by Sun Han
Prof Shoucheng Zhang, a renowned Chinese-American physicist, is the JG Jackson and CJ Wood Professor at Stanford University. He is internationally recognized for his research in topological insulators, quantum spin Hall effect, spintronics and high temperature superconductivity. His notable awards include the top three prizes of international physics field, namely the prestigious Dirac Medal and Prize in 2012, the Oliver Buckley prize in 2012 and the Europhysics prize in 2010.
In the interactive session with NTU scholars and students on 26 August 2013, Prof Zhang shared his personal experience in research particularly in the field of topological insulators.
Thank you very much for the invitation. It's my great pleasure to come here to NTU. I always find one of the greatest rewards as a professor, as an educator, is to keep in close touch with young people; this is what keeps us young. This year, actually, is my 20th year at Stanford University. During these 20 years, we have done some exciting research, but what I found most rewarding was that I had some very successful PhD students. They are now all teaching in leading institutions and some of the elite universities in the United States.
Before I came here, my son had just returned from Harvard to spend 10 days with us and he told me that a good friend of his is here. I think they went to the International Physics Olympiad together; my son is around the same age as some of the CN Yang Scholars from NTU. In teaching my students, in advising my students, and interacting with my son, who is also a physics major at Harvard, I also thought a lot about how to help young people grow. Hopefully, this will become an active interaction; you have questions, I can give you some answers.
To start with, maybe I can tell you a little bit about this exciting research topic called topological insulators. I think in science, we should always be driven first by curiosity, and not think about whether something is useful or not. This topic was started by asking questions out of curiosity, looking for interesting mathematical structures. It sounds a little bit abstract but the topic itself, when we look at the subject, is a confluence of two words which usually donít seem to fit together.
Topology is a very abstract mathematical idea, which I think in today's world of mathematics is viewed as one of the highest subfields within mathematics. A few years ago, the Poincare conjecture, which is one of the most fundamental conjectures in topology, was proven after one hundred years, so it is a really exciting kind of mathematics.
On the other hand, insulators, which usually sound pretty boring, are materials that insulate and they are used for many different purposes. For example, insulators are used as a gate material to support and separate conductors without allowing current through in the semiconductor.
On the topic of topological insulators, we have somehow found a way to put these two things, these very different sounding names together. So this field is both interesting from a very fundamental mathematical point of view and theoretical physics point of view. That was what originally drove our interest and led us to conduct this research. It could be extremely useful, but it has not been proven yet.
When you look at what the fundamental driver for the information industry is, as we have today, it is something called the Moore's Law, which states that the number of transistors on the semiconductor chip doubles every 18 months. For most industries, like the car industry, the increase in productivity happens on a very flat linear scale. But for the semiconductor industry and information industry, the productivity increases exponentially, and that's driven by Moore's Law. It has been going on like that for almost 60 years.
More than 60 years ago, physicists played a very important role in kicking off the information technology revolution because we understood quantum mechanics. Quantum mechanics tells us that there are materials, and the energy levels of these materials are grouped into different bands. That is the band theory of materials. We have a valence band and a conduction band. If the Fermi level is in the middle, we have insulators; if the Fermi level lies inside the conduction band or the valence band, we have hole-type or electron-type of carriers. That should give you an idea that the densities of N-type carriers and hole-type carriers are low, and so we can do all sorts of interesting things.
When physicists invented quantum mechanics, they also discovered semiconductors, just like Bardeen and Shockley. But after the discovery, the physicists basically handed off the whole subject to the engineers because the fundamental problems were understood, and we went on to the next exciting thing that inspired our curiosity; we didnít want to touch these engineering topics, so we left it to much more capable engineers to worry about. Over the past 60 to 70 years, they have done miraculous things with it and they were responsible for these marvelous milestones.
But history has now come to a point where Moore's Law is at a standstill; it's not increasing anymore in an exponential fashion. In the early days, people thought about all sorts of reasons why Moore's Law cannot keep on going, but the engineers were so clever, they always found some way to bypass them.
Now, the fundamental problem is heat dissipation. When we devise a transistor, the energy it dissipates per computation roughly stays the same. If you increase the number of transistors exponentially, the amount of heat it generates increases exponentially too. So, if you pack more transistors, the heat generated by these transistors will also increase according to Moore's Law. This problem is preventing us from packing more transistors because eventually, it will heat up so much that the computing chip wonít even work.
