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Credit: Brigitte Lacombe
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Interview of Charles Kane by David Zierler on May 13, 2021,
Niels Bohr Library & Archives, American Institute of Physics,
College Park, MD USA,
For multiple citations, "AIP" is the preferred abbreviation for the location.
Interview with Charles Kane, Christopher H. Browne distinguished professor in the Department of Physics and Astronomy at the University of Pennsylvania. Kane surveys the interplay of theory and experiment in condensed matter over the course of his career, and he recounts his childhood in Iowa City, where his father was a professor of civil engineering. He discusses his undergraduate work at the University of Chicago, and the formative influence of Tom Rosenbaum on his interest in theory. Kane describes his graduate research at MIT under the direction of Patrick Lee to focus on mesoscopic physics, and he conveys the excitement surrounding High Tc. He discusses his postdoctoral work at IBM to focus on free-floating theory and he explains the exciting prospect of joining Penn which had a strong condensed matter group. Kane describes Steve Girvin’s role in introducing him to the quantum Hall effect and his key collaboration with Matthew Fischer on calculating electrical conduction when a one-dimensional conductor has a weak link in it. He discusses his subsequent interest in carbon nanotubes and graphene and his realization that graphene should have an energy gap. Kane describes the feeling in winning both the Dirac and Buckley prizes and he discusses advances in the phenomenology of topological insulators. He explains the controversy surrounding Majorana modes and he discusses the recognition by the Breakthrough Prize for his work in topology and symmetry. At the end of the interview, Kane reflects on the growth of his department at Penn and he explains why improved applications of quantum mechanics and improved understanding of quantum mechanics must progress in tandem.
OK, this is David Zierler, oral historian for the American Institute of Physics. It is May 13th, 2021. I am so happy to be here with Professor Charles Kane. Charlie, it’s great to see you. Thank you for joining me today.
Thank you, it’s great to be here.
Charlie, to start, would you please tell me your title and institutional affiliation?
I’m a Christopher H. Browne distinguished professor in the department of physics and astronomy at the University of Pennsylvania.
Who is or was Christopher H. Browne?
[laugh] OK, so, I actually never met the man. He was an undergraduate at Penn. I think he graduated in 1969. And he went on and did very well for himself, making a fortune in investing, and he became a very generous donor to the University of Pennsylvania, and was a member of the board of trustees. And, so, he endowed several professorships in the School of Arts & Sciences. I think there are 10 of them, and so I have one of those.
Charlie, just as a snapshot of where the field is right now for you more broadly among your colleagues, what’s going on in condensed matter theory these days? What’s exciting?
Well, you know, condensed matter is a very, very broad topic, which covers, many aspects of matter. And there are two broad categories. There’s quantum matter, and then there is more classical matter. And, so, there’s a lot going on in quantum matter, understanding the implications of quantum mechanics for materials and things that people can make. And then there’s also a very broad class of problems in what people call soft matter, and that borders then on biology. And, so, there’s a huge span of topics, and it’s too much for one person to be able to cover.
Charlie, this might be as much a nomenclature or sociology question as it is a science question, but in your career span, was it one solid state, and it became condensed matter, or that transition and what that means, particularly with the rise of soft matter as a mature field in its own right, did that transition already happen?
Well, in my career, condensed matter had already started taking over as the nomenclature. But that was before the advent of soft matter. The term “condensed matter” was actually coined by Philip Anderson. And this was a little bit of a reaction to solid-state, you know, the solid-state which seemed more specific about solid materials. And of course, Anderson was a very deep and broad thinker, and he realized that these ideas had a much more general applicability. And, so, when I was an undergraduate, I took a solid-state physics class, and that was my first introduction to that. But when I went to graduate school, the group that I entered had a title on the door that said, “condensed matter theory.”
And that’s what I’ve identified with for my entire career. But, certainly at the beginning, I thought of that as more quantum and that has grown and bifurcated in many directions over the last 30 years, 40 years.
Charlie, this will be a theme that I think repeatedly crops up in our conversation, and that is, from your perspective, the interplay between the world of experimentation and the world of theory, and moments in the field where one guides the other. So, just generally in broad historical brushstrokes, when for you as a theorist have advances in experimentation really been efficacious to the kinds of things that you do?
Well, for me, the root is always [laugh] experiment. The formative example for me for many of the things that I’ve come to know and love is the quantum Hall effect, which was really discovered as an experimental observation, This was back around 1980 when it was observed that the Hall conductance of a two-dimensional electron gas had this very precise quantization. And, you see, at the time, what people were trying to do is they were trying to understand the fundamental properties of semiconductor devices, and that’s an important technological problem. And, so, they were trying to understand the basic science. And, so, there’s this phenomenon that arose from that, and that posed a question for giants in theoretical physics to think about. And what emerged from that was a set of ideas, and that set up this sort of glorious interplay, back and forth, between experiment and theory. And, so, that to me is the way things should work [laugh]. And that’s been a recipe for a tremendous amount of progress. Now, sometimes there are some things that come up as a theoretical idea first, and then that motivates experiments, and there are other things that come up as experimental observations that then motivate new ideas. And, you know, usually, it’s the experiments that come first. Sometimes it’s the theory that comes first.
Charlie, as you mentioned, condensed matter is so broad, many people are surprised at all of the value that condensed matter has in other branches of physics. So, for you specifically, what are some of the other subfields in physics that are most useful for you, and, conversely, where do you see your own research as very valuable for many of your colleagues in the department?
OK. So, look, I sort of feel like I straddle [laugh] some very diverse areas. On one hand, there is the physics of materials, which borders on material science and engineering, which, is really concerned with what kind of materials can you make? What can you do with them? And, so, that’s one, direction that the things that I’m interested in has an important impact on. And then there’s another direction as well, which is the sort of more abstract mathematical physics: the ideas of what kinds of phenomena can theories describe? [laugh] And, so, you know, this is the kind of thing that, for instance, high-energy theoretical physics is very concerned with. They’re very interested in understanding the sort of structure of theories of physics, the structure of field theories. And this is something where, what I enjoy doing is being able to borrow ideas from that collection of work, and apply that in another direction. And there have been some ways where ideas that have emerged from thinking about materials have then gone back to inform the more abstract mathematical physics. And, so, in a way, I like sort of living in that middle world where I have, you know, connection to both of those sides, if I can. It’s kind of hard, though. I mean, there’s this big disconnect between people who spend all their time thinking about abstract theories, and people who spend all their time thinking about nitty-gritty materials. And it’s hard to connect those. And, so, that’s, in the best of all possible worlds, that’s where I would be making that connection.
Charlie, as we’re still—still—sitting in our home offices in—
—May of 2021, the question is begged, how in this past year-plus in the pandemic has your science been affected one way or another? In other words, as a theorist, perhaps you’ve had more bandwidth not commuting, not going into work on some long-standing problems. But, on the other hand, in what ways has not having had the opportunity for physical interaction, in-person interaction with your colleagues, and the spontaneity of just seeing people—
Yeah, I really—
—how has that affected your science?
