind of willing to be wrong, going forward and exploring something. And science, it seems like a lot of times you're trying something and you might be wrong, but you try it anyway. That's one of the points of working on it. But then it seems like collaboration is really important ultimately, too, to find the broader picture. Yeah, I think one needs to, you know, theoretical physics is a very social subject. Really, I mean, there's this view of Einstein was sitting in his Peyton office desk in Zurich working out things by himself. Well, a few times that happens, but really we spend our time kind of fighting with each other or chatting, discussing. I think through getting together and discussing and trying to say, my theory is better than your theory or whatever, or explaining it. It's a, there's both competition and collaboration, but I don't think it, you know, it's a very kind of, it's a very cool subject, really. And obviously there's a barrier to getting into it. Well, you need a little math. Need a little math. But there's something for everyone there, there's experimentalists, there's people who do very fancy math, there's model builders. Yes. So I think, I love hearing what you're talking about. I think we're just about out of time, but I just like to say just in terms of some concluding thoughts, I'm really always kind of struck by how things that are very, very small can have very, very large impacts and how, you know, very large impacts. So we're looking at quantum mechanics, but also it could be ultimately potentially used for solving very large problem sets with quantum computing, perhaps, but maybe, maybe it will lead us down even many other trails because it's just really interesting to understand how the world works. And I think that's one of the great, wonderful things about science. I'm also struck by the competition and collaboration aspects. So I guess, I guess the thing I'd like to leave everybody with is, you know, to draw inspiration from kind of wild ideas sometime, to be willing to share them and you might have to wrestle with people a little bit to get them through, but I really enjoyed learning about your work. Thank you very much. Thank you. Dr. Halding. Thank you.