For young people who want to make great discoveries, you have to be intelligent enough to identify whether weíre at the golden age of something. Earlier, I told you that 60 years ago, physicists played a very important and exciting role. Not only did we discover fundamental principles such as quantum mechanics, we also discovered practical devices like semiconductors. Now that the engineers are facing a problem that they can no longer solve by engineering, maybe the problem should be handed back to us. That is our golden opportunity. In Chinese, the word ďcrisisĒ is written as ďő£ĽķĒ, where the character ďő£Ē means both danger and risk, and ďĽķĒ means opportunity. As physicists, we are once again in an important moment in history where we can play a very significant role to really help civilization keep advancing in the information age.
When we look at the root of the issue, the reason why the chip heated up is left because of electrons. The information age is built up upon two elementary particles: electrons and photons. Communication is built on photons. Photons have very weak interaction; that's why theyíre best used as carriers of long-distance information. Information can be sent over long distances without much dissipation. However, due to their weak interaction, it's difficult to control them. Thereíre not many knobs you can turn to make photons behave differently.
Electrons are used for logic processing. The very reason we can use electrons for logic processing is that electrons interact with each other strongly. Now, when you have electrons inside a chip, it is like having Ferrari race cars in a crowded marketplace. The Formula One race is happening here in Singapore, but we have to clear all the streets in order to ensure the race can take place. If you let the world's best race cars move in a crowded marketplace, it doesnít help at all because theyíd keep on bumping into each other, bumping into impurities and so on. So you will find that the solution to the congestion of electrons inside a chip is quite simple: why donít we just build a highway? The purpose of having a highway is so that traffic moving in opposite directions can be spatially separated into different lanes. That way, you can regulate the electrons very well and there will be no collisions, no dissipation, and so on.
In society, in different nation states, we pass different traffic laws so that we can get the cars to move in different ways, right? Singapore is one of the nation states where the cars move in opposite directions, as opposed to the traffic laws of the United States; it's a different chirality compared with the rest of the world, but different nation states have different traffic laws.
So, in order to have different traffic laws for the electrons, you need a different electronic state of matter. And that's what we discovered. We discovered topological insulators, where the electrons are moving in this chiral fashion so the spin-up electrons go around only in one direction. On the right hand side they only move forward, and on the left hand side they move backward, and vice versa for the spin-down electrons. In order for such things to happen, just from the words I used to describe it, you know you need something which looks like the spin of the electron; it is fundamentally correlated with its orbital motion. That's a form of interaction called spin orbit interaction.
So, not only do we have this idea that maybe we can get the electrons to move in a highway system, but we have some hints of where and what kind of fundamental interaction can make this possible. And that interaction is the spin orbit interaction, because the spin direction of the electron dictates how it moves around in the material. And that, roughly speaking, is the topological insulator that we have discovered.
When I was a student, I was always very interested in reading journals like Physics Today and Scientific American... For those who are interested, you can read the January 2010 issue of Physics Today; there is an article which talks about topological insulators in language that should be understandable to undergraduate physics students. We also have an article in Review of Modern Physics which goes into more detail. Does any one of you watch the show Big Bang Theory? Actually in 2011, we were on Big Bang Theory — when Sheldon Cooper walked into the lecture hall, he started talking about topological insulators. He asked whether anyone had heard about topological insulators and better yet, whether they understood what topological insulators were. And everybody raised their hands. This was a moment. As a scientist, you mostly lecture in some universities, and you have a student audience of maybe 100. But suddenly, this buzzword that we invented reached 40 million viewers with one episode instantly, and that was an exciting moment.
That is basically the story of topological insulators. The physics is so interesting and so exciting because this type of mathematical concept is purely conceived in the abstract mind. The field of topology was developed a hundred years ago and I think for mathematicians, their most fundamental guiding principle is the sense of beauty they perceive when they conceive an idea.
So what really separates good mathematics from not-so-good mathematics? In physics, if I write a law, I can check experimentally whether this is true or not. In some sense, physics is about truths, whether something we think about fits nature or not. But in mathematics, they can invent an axiomatic system that is totally independent of the way of observing nature. Euclidean geometry, for example, was discovered in exactly this manner; Euclid was of the view that two parallel lines in our world will never intersect and therefore he postulated these axioms. But one day, some mathematicians came and said, what if I move these axioms in a strange new world? That lay the foundation for Riemannian geometry.