I really, really miss that.
You know, of course, I talk to people on Zoom the way I’m talking to you. But that’s always with an appointment [laugh], you know, and usually there’s an agenda. And what I really miss is being able to just on the spur of the moment have conversations with my colleagues. I miss going to conferences where I have friends all over the place that I like talking to. And, a lot of times, I learn things by doing that, and there’s a back and forth, and I really deeply miss that. And I [laugh] very much look forward to getting back to that when things return to normal.
What’s the game plan for Penn at this moment? Is in-person, in-class for September on the schedule?
Yeah, it is—so, fingers crossed. I mean, my hope is that if things continue trending in the direction that they’re going in, that we’ll be able to do that. It’s not going to be completely back to normal. But, hopefully, we can be in-person, and we can start having more regular interactions that aren’t through a computer screen.
Well, Charlie, let’s take it back to the beginning. Let’s start first with your parents. Tell me a little bit about them and where they’re from.
[laugh] OK. So, my father grew up in Brooklyn in the Depression. He was 16 years old when World War II started, and like everybody in that era, he immediately joined the ROTC [laugh], and was then in the pipeline to go into the war. So, he had the good fortune—he was in the pipeline to go to the Pacific when they dropped the bomb, So, fortunately, the war ended before he got over there. But he still went over to the Pacific, and he was involved in the aftermath of that. Afterward he went back and went to college at City College, and studied engineering, and became an engineer. And, in the early 1950s, took a job in Germany, working as an engineer for the army in Würzburg. And, at that time—and so this was—I think back at it. It must’ve been an incredible adventure to be in your 20s, and go over to the immediate aftermath of the war, and live there. And, so, he was there working as an engineer, and that’s where he met my mother. So, my mother had a very different background. She grew up in a little town in Nebraska, a little town called Wymore, Nebraska. Her father was a banker in—a little town banker. And, so, she was an artist. She studied art at the Art Institute in Chicago and was sort of that type. And, so, she also had this worldly adventure at that time to go over to Germany in her 20s to live there. And, so, my parents, they met there, and they fell in love, and they got married, without meeting each other’s parents. So, I think it was a little bit of a scandal [laugh] in my mother’s family [laugh]—
—that she went off and met this guy from Brooklyn, and [laugh] married him. But that’s the way it evolved. Then they moved back. And, so, my father then worked as an engineer for a while, but then decided he wanted to go into academia. And, so, he went to graduate school, and ended up becoming a professor of engineering, civil engineering, first at the University of Illinois in Urbana. That’s where I was born. I was born in Urbana. I only lived there for two years, so I don’t really remember it, although I have—I did go back. Now I have friends in Urbana, and so I went back and was able to see the house that I lived in when I lived there. But, so, I was there, and then we moved to Iowa City, Iowa, and that’s where my formative years were. So, I grew up in Iowa City.
Charlie, was your dad’s parenting style such that he involved you in his research? Did you have an idea first—
—[??] had to be a professor, what civil engineering was?
[laugh] Well, I distinctly remember when I was a young child, I sort of knew that my father was an engineer, but I was confused about what that meant. I had it confused with a railroad train engineer—
—and that’s sort of [laugh] what I thought it was. And then, you know, as I got older, I knew my father was a professor, but he didn’t really talk about his work very much. It wasn’t something that I was really aware of at the time. Even in high school, I didn’t really engage with that too much. I mean, he was always very supportive of me in terms of giving me math lessons when I was a little boy and teaching me things. And he was always very encouraging and he always expected me to excel. But I didn’t really have much of a conception what he actually did [laugh] when I was growing up.
Charlie, where would you say you spent most of your childhood?
Where did I spend it?
Iowa City, Iowa, that’s where I spent all of my childhood basically.
Did it feel like a college town, your upbringing?
Oh, very much so, yeah, it was a college town, yeah, yeah. And, you know, it’s a very nice college town. The University of Iowa is there. It’s—I have very, very fond memories of living there. Of course, by the time I got to be 16, 17 years old, I wanted nothing more than to get out of there because it is a very small town. And, you know, I knew that my father was from New York City, but we didn’t travel very much when I was a kid. It was a different era. People travel much more than they did now. We would—oftentimes, our summer vacation would be driving to Nebraska [laugh] to visit my mother’s family. And, so, we didn’t go very far. So, I didn’t really—I hadn’t really traveled very much, and so I had this envy of, big cities and places to go. And, so, I really wanted badly to get out of Iowa City when I was that age. But it was a—as a place to grow up, it was a very nice place. It was safe. I had free run of the whole town. I had a freedom that you wouldn’t have had growing up in a more, you know, a populated place.
Sure. Charlie, when did you start to get interested in science yourself?
Well, when I was a young kid, I always loved math, I mean, and that was really where it started with me. Even in elementary school, I remember just loving math. And I was pretty good at it, so, and I had some teachers that recognized that I was good at it, and they encouraged me. And, so, I always—that was always part of my identity, that I was kind of good at math, and I really—I would spend time thinking about it a lot. And, so, that was really my first love, and that went all the way, starting in elementary school. It went all the way through high school and, you know, starting college that what I really liked was math. I went to the public schools in Iowa City, and the math at the public schools wasn’t that great. So, I finished the public school math by the time I was in 10th grade or so. But I had the opportunity to take classes at the University of Iowa, so that’s what I did. And, so, by the time I finished high school, I’d basically taken most of the elementary college math courses that one would take. So, I knew calculus and linear algebra and some differential equations by the time I went to college. And, and I thought maybe when I went to college, I would study math. And, so, it was really when I went to college that I started realizing that the things that I liked about math were more the way a physicist thinks about it.
Yeah [laugh]. Charlie, what kinds of schools did you apply to for undergraduate?
Well, I didn’t apply to that many places. And, again, in my family, both my—I have an older brother and an older sister, and both of them went to the University of Iowa, and that was …you know, we weren’t a wealthy family, and that was basically what my parents felt like they could afford. I was the last one, and so they decided that they could afford to send me to a private school. So, I was the first one. But I didn’t have a very [laugh] wide worldview, so I didn’t apply very far. The places that I applied to were Northwestern, Washington University in St. Louis, and the University of Chicago. And what I really wanted was the University of Chicago.
Yeah, and you were in the Midwest—
You know, I didn’t really think much for it.
You were in the Midwest [??].
I mean, it was all midwestern, and it didn’t occur to me to go further.
Somehow, that was the mindset that I was in.
But you could always drive home for holidays from those schools.
Well, right, yeah, it’s just—I don’t know. It just wasn’t on my radar at the time to go further. But, I very much wanted to go to a place that was a big city. And, so, what are the big cities? [laugh] There’s, you know, near Iowa, there’s Chicago and St. Louis, OK. Those are the nearest [laugh] big cities. But I had a friend who had an older brother that went to the University of Chicago, and so through that, I knew a little bit about the University of Chicago and had learned that it’s a pretty high-level place. And so, I had my dreams and hopes invested in that, and I was lucky enough to get in.