Just as mathematicians experienced a kind of excitement when they conceived ideas of Reimannian geometry, we were also excited upon discovering topological insulators. Of course, for mathematicians, their judgment of what is good and what is not may be more subjective, as their inspiration is drawn from the beauty of mathematics. But when Einstein needed to formulate his theory of general relativity, he found that he couldnít exactly borrow the framework of Riemannian geometry, so one of the greatest moments in the history of physics came when Sir Arthur Eddington conducted an experiment and confirmed Einstein's theory of relativity.
So, to a much lesser degree compared to Einstein, but I would say in roughly the same flavor, the discovery of topological insulators is somewhat similar to the discovery of the theory of relativity. Einstein only used geometry, but when you ask any mathematician, they will say topology is much more fundamental than geometry. The fact that topological concepts, which were conceived purely from the beauty of mathematics, were discovered to be true, is in itself a tremendous moment in physics.
Such discoveries rarely happen in other disciplines. Usually, most other disciplines are a lot more empirical in nature. They do some experiments, they discover something randomly, something different, and even when they try to explain them it doesnít appear to be as elegant as the laws of physics. What excites me about physics, what I try to communicate with this sense of excitement to younger people is that over and over again, it happens throughout the history of physics that ideas conceived of beauty always turn out to be true at the most fundamental level. And that, to quite a nice extent, is what happened in topological insulators.
Taking the areas of condensed matter physics and material sciences as an example, it is mostly true so far that other disciplines were discovered accidentally, such as superconductivity, quantum hall effect, superfluidity; even magnetism was discovered by the Chinese 2,000 years ago, and so on and so forth. In all these cases, the empirical knowledge came before the abstract theory. But in the case of topological insulators, it is a singular example wherein we conceived these ideas mathematically, in abstract and theory, into six predicted materials. The mathematical framework was so powerful that it guided us to predict an actual material called mercury telluride (HgTe) and anticipate under what kind of circumstances it would show topological insulator behavior. One year later, it was proven experimentally in Germany.
This feeling of excitement is on a similar scale to when Einstein and Eddington discovered relativity, but the sense of excitement if you are the one who made the discovery... you can feel pretty proud that the understanding of nature has advanced to such an extent that this kind of prediction becomes possible.
You were talking about spin polarized currents, but how do you link this to solving the problem of Moore's Law?
Very, very good question. First of all, if you have these spin orbit coupled systems, a lot of material has strong spin orbit coupling; even gallium arsenide has strong spin orbit coupling. In topological insulators, it is a spin orbit coupled, but to such a strong extent that the electron current only moves on the boundary of the system. So if you have a three dimensional material, the boundary will be the two dimensional surface. If you have a two dimensional material, the boundary is one dimensional. So that really looks like the lane on a highway, because if you have a square-like material on the right side, you are moving forward, and on the left side, you move backward.
There are two different states you can talk about. One is called quantum spin hall effect and the other is quantum hall effect, or more recently, that's also the theoretical prediction we tried to get rid of. Quantum hall effect was originally observed in intensive magnetic fields, but if you have spin orbit coupling and magnetism, you can have what is called the quantum anomalous hall effect. That is the closest analogy to a highway system, where the overall sense is picked by the magnetization, and electrons on the right side will move forward and the ones on the left side will move backward.
If you donít have magnetism, you will get a pure topological insulator; a non-magnetic topological insulator, that is. Then you will have this spin polarized situation where up-spin is probably like the one-traffic rule. It's like up-spin is Singapore and down-spin is China; they have two different traffic rules. But it turns out that there's a fundamental reason to explain why even though they are moving along one side of the street, they cannot collide.
Maybe I should conduct a poll among the students: when you learn quantum mechanics, what appears to you as the most mysterious aspect of quantum mechanics?
Feynman used to say, whoever understood quantum mechanics the first time he was learning it must be an idiot somewhat. That makes sense. So something about quantum mechanics must be deep and mysterious, right? Like the Heisenberg uncertainty principle, and so on. There are a lot of things that are mysterious about quantum mechanicsÖ Superposition is mysterious, and what else? Collapse is mysterious, entanglement is mysterious, identical particles are also mysterious.
For me, when I was a student, the most mysterious thing about quantum mechanics is this very, very strange fact: if you have an electron which carries spin one-half, and then you rotate it by 2, the wave function does not come back to itself. Instead, it acquires a minus sign. That was deeply, deeply mysterious to me as a student; it was the most mysterious thing.
Incidentally, it's exactly this funny sign which prevents two electrons moving on the same side of the lane from colliding with each other. If they collide or if an electron hits something and tries to turn back, it turns out that thereíre always two different paths of turning back and they differ in the electron spin configuration by 2 rotation. That 2 rotation gives you a minus sign and that always leads to a destructive interference if you try to scatter them backward. Because only the spin-up can move forward and only the spin-down can move backward on one side of the lane, if you try to move back, there will always be a minus sign associated with this; it's a funny sign. This really gave people a sense of why topological insulators are so fundamental. It is related to something very, very fundamental to the law of quantum mechanics.
Since 720o rotation is related to the topological structure of the Mobius stripe, in this way, does the theory of topological insulators have any influence on the foundation of quantum mechanics?
Very, very good question. I donít know how familiar are the rest of the people here with quantum mechanics... Has anyone heard about a theory of quantum mechanics called Kramers Theorem? Did you learn that in quantum mechanics class? I find this is always a problem with quantum mechanics textbooks; a lot of them skip over Kramers Theorem. The discovery of topological insulators is related to this fundamental theory of quantum mechanics.
Kramers Theorem says that in a time reversal invariant system, but with spin one-half particle, the energy level always has to form doublets. And that doublet theorem says that when at that energy level, you have a conduction band, you have a valence band, and usually even in trivial insulators you can have some surface state, and that will be some state that comes from the conduction band and then goes back to the conduction band, comes from the valence band then goes back to the valence band. Actually, in today's semiconductors we already use this kind of surface state. Weíre trying to induce this kind of surface state by some kind of electric field, but they always come from conduction band and go back to conduction band, they come from valence band and go back to valence band.
What's different in the topological insulator is that this surface state connects the conduction band with the valence band. But if they connect, they will cross at one point and the point at which they cross is a time reversal invariant point, and Kramers Theorem forbids that to avoid crossing each other. If they avoid crossing each other, they would come back, from conduction band back to conduction band, from valence band back to valence band. But Kramers Theorem says they have to cross, and that is fundamental. The reason why we have Kramers Theorem is exactly related to this fact that when you rotate spin one-half particle by 2, itíll give you a minus sign. In one microscopic world, we can also do a time reversal operation. If I play a movie, I can just turn the movie backward, and play the movie backward. But in a microscopic world, if you have time reversal symmetry, and you reverse your arrow of time, then past becomes future, and future becomes past. But if you do it twice, then past becomes future and future becomes past, and nothing changes. So in your microscopic world, if you do the time reversal test twice, it's like you didnít do anything.
But in the microscopic world of the electron, imagine you are doing the time reversal operation on the spin of the electron. Time reversal changes the direction of the spin because the spin is like an angular momentum. Angular momentum is like r cross p, r is invariant and the time reversal, but p has a time derivative so it's r and the time derivative. Spin is r in time reversal, so we find that when we reverse the arrow of time, the spin has to change to the opposite direction. If I reverse the arrow of time once, up-spin becomes down-spin, and if I reverse it again, down-spin becomes up-spin. So if the spin acts like a little arrow in a microscopic world, it's like we have not done anything. But if you did that to the spin of the electron, youíll see it rotating by exactly 2, which gives you a minus sign. So for spin of the electron, when you do the time reversal operation twice, itíll give you a minus sign, and that's the reason for Kramers Theorem. These things are all connected to each other in a very deep and profound way, such that when you learn quantum mechanics for the first time, you donít really appreciate how profound it is.
Prof Peter Preiser (then Director of CN Yang Scholars Programme): Maybe I will introduce a slightly less technical question, because not everyone here is an expert in quantum mechanics. I slept through part of my quantum mechanics, some of it didnít even exist when I last left, and I am a biologist. But I think what is common here is thereíre a lot of people who are progressing towards graduation as an undergraduate and one of the challenges is, should they continue with a PhD? What will the future bring? Is there a future for basic science? Everything is pointing in translation, you know. From your perspective, what would you advise as guidance?