And it would’ve been, what, 1981 when you started?
I graduated from high school in 1981, that’s right—
—yeah, more than 40 years ago [laugh].
[laugh] And did you declare the major in math right away? KANE: No, I didn’t declare a major. I was unsure whether I wanted to do math or physics at the time. So, I was—I think I said both. So, I took a physics class. I took the honors introductory physics class, which is—it’s a wonderful class. It’s a class I’ve actually taught at the University of Pennsylvania many times. And, so, that was the class that really sort of inspired me in physics. So, when I got to Chicago, I took a class in analysis. That was the math class that I took. And I took physics. And, the analysis, it was really an eye-opening experience for me. This was the first time I’d experienced a math class that was for mathematicians.
Well, yeah, exactly. And, you know, it was hard for me, and I worked very hard at it, and I liked it. But, somehow, there was so much emphasis on proofs [laugh] and—whereas what I liked about math was just understanding it, you know, the sort of gut-level understanding. The thing about math is that you can know that you’re right [laugh], and I really liked that feeling. Now, of course, mathematicians, they know—they have ways of knowing they’re right as well, and proofs are part of that story. But I found that the way a physicist thinks about math, there’s this sort of gut-level understanding that you develop…you know, I think in terms of pictures, that’s what really appealed to me. And, so, over the first year or two, I got a little bit disillusioned with math, and particularly the next year when I took algebra. I took an algebra class, and that was—it was very abstract, and I just had a hard time understanding why we were doing it.
I didn’t understand what the purpose was. Now, actually, looking back, you know, I was learning about things at that time. I was learning group theory and, things like that, which nowadays are part of the things that I think about a lot. But, at the time, it didn’t have any context, and I didn’t appreciate what it was for. And, so, that’s sort of when I sort of really went full into physics.
Charlie, were there laboratory experimental type opportunities for undergraduates at Chicago? Did you ever try your hand at experimentation?
Well, yeah, so, certainly, there were labs in the classes, which I dutifully did, but I didn’t really enjoy that much. But I did have a very formative experience during my senior year in college where I worked in an experimental lab for Tom Rosenbaum.
OK. And, so, Tom, you know, so, Tom has done very well for himself. He’s the president of Caltech now.
But he was—he had just started as an assistant professor.
Oh, so, this is young Tom Rosenbaum?
This is young Tom. He was I think 30 years old at the time.
And, he had a group, and he took me on, and—
Do you remember what he was doing at that point in his own research?
Oh, yeah, oh, absolutely, yeah. So, he was very involved in studying the metal-insulator transition. So, this was a little bit of an exciting time. There was—a few years before that, there was a very influential work that came to be known as the Gang of Four, which was the development of the scaling theory of Anderson localization. And, so, Tom had done some important experiments on that, measuring the critical behavior of the metal-insulator transition. And, so, he was doing follow-up experiments on that. Now, of course, at the time, I didn’t really understand what was going on—so he started me off doing what experimentalists have to do, which is build things. And, I wasn’t really very good [laugh] at that. I didn’t really ever get the hang of soldering and machining and all of those things. And, so, the things that I built didn’t really work very well [laugh]. And I didn’t actually really do any experiments. But I did get exposure just being in the lab, and that was really a big deal for me. I got to know the graduate students, and there were two graduate students in particular, Stuart Field and Dan Reich. And, so, they were sort of big brother figures for me, and they were very nice to me, and they introduced me to the culture of condensed matter physics. And that had a huge impact on me, so.
Charlie, this is definitely something that would’ve been out of your purview as an undergraduate. But perhaps looking back and seeing how these things played out, was Tom Rosenbaum’s hire at Chicago a sign that Chicago really needed to build up its condensed matter program, specifically because of the University of Illinois and its heightened status in that field? Or was Tom already joining a really well-established group at that point?
Yeah. Well, certainly at the time, I had no concept of those—
Right, of course, of course.
—things. So, you know, so, at the time, yeah, I would say that, you know, Chicago was trying to build up. And they had—so, certainly in theory, they had Leo Kadanoff, who was of course very eminent a person, and—
Did you ever get to interact with him?
Yeah, I did take a class from Kadanoff, yeah, yeah. He was, yeah, he was a very interesting character [laugh]. But, yeah, I can’t say I really had that much of a concept of what the physics department was trying to do at that time.
When was it going to be theory for you? Was that just sort of a natural transaction from there?
Well, you know, what I really loved about physics was the interplay between mathematics and the physical world. And the math, you know, the math part was always the thing I really enjoyed doing [laugh]. I love fiddling with equations, and thinking about things. And certainly, working in Tom’s lab, I became certain that I was not very good working with my hands, which is a lot of what experimental physics is about.
And, so, one of the things—so, I was kind of hopeless building things in the lab, and so I think Tom probably had a [laugh]— he was trying to figure out what he could have me do [laugh]. And, so, he had a brilliant insight that one thing he could ask me to do is to read papers, and then explain them to his students.
And, so, that’s something I actually embraced. So, he assigned me to learn about the metal-insulator transition, the Gang of Four paper, and, you know, read some papers, and give a group meeting talk about it to his group and the students. And, so, it was in doing that that I immersed myself in that field.
He saw a professor in the making, it sounds like.
Well, or maybe he [laugh], he finally figured out something that I could do [laugh].
[laugh] Charlie, when it was time to start thinking about graduate schools, what was within range, and how well formed was your identity in terms of your subfield, who you might work with, the best programs, that kind of thing?
OK, yeah. So, it was actually interesting. It was my senior year that I went to work for Tom, and that fall was when I was applying to graduate school. So, even at that time, I wasn’t sure about what field of physics. I was pretty sure I wanted to do theoretical physics, but I wasn’t sure about field. So, I also had a little bit of experience in E&M [laugh]. I had a summer undergraduate experience at the National Center for Atmospheric Research in Boulder, working for a guy named Boon Chye Low who did theoretical solar physics. And he was interested in the dynamics of the magnetic fields on the sun. He was also a former student of Eugene Parker, who is another eminent professor at the University of Chicago, who I had actually taken E&M from. And, so, I was inspired by Professor Parker, and I thought that maybe I wanted to do something involving E&M, so I was thinking maybe plasma physics, something like that. And, so, those were the two directions I was thinking of maybe going into, either plasma physics or, maybe solid-state physic…condensed matter physics. So, those were the things that I put on my applications. And I applied to lots of graduate schools, and, I was a pretty good student. I got into most of them. I think the only one I didn’t get into was Princeton. I didn’t get into Princeton.
Was the advice specifically not to stay at Chicago?
You know, actually, I didn’t apply to Chicago. And, so, I think I—I’m not sure if it was because of advice. I think I just wanted to go somewhere else. So, yeah, so I didn’t even consider staying at Chicago. But—
What was it about MIT that won out?
What was it about MIT that won out?