I think everybody has to struggle through that. I live in Silicon Valley, and a lot of students, not just my own students, but also a lot of Stanford students have totally different aspirations; you may want to be the founder of the next Google, which is a good aspiration. I went through exactly the same struggle when I was a student.
I did my undergraduate degree in Germany. I was sent on an official exchange program from China to Germany. That was in the 1980s, and back then there were not many opportunities. At that time, I knew I had to go back to China, but not much fundamental research in physics was going on there. I was worried about this issue, and a lot of my fellow students switched to something more practical like electrical engineering, or some engineering topic which was more useful; if you build things, you can change the world more directly and physically. I was struggling with that exact issue.
That summer, since it was my first time in Germany, I tried to go around the country for sightseeing in summer vacation. I went everywhere, and I actually had no money to travel so I had to hitchhike everywhere on the autobahn, on the freeway. From this experience, I got a firsthand sense on how the German autobahn works. I went to many places, and I also spent quite some time out of my own interest to learn about European history and so on. Whenever I tour a city, I was always very happy because I learned a little bit about the history; I admired the architecture, the arts, the museums, and so on.
During this trip, the one place that made a lasting impact on me was the city called Göttingen; that is the place where many theories of quantum mechanics were discovered. I still remember the story of a beer hall where a lot of physicists had their discussions, and the first time Max Born wrote down the |(x)|2 equals to probability was on a napkin at a beer hall table somewhere in Göttingen. So in my mind, it was a very holy place. But even holier was not just the city square, the city or the beer hall itself. I went to visit a seminary in Göttingen. A seminary is a very good place for you to go and contemplate the meaning of life, to see what that is. There, you can think about what your purpose of life should be.
Gauss was a professor in Göttingen; his student Riemann was a professor in Göttingen; David Hilbert was a professor in Göttingen; Otto Hahn was a professor; Max Born was a professor and Heisenberg spent quite some time in Göttingen. So in the seminary, all these famous mathematicians and physicists were buried practically next to each other. When you look at their gravestones, it's always very simple; it states their name and the year. They only have a very small piece, but there's always written either a formula or something that characterizes their scientific writing into one simple formula.
I still remember the case of David Hilbert. Because he has done so much — he introduced 23 problems in mathematics — they couldn't fit everything into his gravestone. So the engraving was simply a quote by David Hilbert, which said "WIR MUSSEN WISSEN, WIR WERDEN WISSEN" and it means "we must know, we will know" That characterized his strong determination, and maybe he was referring to these 23 problems in mathematics that he introduced. He said we must know the answer. In Chinese we say, ďňņ≤ĽÓ®ńŅĒ. So when he died, he still couldn't close his eyes, because not all 23 (actually quite a fraction of problems) were solved by the time he died. But a lot of them, especially his favorite one, the Riemann Hypothesis, still remain unsolved today. But he said "we must know, we will know".
That tells you the meaning of life is to leave some information behind that will be everlasting. Before humans came along on this planet, there was only one way for a living thing to pass something on when the physical body perishes, and that's to pass on their genes. As you know, genes are a form of information. In the biological world that method of passing on information was possible, but it seems that in human civilization, we have an alternative way to leave behind information. We can pass information through the genes that we pass on to our children, but there's another way to create a piece of knowledge that will be with humanity forever. These guys, after they passed away, we may not be able to easily identify their genes anymore after several generations. But they each created pieces of information, pieces of knowledge, that will be, I think, with humanity until the end of time.
I always ask my students this favorite question. We can have a poll here, and that question I raised last year was very, very good because that was the year of 2012, when the world was supposed to come to an end. I asked: if you are walking toward Noah's Ark, and you can only bring one piece of paper to summarize the entire knowledge of the human civilization, what would you write on this piece of paper? Is it the name of the emperor? Is it the name of the conquerors? Would you write down the name of Napoleon? Or would you write e = mc2 that summarized the highest achievement of humanity?
I think the answer, at least for me, is pretty unique — you should carry these formulas up to the Noah's Ark. So, at Göttingen cemetery I learned a great lesson: the highest purpose of life is to leave something behind, leave a piece of information behind that maybe you created. And from then on I was determined to be a physicist without worrying about these questions about how to earn my bread. But of course I think in today's world thereíre many other ways — to be the founder of Google is a pretty cool thing too.
Some of us might not know, Professor Zhang actually enrolled in Fudan University when he was 15; he skipped the whole JC period. After that he became a full professor in Stanford at the age of 32, which is very impressive anywhere in the world. Have you ever experienced any setbacks in your research and how did you get through that?
I think most of the time when youíre doing research, you donít hear Sheldon Cooper talk about your research to 40 million people. Most of the time, you feel you are going towards a dead end, and youíre just not making progress. Before the field of topological insulators, I worked on high temperature superconductivity. So, talking about Chen-Ning Yang and so on, I think there's this ideal that's best exemplified by three unique personalities: Albert Einstein, Paul Dirac and Chen-Ning Yang; they have this deep conviction that the most fundamental laws of physics should be inspired by mathematical beauty. Einstein felt that Riemannian geometry was a good way to describe space time, and as for Dirac ó I always tell this story. Last year, I was very fortunate to receive the Dirac medal. Dirac is one of my greatest heroes, so what would you say is Dirac's greatest contribution to physics? Either the Dirac equation or the prediction of the positron, right?
Sometimes I talk to a different audience or another physicist and when I say Dirac, no one knows who Dirac is. But when I say Angels and Demons — have you guys seen the movie Angels and Demons? Or read the book? The bomb which was supposed to blow up the Vatican City was an antimatter bomb. It's the highest form of energy density storage that you can imagine. When he needed to take the square root of some equation, he remembered his high school teacher saying that when taking the square root of 4, the answer is not just 2, but also -2, so youíll always have 2 roots. From there, he figured out that all matter has two forms: either the positive form or the negative form known as antimatter. And Chen-Ning Yang is another great example of that; just by thinking about the structure of the Maxwell equation, how to mathematically generalize it from abelian to non-abelian, he discovered Yang-Mills, which describes two out of the four fundamental forces of nature.
This kind of thing was always an inspiration to me, but it does not always work successfully. I tried to apply this kind of philosophy or idea to what is viewed as maybe one of the greatest problems in condensed matter physics: what is the mechanism of high temperature superconductivity?
So I dreamt of a mechanism using the beauty of the symmetry to say that high temperature superconductors always evolved out of the parent state, which is actually the most counterintuitive. You would think that if you wanted to discover superconductivity, you start with something which is a pretty good conductor and then you do something to it and it becomes a superconductor. But when Ben Motts and Miller discovered superconductors, they started at the worst conductor which was a piece of ceramic insulate, and then they did something to it and it became a superconductor. That empirical observation always inspired me and I said that the antiferromagnetic insulator and the superconductor is basically one and the same thing and theyíre unified by symmetry which I introduced that unifies antiferromagnetism with superconductivity, called the SO5 symmetry. I first discovered this in 1997.
At first I was quite lucky. At that time, I was still a pretty young professor and the field was what everybody viewed as a very important field, so a lot of very senior theorists were already working on it. I was a full professor by then but I was still young and so... But I had this idea, and when I conceived this idea I was really, really was fascinated by it, and I was sure that I had solved the entire problem of high temperature superconductivity. So I wrote a paper called the SO5 symmetry between antiferromagnetism and superconductivity and I took the bold step of sending it to a science magazine.
Everybody at that time told me: Shoucheng, you have absolutely no chance, every senior theoretician referee will instantly reject your paper; how can they tolerate competition? And in condensed matter physics, people didnít think this kind of, Chen-Ning Yang, Dirac, Einstein approach would ever work because there was no other example of that. Everybody said this would be instantly rejected. But not only did I decide to send it out to the referees, which is already a big deal, the two referees came back after one month, instantly accepting my paper with some minor modifications some minor modifications. That was really... I wrote like five pages of science magazine pure theory paper, that's also quite unheard of. Not only unheard of, it has never happened before in the field of condensed matter theory, to have such a long theory paper published in a science magazine.