Well, by the time that I was making decisions, so that was now—this is now in the spring of my senior year. And, by that time, I’d been working in Tom’s lab for the entire—for the school year. And, so, I’d gotten to know Tom and his students much better at that point. And, so what really solidified my decision to go to MIT was Tom’s advice. Tom gave me the very wise advice to go to MIT and work for Patrick Lee.
What was Patrick Lee doing at that point?
Well, he was doing mesoscopic—he also was in the same general Gang of Four area of physics. But he was, at that time, developing more facets of the effects of disorder on electronic conductors. And, so, Tom knew Patrick, and knew him as an up-and-coming, rising star figure. And at the time, I also was thinking about going to Harvard, just, you know, Harvard is Harvard, so, just the name itself has an attraction to it—but the advice that Tom gave me was that, culturally, MIT would’ve been a much more supporting and happier place than going to Harvard. And I think, probably that was true at that time, yeah.
What were your initial impressions of MIT when you first got there?
Oh, it was great. I loved it, yeah, yeah. So, you know, I went to MIT. I made a bunch of friends. And, you know, the first year was mostly taking classes, which were challenging but I could do it. And, and I slowly got to know Patrick. So, actually, I was a little bit lucky when I went to MIT. So, I told you that I—when I—at the time I filled out my applications, I checked either plasma physics or solid-state physics. So, when I was accepted to MIT, I was accepted by the plasma physics group, and so—
Who was doing plasma physics at MIT at that point?
Oh, let’s see. I thi…so, there was a guy named Ron Davidson. You know, I don’t remember all the names. I never really interacted with them. I interacted with them when I went to interview. But then I was lucky that I got a fellowship, so I had my own money so I can work for whoever I wanted.
If that had not been the case, then I would’ve, if I went to MIT, I would’ve been forced to do plasma physics. So, that may have—that might have made me go somewhere else.
Was this NSF support?
Yeah. Yeah, I got an NSF fellowship. So, that was a very fortunate thing for me that—because it wasn’t the condensed matter group that accepted me. But I was able to sneak in because I had a fellowship. ZIERLER: [laugh]
What was the state of mesoscopic physics at that point? Was it a pretty well-developed field?
Well, yeah, at that time, people were very interested in studying the properties of semiconductor devices. And there was lots of experimental developments on that, and that opened up a number of questions for theory to address. And Patrick was in the middle of all of that. And, so, at the time, he—I think the summer before I went there, he had developed this theory of universal conductance fluctuations, which explained the noise-like features of the electrical conductance of semiconductor devices, and various kinds of electrical conductors. It was a universal feature that emerged out of the disorder, and it’s sort of a deep concept. And that was something which was very, very closely, tied to experiments, and it both motivated new experiments and then there was feedback on that. And, so, that’s what I started off sort of being involved with—understanding the role of disorder in electrical conductors.
And, to go back to earlier in our conversation, were there any advances in experiment that were particularly useful as you were thinking about thesis topics to pursue?
Well, yeah, people were making smaller and smaller devices, and measuring their electrical properties. To be honest, at the time, I didn’t have that big a picture of what was going on in the larger world. I was focused on what was in front of me, which was what Patrick was telling me to do. So, in terms of the thesis topics being motivated by some larger picture, I was—I didn’t know very much at that time, and so I was dependent on Patrick’s guidance for that.
And, so, he—did he essentially hand you a problem, and that became your thesis research?
Well—yeah, he handed me several problems [laugh], and actually there was a shift in the middle, which I’ll tell you about.
But, so, certainly, the sort of thesis problems that I ended up working on were—Patrick had a very deep hand [laugh] in all of that.
So, what was the start and what was the shift?
Well, OK, so, the start was doing these—understanding the mesoscopic fluctuations in electrical conductors. This was understanding the role of disorder in the transmission of waves, and so there were several different problems that we worked on, applications of these ideas that we worked on. And it was all very interesting, and there were experiments, and some of those things people are still actually thinking about, even today. But what happened in the middle was 1987, and in 1987, high-temperature superconductivity was discovered.
Yeah, and did you recognize how earth-shaking this was at the time?
Yeah, well, certainly, I was there, and listening to Patrick. And Patrick was—and, so, I remember one day going into Patrick’s office, and saying, “Patrick, can I work on high Tc?” [laugh] And, you know—
He must’ve had a million graduate students who were having that same conversation right at that moment.
Well, I was fortunate that I was his graduate student at the time.
And at that time, I think I was his only graduate student.
Oh, so, he kept a small group?
He had a fairly small grou…I mean, he had—I mean, there were several other graduate students that I overlapped with—a few that were ahead of me, and a few that were behind me. But I think at that particular time, I think I may have been his only one.
So, what was his response?
But in any case—
What did he say when you said you wanted to work on this?
Well, he said, “Yeah, but it’s going to be hard [laugh].”
Because this is simply a new frontier?
Because it’s a new frontier, and it was a hard problem, and it is a hard problem.
And it is a hard problem. [laugh]
[laugh] OK? But, you know, the truth is that, of all the people to—whose office to go into and ask that question, Patrick was the right one. [laugh]
And so, why was Patrick—I mean, besides being a great scientist with great intuition, what made him so well-positioned intellectually to recognize in real time what a difficult long-scale problem this would be?
Well, no, so, the thing is—the thing that Patrick had at that time is that he had a deep understanding of the role of electron-electron interactions in materials. He had worked on, for instance, heavy fermion materials… there are all kinds of things that he’d worked on that positioned him [laugh] to be, ready to think about these things. And, the other thing that really distinguishes Patrick is that he knows how to read experiments, and he has a very deep appreciation and understanding of what experiments are telling you, and what to believe and what not to believe. He has this very deep physical intuition.
Meaning that he recognizes hype when he sees it?
Well, yes, and, you know—right. And I think he was also—you know, of course, at the time, there was Philip Anderson. Now, you know, so, Patrick, in a way, he was one of Philip Anderson’s, you know—
—descendants, right [laugh].
You know, Patrick knew Philip pretty well. And I remember one of the things that Patrick said is that “The thing about Philip Anderson is you have to know when to listen to him.” [laugh] ZIERLER: [laugh]
“You can’t listen to everything he says.”—
Because it’s a geyser?
Well, because it’s a geyser and— “But you have to—but he has real gems.” And, you know, at that time, very shortly after the experimental discoveries of high-temperature superconductivity, Phil Anderson came out with this idea of resonating valence bonds. And that was not a fully developed idea at the time, but it was a brilliant idea.
What was so smart?
Well, because it was so thinking outside the box.
So, what’s the box? That’s—this is great. What is the box to think outside of?
Well, the box was thinking about electrons starting from free fermions, from non-interacting electrons. That is the way that one was taught in school to think about the electronic properties of materials, is you start with non-interacting electrons, and then you add interactions, and hopefully they don’t do too much. And what Anderson was trying to do was to step out of that [laugh]. And he had this concept which was a very deep concept, which, I certainly didn’t understand at the time, and I don’t think many other people did. But it was a concept that really had legs. And I think Patrick appreciated that probably more than other people did.