But after its publication, that's when the attacks started. All the senior theorists attacked me, saying this cannot be true. Usually you get two types of reactions this field; either "it's wrong" or "I did it before" I think I got maybe 70% saying it is wrong, and the other 30% saying they had already said the same thing before. So the paper had some success but basically it didn't really go anywhere. Well, it did go somewhere; they still referred to it — I think the paper had 700 citations already. There were people basing their literature on it, and it was viewed as one of the theories. But it was clear to me that it would not be universally accepted. I wanted to do something; I was really inspired by my mentor's style, that I think if it's about fundamental physics, it should be done this way. You can see beautiful mathematical ideas and nature will realize that somehow. But I fell down for a few more years and it was pretty clear to me that it would not be universally accepted.
At the time, you could have two kinds of reactions: you can keep on working on it to try to push it through, which would be a nice thing to do, but then you can say, well maybe it has never been successful before. In what is called fundamental physics, in Einstein's general theory of relativity, in Yang-Mills, in parity, in Dirac's examples, thereíre a lot of examples that you think about, dream about, about beautiful ideas and nature instantly realizes it. But in condensed matter, it has never happened before. I tried and it didn't quite work and I thought maybe I should just give up the whole approach. That was my struggle. But eventually I thought, I can have many other opportunities but if I stick with physics, the only thing that excites me is to pursue physics in that stand. So I tried to look for some other directions, and eventually I discovered topological insulators, which I think everybody would say is a very good example of this Dirac style of research.
In the field of quantum field physics especially particle physics, there have been a lot of theories proposed and one theory that was quite hot during the 1980s or the late 1970s was bootstrapping. But that fell out of favor because of Quantum Chromodynamics (QCD). Of course, QCD is the most popular theory now, but is there a slight chance that this theory isnít exactly what the whole picture is, and there are quite a lot of things to be explained and it's just part of the picture? Maybe bootstrapping is correct in some ways and QCD is also correct in another way?
First of all, bootstrapping is not incorrect; it's just not very powerful. The idea was, but I think the reason was because that field had a lot of very smart people for quite a long time. It has some mathematical elegance, and some complicated stuff too; I especially like the "nuclear democracy" it always sounded very profound!
But eventually, I think it was not powerful, and that's the problem. QCD is not an understood theory — one of the seven Clay Institute of Mathematics problems including the Riemann conjecture, is the Yang-Mills problem: to prove confinement. And the Yang-Mills theory... it's mathematically not understood why quarks are combined. We have some ideas but we don't know, because the theory is strongly interacting so we can explain things at very, very high energy when the coupling is weak, but we cannot explain things at lower energy when the couplings are strong.
As a mathematical problem, a lot of people are still working on it and new insights keep coming up, so if you do not solve the Yang-Mills theory, but the supersymmetric version of the Yang-Mills theory, you can actually more or less solve it mathematically; it's absolutely beautiful, the solutions by Seiberg and Witten. And then a lot of the ideas about duality, monopoles, can be checked.
Another thing is when you get these theories you cannot solve analytically. A lot of people put them on a computer and IBM before they built the Jeopardy machine. Actually, the Jeopardy machine was motivated by the Yang-Mills question; they tried to solve QCD. I forgot the actual name, it's always Deep something, Deep Blue, Deep something; but at that time they built a QCD machine to try to solve it. I think people accept this fundamental theory because you can compute on a computer and what comes out of the computer is pretty sensible. You can just solve it in close analytic form.
So, going back to the topological insulator. When you mentioned this spin orbit interaction, how did you envisage the information encoded? What is the classical? It's going to be...
When we talk about potential applications of topological insulators in information processes, it's still classical but it could solve some problems in dissipation. There's also a proposal to use topological insulators for quantum computing and that has something to do with the beautiful idea that topological insulators can host a novel type of excitation called Majorana fermions and they can lead to topological quantum computing. But that's much, much farther away. Back to solving the problem of heat dissipation; in the US there's a very famous funding agency called DARPA (Defense Advanced Research Projects Agency). They were the ones who funded the Internet. They are funding us too I'm leading a big DARPA project in the US; they are trying to make topological insulators useful, but not for quantum computing.
You mentioned previously that it would take at least five years for topological insulators to be scaled up for industrial applications. Have you ever considered collaborating with industrial R&D or being involved in some startup company?