Now, the breakthrough—again, the interplay here is there’s something that happens experimentally that allows for a theoretical breakthrough, or to what extent are these things decoupled as Phil Anderson is thinking of them?
Well, so, look, I mean, it was a tremendous surprise that high-temperature superconductivity was observed. And because—
Meaning there was no theoretical guidance for this?
There was no theoretical gui…well, I mean, there was the chemists’ intuition [laugh] that the experimental physicists who discovered it used. But that—
But there’s no, like, we know—
—where the Higgs is roughly, kind of [??]?
No, no, absolutely not. And, in fact, at the time, people believed that there was an upper bound to how high Tc could be, and this broke that upper bound.
And, so, that then became a very interesting theoretical problem, and I think Phil Anderson appreciated it. He got—he zooms right in on what the theoretical problem was, which was to understand the effect of strong interactions. And he immediately identified the two-dimensional Hubbard model as the thing to focus on. And that’s a very hard theoretical problem, which then led to a lot of effort.
And, so, for you, where does this all shake out in terms of that shift for your thesis research?
Well, so, then I shifted, and I started thinking about the Hubbard model and some variants on that. And, with Patrick’s guidance, we were able to do something, which, you know, it’s still nice work. And that became the second part of my thesis, which had to do with understanding the way holes move in an antiferromagnet. That was the topic, which was a good problem and I can’t take credit for that—I mean, it was really Patrick who had this insight that this was a good problem to do. And I was able to do some calculations, and write the paper, and that’s what I was able to do. But I was, still at that time, I was pretty young, and I didn’t—the thing about the high Tc field is at that time, it was wide open, and so it was hard to know what to do, and I wouldn’t have known—
—what to do.
Including industry? Were people starting to think about industrial applications for high Tc at this point, or it was strictly basic science?
Well, certainly from my perspective, it was basic science. But, so, yeah, sure, people were trying to think about what they could do with high-temperature superconductors, and that became a very active field. But that sort of question was sort of separate from the kinds of things that I was thinking about.
Yeah, yeah. What would you say, I mean, to the extent you want to give credit to yourself, and where Patrick rolls in, altogether, what were some of the central conclusions of your thesis?
Well, the central conclusion was that the effect of an antiferromagnetic background strongly renormalizes the motion of a hole. But it’s still a quasiparticle, and so it retains some particle character, and—
Which tells you what, more broadly?
Well, it—yeah. [pause] Yeah, it tells you that that the holes are strongly renormalized by the interaction. So, it didn’t explain the superconductivity. What it could potentially explain is experiments that one could do by measuring reflectivity or conductivity in these materials and could provide some guidance for thinking about those experiments. But in—
But in terms of the big picture of, you know, what’s the mechanism for high Tc, it didn’t really address that.
And where might Ken Wilson be in all of this as an intellectual influence?
I would say that’s completely separate.
Yeah. Yeah, I mean, of course, you know, Wilson invented the renormalization group, and certainly that was not something which was figuring very prominently in our thinking about that problem at that time.
Besides Patrick, of course, who else was on your thesis committee?
Oh, gosh. Let’s see. I think it was Gabi Kotliar, I think, who was—so, he was at MIT at the time, but he moved to Rutgers shortly after. And Boris Altshuler. Who else was on my committee? I don’t even remember. [pause] Maybe—there were some experimentalists. Maybe it was John Graybeal, I’m not sure, yeah. [laugh]
Were there any—?
It was a long time ago.
Were there any opportunities for crosspollination with Harvard? Like, would interacting with Bert Halperin been on your radar at all?
I did go to seminars at Harvard sometimes, and so I certainly knew who Bert Halperin was. I’m certain he didn’t know who I was at that time. ZIERLER: [laugh]
So, I remember a number of times going to seminars there, but it wasn’t—I didn’t really get to know people there that much. I probably could’ve taken more advantage of that than I did. But, yeah, I didn’t.
Charlie, what postdoc opportunities were available? What was most compelling to you at that time?
OK. Yeah, so, there were three choices that I had for postdocs, which were all good. I could’ve gone to Bell Labs. I could’ve gone to the ITP in Santa Barbara, which is now the KITP, but it didn’t have the “K” back then. And then IBM. And I ended up choosing to go to IBM.
Now, was the writing already on the wall at Bell? Was that part of your consideration?
No, not yet, no. In fact, I think Patrick wanted me to go to—you know, Patrick was a Bell Labs person. And, and in a real sense, Bell Labs was more of a center for this field of physics than IBM was. And, so, I think Patrick thought that I should go to Bell Labs, and I think he was a little bit disappointed [laugh] with me when I chose not to. So, my decision to go to IBM was based a little bit on the make-up of the group that was there. And I’m not sure I made the decision for the wisest reasons, but in hindsight, it was probably one of the best decisions I could’ve made—
—going to IBM.
What was that group that you initially joined?
Well, so, they had a small group of young condensed matter theorists, And so I was able to go into this group. I was sort of a free-floating theory postdoc. So, I wasn’t tied to any particular person, so I could do whatever I wanted. But there was a group of, several, young, rising star condensed matter theorists who were there, and that very much appealed to me. And, so, the people who I got to know, there was, Dung-Hai Lee, who’s now a professor at Berkeley. There was David DiVincenzo, who is now a very distinguished quantum information guy. And there was Matthew Fisher, who I ended up getting to know the best, and Matthew had a huge impact on my trajectory. And, so—
In what way? What was Matthew doing at that point?
Well, Matthew [laugh] did a lot of things. But he had a very deep understanding of the interplay between quantum mechanics and matter. And, so, he was actually doing some things on high-temperature superconductivity at that time, but also doing things on the quantum Hall effect. And those were things that I started to learn about and—
What about Charlie Bennett? Did you interact with Charlie at all?
A little bit, a little bit, yeah, I mean, more socially. I didn’t do work with him. I certainly was aware. I remember that he was setting up these experiments for quantum encryption, teleportation, things like that. I remember that stuff going on at the time. I didn’t appreciate at the time how significant it was. But I do remember that stuff. And I remember, we would be in the same lunchtime group, that we’d all sit together, and Charlie Bennett would be there sometimes.
I’m trying to pinpoint where intellectually quantum information sort of enters your mindset.
Well, that was much later.
It was, OK. So, nobody—
At that time—
At that time, I didn’t—yeah, I wasn’t really clued in.
Even—I’m just thinking at IBM, who might be thinking really far out in terms of computation?
Well, I mean, at the time, there was Rolf Landauer.
I mean, I’m talking about beyond classical computing, if anybody was thinking like that.
Well, Charlie Bennett—
—yeah, and then later, David DiVincenzo, so. But that was after I left IBM at that time. So, this was, you know, around 1990, and, at that time, David DiVincenzo was still mainly focusing on mesoscopic physics. But then, he went on, and helped found this field of quantum information, so. But, yeah, I wasn’t really connected to that at that time.
Now, at Bell Labs famously, there’s always going to be lots of interaction between theorists and experimenters. Was that the culture at IBM as well?
Yeah, it was, yeah, yeah. So, I didn’t interact that much with experiment, but I did get to know one guy, Richard Webb, who did mesoscopic experiments, and I got to know him pretty well. And that, you know, was something that did sort of figure in on things that I ended up doing, so, yeah.
Could you have stayed on longer at IBM if you wanted to? Was there opportunity to transfer into a staff position?
You know, no, I didn’t, yeah, I didn’t apply for one, and it didn’t seem like that was something that was going to happen. So, when I—at the time I was applying for jobs, I was lucky enough to get one [laugh].
And what was your professional identity at that point? Were you applying for specifically condensed matter theory jobs, or it was more broad, the offerings?
No, condensed matter theory, yeah.
Where? What was available at that point?
Well, let’s see. So, where did I apply? So, I applied to—I think there were four—there were—I applied to lots of places, but I got four interviews. So, I can’t remember all the places I applied to. But, so, there was San Diego, Brown, Stanford, and Penn. Those were the four interviews that I remember doing.
Very clear East Coast/West Coast choices for you?
Yeah, yeah. In the end, I only got one offer, so that the decision was made for me.
Now, actually I think of those four, I think I landed in the best place for me, but—yeah.
What was going on in condensed matter at Penn at that point? Who was there?
Well, OK, yeah, so, there was—so, in theory, there was Gene Mele, Tom Lubensky, and Brooks Harris, and then in experiments, there was Eli Burstein, and Gerry Dolan, Ward Plummer. And, then there were a couple of younger experimentalists, Paul Heiney and Arjun Yodh, who was a young assistant professor at the time. And there’re probably others that I’m missing right now, but—yeah.
Was Paul Steinhardt there already when you got there?
Yes, he was. Yes, he was, though, at the time, he identified more as a sort of high-energy theorist than a condensed matter. He sort of straddled both. You know, he was famous both for inflation and for quasicrystals, right. So—
Did you engage him at all in quasicrystals? Did you know he was working on that at the point?
Oh, I certainly knew he was working on it. But, no, that wasn’t an area that I was really focused on at that time.
Did you take on graduate students right away?
Yeah, I took—I had a graduate student when I started, yeah, yeah.
And what were your research interests at that point? What was your [??]?
Well, OK, right, so, at that time, I sort of had shifted away from the high Tc. That was one of the things that when I went to do the postdoc, you know, high Tc, it seemed too hard [laugh], and—
Sage advice from your advisor?
Well, no, no, it wasn’t so much that. I got introduced to other areas, and I started learning about the quantum Hall effect. And there was actually a formative experience I had where I met Steve Girvin, and Steve became a very influential figure for me in my early career. And he introduced me to cool things about the quantum Hall effect, and got me very—
Where did you first connect with Steve?
Well, Steve invited me to give a seminar when he was at Indiana. And he was very, very kind to me and invited me to come, and I gave a talk about my high Tc stuff. But then I remember sitting in his office, and he was telling me about fractional statistics and things like that, and it just seemed like the coolest thing I’d ever learned. So, I was very—I got very excited about that. And then I went, you know, and started talking to Matthew and Dung-Hai about these kinds of things, and started learning. And, so, that started a shift—to starting to think about those kinds of things. And that sort of morphed into, at the time, thinking about—it wasn’t the quantum Hall effect but it was kind of related, which is thinking about one-dimensional electrical conductors. And, so, that’s where my interaction with Matthew Fisher began to flourish. This started the last summer that I was at IBM. And, at the time, we were thinking about experiments at the time about something called the Coulomb blockade, and we were trying to think of something we could do with that. And we had the realization that things were very clean if we thought about the Coulomb blockade for a one-dimensional conductor. And Matthew had some insight about this problem, which is that it related to another problem that he had studied with Tony Leggett. And, so, we were able to make a connection between this one-dimensional problem and this kind of Caldeira-Leggett type understanding of quantum tunnelling. And, so, that was the beginning of something. So, that happened when I was just about to leave IBM, that we made this connection. And, so, then over the next couple of years, Matthew and I had this sort of telephone and fax machine collaboration— ZIERLER: [laugh]
—that was wonderful and—
What was the partnership intellectually? Who contributed what during this communication?
Well, you know, the thing about it was that we would talk, and things would happen. I mean, Matthew had a lot of,—so, Matthew was a couple of years older than me. But he was much more mature scientifically than that two- or three-year difference.
It helps when your father’s an eminent physicist also.
Well, yeah, that—but, frankly he was just plain smarter than me too [laugh]. So, Matthew had a lot. And, you see, the thing about Matthew is that he had a way—
I know Matthew’s story very well about how he was unwell, and he would—he describes himself as being reborn, so to speak.
Well, OK. But, certainly, Matthew was not unwell in that period. He was—
No, right, this is the point when he talks about being super-energized.
Oh, yeah, and super-energized and brilliant.
So, the thing that Matthew could do that I really admired is he had a way of understanding things even when he didn’t know it was right [laugh]. ZIERLER: [laugh] That’s great. KANE: [laugh] So, he had this very deep intuition for how things go. And, oftentimes, it was only much, much, much later that I came to appreciate the way that he was thinking about things, and realize that, yeah, he did know [laugh] even though he couldn’t do the calculation. And, so, one of the things that the two of us together learned about was the theory of a Luttinger liquid, And, so, we read these papers by Duncan Haldane. So, Duncan, several years earlier, had developed this theory of the Luttinger liquid. Duncan actually wrote two papers. There was one paper where he did all of the calculations very, very precisely, and step-by-step. And there was another paper that he wrote where he painted the intuitive picture for how to think about a Luttinger liquid. And I resonated with the step-by-step [laugh] paper, and Matthew resonated with the intuitive picture. And, so, in a way, that was kind of how we meshed. I was doing lots of calculations, and Matthew had this vision.
I wonder if you can explain, Charlie, exactly what it was that you were calculating? What—how were the calculations informing the vision? How’s the vision informing the calculations?
OK. Right. Well, so, the calculation that we were doing was to understand the electrical conduction when you have a one-dimensional conductor that has a weak link in it. So, you cut it apart, and then you have to hop from one side to the other. Or you could imagine an electrical conductor where it’s pretty much you go straight through but it has a little bump in it, and then you can scatter off of that bump. And, so, in order to understand that, the electrical conduction, you have to have a model of it, which is the Luttinger liquid model, and then you have to do a calculation of the conductance. And, so, that’s some perturbative calculation, and that’s—I learned how to set up those perturbation calculations and do this calculation. We got this power law prediction that the conduction should behave as a power of the temperature, and that was a nice thing where the exponent told you something deep about the Luttinger liquid.
What were some of the most significant papers where you conveyed these ideas?