Indeed, in the States, quite a number of projects from DARPA have been successfully spun off into startup companies. DARPA has a very good system. If we look at funding agencies in the States, for example, the Department of Energy or National Science Foundation, the basis of project funding is not so much the possibility of industrial applications, but rather the intrinsic scientific value of the project. As for DARPA, it mainly funds projects that have the potential to be commercialized. DARPA is willing to take the risk before private capital comes in. So if the topological insulator project shows clear promise in the next two years under DARPA support, private capital will then step in and take care of subsequent commercialization.
Do you think the scarcity of raw materials will be a great limitation in the commercialization of topological insulators?
That is a good question. So far, the materials that we use are relatively rare. But just recently, a Chinese professor Rui-Rui Du has confirmed the existence of a more commonly available material, which we had predicted theoretically in 2008. This material, InAs/GaSb, is already widely used in the semiconductor industry. So in the next five years there still remains a lot of work to be done, but this can probably be done concurrently. While current topological insulator materials used might still require some special treatment, we can figure out their working principles. At the same time, we should continue the search for new materials. Hopefully, more commonly available materials will be found. It would definitely be ideal if those materials can work with current semiconductor technology as well.
A lot of young people nowadays may find it difficult to decide if they should focus on theoretical physics research. You also mentioned previously that it requires a great deal of determination for young people nowadays to decide to focus on theoretical physics research. What would you advise students if they want to work on theoretical physics? What kind of qualities do they need to have in order to do well in this field?
First, I think you need to feel the beauty of it. If there is an existing idea that you are interested in and that many others are already working on, it can be quite exciting to discuss your research with others. But this kind of work has limited scientific value, as the basic framework has already been laid by others. If you wish to create a framework of your own, it will definitely be a lonely path. So under such circumstances, you have to have some sort of drive, some sort of faith, some sort of belief. This takes some character indeed. But I think for students, they can start small, and gradually progress to greater success. In the process of learning, I believe a good student of theoretical physics will be particularly excited and inspired, especially by the stories of scientific legends like Dirac and Chen-Ning Yang, and these stories will have a lasting impact on their character and style. So it is good that we have programs such as the CN Yang Scholars Programme in NTU, to inspire future generations of students with the spirit of these legends.
Indeed. Theoretical knowledge is in fact greatly critical in practical industries and we need to attract more young people to this significant field. ďDo you agree?
I agree, and I think it is definitely possible to do so, especially as the wealth of our society as a whole keeps growing. We see this trend in the States as well: first generation migrants from mainland China were focused on making a living and would tend to choose degrees with practical value in order to gain a foothold. However, the second generation no longer needs to worry about such issues. This gives them more freedom of choice and I believe more and more will be encouraged to study theoretical physics.
You have been interested in the arts, philosophy and history since young. Do you think this has had any impact on your research?
Yes, it does have a great impact on my research. This is something I have been thinking about. Let's look at history for example. We are not talking about the history of science, but just normal history such as European, or Chinese history. Do you think it is relevant to physics research at all? Perhaps at first glance it does not seem so, but if you look at history you will see a fundamental problem: what is left behind, and what is not.
Frankly speaking, in the field of scientific research, once you get to a certain level everyone is pretty much equally capable. Theoretical physicists are good at logical derivation, while experimental physicists are skilled at handling instruments. But if all these researchers are of equal capability, why is it that only some are able to go beyond and reach a higher level? I believe this is beyond the realm of physics. Let's say there are ten paths in front of us. You might pick one path, while I may pick another. But in the end, the one who succeeds isnít necessarily the more capable one. He simply has chosen the right path. In this sense, scientific research is in fact greatly similar to the arts: it's all about taste. In some sense this also relates to history, especially in the study of the choices made at crucial junctures throughout history. Knowing that may help when you are making your own choices.
Indeed. Many things may seem like random events due to chance, but are in fact due to knowledge accumulated over the years. What are your thoughts?
Yes, indeed. I often tell this story of my early childhood enlightenment. As this was during the Cultural Revolution in China, scientific books werenít readily available. I would read any book I could find in the attic of our house then. Even though my father had studied engineering, all my uncles were in the field of humanities, and the books they had left behind were all on European philosophy or art history and so on. And so, the bulk of my initial education ended up centered on the humanities. Even now, I still greatly enjoy these.
Sun Han is a Senior Editor at World Scientific Publishing. For more information about the article, please contact Dr Sun at email@example.com
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