Well, so, there was a series of papers that Matthew and I wrote. We actually wrote a bunch of papers together. I mean, the most—there’s a long paper that we wrote, which we wrote in my first year as an assistant professor, and I think that’s the one that has the big ideas. And, so, there were a couple of things. There was another set of calculations that I did, which was applying the renormalization group to this Luttinger liquid problem, and that’s another thing that we did in this long paper. And, so, again, I learned the renormalization group from Matthew. You know, of course, Matthew, I’m sure, learned it from his father. But there were a series of calculations involved in that as well that I feel like I contributed to in an important way. And, so, setting up the renormalization group theory of the Luttinger liquid, I think that was a major contribution that we did.
To go back to the interplay with other subdisciplines, given how influential this was, who else in physics was paying attention? What were—who else found the Luttinger liquid research valuable?
Well, so, certainly, experimentalists did, OK, so—and there was also another direction in which the Luttinger liquid theory shows up, which is in the fractional quantum Hall effect, OK. And sort of parallel at that time with this work that Matthew and I were doing on one-dimensional conductors, Xiao-Gang Wen was developing the Luttinger liquid theory of the edge states in the fractional quantum Hall effect. And it turns out the mathematics of the one-dimensional theory and the edge state theory, they’re very, very closely related to each other. And I remember there was a point at which time we sort of realized, wow, they’re kind of the same, and that was a very exciting moment. So, that was one collection. But, certainly, experimentalists were very interested in—you know, because they can measure the electrical conductance across a weak link, and then you ask whether or not it behaves as predicted. And, so, that was something. So, Richard Webb, for example, the guy from IBM, was very interested in doing experiments on these kinds of things. There were also fruitful connections within theoretical physics to boundary conformal field theory, which was introduced by John Cardy and applied to condensed matter physics by Ian Affleck and Andreas Ludwig and others.
Charlie, on the administrative side, initially, when you got to Penn, what was your sense of the culture of promotion from within or not?
You know, I was pretty naïve at that time, and my impression was if I did OK, I’d get promoted. If I didn’t do [laugh] OK, I wouldn’t get promoted. As time went on, I became more anxious about it. The promotion period was not a happy period for me. But I didn’t—I never had the concept that it was political or unfair or anything like that. That was certainly not something that was on my radar really. But when I first started, I was more focused on, you know, what was immediately in front of me rather than down the road.
Was the department in the 1990s, would you say it was in growth mode?
It was in transition. So, at the time, there was a nuclear physics group, and that was sort of waning at that time. And then there was a point at which the astrophysics became merged, and so there was—it was a point of transition. So, certainly in condensed matter, it grew a little bit but not that much while I was—when I was, you know, first starting out.
What were some of your major research projects in parallel or after that with Fisher?
Well, so, we did a lot of things developing the theory of Luttinger liquids, and also the quantum Hall effect. So, once we realized that the Luttinger liquid and the edge states of the quantum Hall effect were kind of the same, we realized that there were a lot of things that we could do on that. And, so, that was a very exciting period for me, and this was like the first five years of my assistant professor where we did a lot of things understanding the role of disorder on the edge states in the quantum Hall effect. One of the things I’m very proud of is a prediction we made about how to measure the fractional charge of the Laughlin quasiparticle using noise. And, so, these were things that experimentalists then went on and actually were able to do, which is something that I was proud of. And, so, yeah, there were a lot of things. Another thing that we did at that time was understanding the flow of heat in the—in both Luttinger liquids and also in the quantum Hall effect. And that is still something that people are thinking about, and there’re actually experiments in the last several years where people finally were able to observe that.
It’s so interesting with the quantum Hall effect, it’s just this enormous body of knowledge to mine, and there’s so many ways of approaching it. What were some of the obvious things for you to be involved with, and what were some that you said it’s best for this to be left to others?
Well, yeah, so, the things that really excited me about the quantum Hall effect was the idea of universality, that there are features, things that you can measure that are insensitive to the details.
Can you develop that a little? What do you mean by that?
Well, OK, so, for example, in this Luttinger liquid theory that we helped develop, if you measure the conductance from tunneling from a metal into the edge of a quantum Hall state, then there’s an exponent. The conductance varies as temperature to some power, and that exponent is universal. It doesn’t matter exactly what’s going on. It’s not sensitive to where all the impurities are, and things like that. It’s something that tells you something deep about the structure of the quantum state. The Hall conductance is a similar sort of thing. You measure this quantized Hall conductance. It’s a number that you measure that is insensitive to the details, but it’s telling you something deep. So, those were the things which really turned me on about the quantum Hall effect. Now, there are also a lot of other things, you know. A lot of times when you— for experiments, you know, the devil is often in the details. Things aren’t always as pristine as the theory. And in order to correctly interpret the experiment, sometimes you have to get into the weeds, and understand the effects of all the details. And that’s an aspect which I feel less skilled at doing, and it also—it has a harder time keeping my interest level up. ZIERLER: [laugh]
So, but it is an essential endeavor [laugh] in order to solidify this contact between experiment and theory, which ultimately is what it’s all about.
And, Charlie, when does the quantum spin Hall effect enter the scene?
Well, that was much later.
Much, much later. There were intervening chapters in my career before that, before that happened.
OK. So, let’s get there. What, so, what happens next?
Well, OK, so, there was the quantum Hall effect and Luttinger liquids, and then there was carbon nanotubes. And, so, this happened at the time when I got tenure and after, which is when carbon nanotubes were discovered. It was discovered that you can isolate them, and study them experimentally. And, so, one of the—one of my colleagues at the time in the material science department, Jack Fischer, was one of the very prominent experimentalists who sort of showed that you can actually make these things and do experiments on them. And, so, he collected Gene Mele and me, and told us, “You should start thinking about these things.” And I was very excited because I had spent a long time thinking about one-dimensional electrical conductors, and carbon nanotubes are one-dimensional electrical conductors. It’s just a new kind of one-dimensional electrical conductor. And, so, I got excited about that. Now, Gene Mele, he got excited about this because carbon nanotubes are basically graphene wrapped into a cylinder, So, you know what graphene is?
The graphene is, you know, it’s an exciting—
I’m excited for my next flight to be built out of graphene [??] [laugh].
Yeah, OK, so, what a carbon nanotube is—it’s you take a plane of graphene, and you wrap it in—it’s like a straw that’s made out of graphene, OK. But it’s a nanometer wide. And, so, Gene got excited about this because in Gene’s earlier career, he had done much work on graphite, and so he knew about graphite. So, in fact, he had done the theoretical work that showed that a plane of graphene is described by the Dirac equation. So, he had a good understanding of graphene. And, so, we got together, and started thinking about this, and this was the start of another sort of exciting chapter in my career where we started thinking about the electronic structure of carbon nanotubes, and—
Charlie, is this a brave, new world, or do you see intellectual antecedence with your previous research?
Oh, absolutely, there was intellectual antecedence. I mean, so, one of the works that I had—this wasn’t with Gene—but one of the works that I did on carbon nanotubes was showing precisely how they are Luttinger liquids and making the predictions for the experiments that you would do in order to test that by doing, you know, basically measuring the electrical conductance, and predicting what the exponent for the tunneling would be. And, so, that was something that was very much connected. But there was also something new that I started learning about by doing this was—which was the specific electronic structure of a carbon nanotube. So, there, I started learning from Gene Mele about the electronic structure of graphene.
Why was this so important, this intellectual connection?
Well, it was—so, it was crucial for understanding the electronic structure of carbon nanotubes, OK. So, it turns out, so, a nanotube, depending on how you wrap it, it can either be a metal or an insulator, and that fact is related to the fact that an infinite plane of graphene is described by the Dirac equation. It has a Dirac point in its electronic structure. And, so, one of the first things that Gene and I did when we started thinking about this was to cast the theory of the carbon nanotube as the theory of graphene wrapped into a cylinder. And then that allowed us to understand a number of things. And that forced me to learn about this electronic structure of graphene, And there were a lot of things that we thought about for that, and we wrote several papers together, and this was an exciting time. But I immersed myself in understanding graphene. And that was something that was new for me that was sort of, separate from my previous understanding of the quantum Hall effect and Luttinger liquids. So, that was a—this was a new thing that I learned about, and I really am indebted to Gene for teaching me about those things.
But to be clear, the origins of the quantum spin Hall effect are embedded in the story of graphene. That’s where it comes from.
Well, yeah, it comes from graphene and the quantum Hall effect. So, the thing is—OK, so, now, we’re moving forward, and so now we’re into the, you know, early 2000s, and I’d been working on carbon nanotubes for several years and, frankly, I was getting a little bit bored with it.
And are there graduate students involved as well in this for you?
Yeah, we had not too many. We did have a graduate student who did a thesis on carbon nanotubes, but not a lot of students. But, so, at the time, in the early 2000s, it was getting to the point where I felt like, for the carbon nanotubes, the main progress was going to be made in the weeds, in terms of forging the detailed connection between experiments and theoretical predictions. And there, the main—the most productive tools for that are probably going to be numerical tools, and things that I’m not as excited about. And, so, I was at a little bit of an impasse trying to understand what to do next.
Are there limitations in experimentation that might be holding you back from advancing this?
Well, no, it’s more that the kinds of experiments that people were doing at that time in order to—they didn’t sort of have a pristine thing that they were getting at. It was more that you had to understand the details. And look, that doesn’t make it unimportant. But I just felt myself yearning for something where I could do something a little bit more—that had a little bit more theoretical interest.
Are you still in touch with Steve Girvin at this point?
On and off, yeah, yeah. So, you know, I’ve known him over the years, and he’s certainly a man that I have the deepest respect for and admiration. In terms of the field, we don’t really—we haven’t—the area that he’s interested in is more sort of quantum information, you know, developing the hardware for quantum computing. It’s not something that I’m directly connected with. But every time I see him, I enjoy talking to him.
So, you’re at a bit of a crossroads intellectually at this point?
Well, so, this was—oh, actually, you’re talking about—I’m talking about now. So, you’re talking about back then?
Yeah, just in terms of developing the narrative.
Oh, so, it’s an interesting story, actually, interesting story. Back then, so, we were doing this carbon nanotubes. And I did meet Steve in the summer of 2004, and I remember this very well because this was at the time when I’d been studying nanotubes for a long time, and I had started thinking about graphene, and just thinking as a theorist, you know, well, what if you could have a single plane of graphene? Would it be interesting? Because I thought about—because I understand carbon nanotubes, and I’d been thinking about the—there was some problem I’d posed myself, which is thinking about the magnetic susceptibility of a carbon nanotube, which then forced me to understand what would happen if I put a plane of graphene in a magnetic field. And that is actually a kind of an interesting problem. And, so, I thought about that, and I was, you know, doing this. And, so, Steve visited, and I remember having this conversation with him, thinking, well, maybe there’s something interesting to think about, but I’m not sure they’ll ever make a plane of graphene. I don’t—it didn’t seem like—nobody’s ever did it. Everybody thought it was impossible. And, so, Steve said, “Well, what I think they should do is just try to peel it off with scotch tape.” ZIERLER: [laugh] KANE: “You know, has anybody tried that?” ZIERLER: [laugh] KANE: [laugh] So, he said that. Now, I don’t know if Steve knew [laugh] that actually at that moment, that’s precisely what Andre Geim was doing.
I don’t think he knew it. I think he was just—had this insight [laugh]. But, in any case, so, at that point, so, this was before I came up with the quantum spin Hall effect.. But I was thinking about graphene, and I was trying to think about something. And, so, then—so, this was in—sometime in the summer of 2004. And then, later on that summer, we heard about this preprint from Andre Geim.
And where was Andre at that point?
I think he was in Manchester, I think, so, yeah, yeah. And, you know, and at the time, it wasn’t clear that it was going to be—that the graphene that you could make was going to be that great. But it was pretty exciting. It was—and it was encouraging that you could make a single plane of graphene. And I remember talking to Gene Mele about this and, saying to ourselves, “OK, this is going to be big. So, we need to think of something [laugh] to do before everybody, the entire world descends on this problem.” And, so, I started thinking more about just individual planes of graphene. And, so, I posed the following question to myself, which is—you see, the thing that’s—that makes graphene so interesting is that it is right on the boundary between being a conductor and an insulator. And, so, it’s like it is an insulator with a zero-energy gap, or it’s a conductor with zero density of states. And, so, it’s right on the border. And, so, and if you think in terms of quantum mechanics, there’s the conduction band and the valence band, and they’re exactly touching each other. And, so, I posed myself the question, which is why is that? What is it about graphene that makes it so this is exactly this precisely tuned critical point? And, so, usually, when you have precise tuning, that has to be some consequence of some kind of symmetry.
OK. And, so, I set about the problem of understanding the symmetries of graphene, and what constraints they would impose on the electronic structure. And it’s not too hard to understand what the symmetries are. So, I wrote down all the symmetries, and I was asking—if you break the symmetries, what are all the ways you can open up an energy gap? And I wrote down all the possible ways that you can do that. And what I realized going through this exercise is that, actually, symmetry does not protect the energy gap in graphene.
And there was a theoretical assumption that it would?
Well, yes, but it’s a sort of yes or no sort of thing. What people usually do for graphene, since it’s made out of a very light element, carbon, is to ignore the spin orbit interaction. And if you ignore the spin orbit interaction, if you set the spin orbit interaction equal to zero, then graphene has a higher symmetry. It has an extra symmetry, which is basically that you can independently rotate the spins independent of the orbital degrees of freedom. And if you have that symmetry, then you can understand that the critical point is protected by that symmetry. So, I can understand why as a practical matter graphene has this finely tuned critical point. But, as a matter of principle, the spin orbit interaction is not equal to zero. It’s just small. And, so, what that made me realize is that as a matter of principle, graphene should have an energy gap.
Ah, this is—
—like a eureka moment? This happens dramatically?
It was—well, I mean, at the time, I realized this, and, you know, I thought, oh, yeah, it’s kind of interesting. And, so, I go in, and I talk to Gene Mele about this, and he looks at me, and he says this, “But it’s going to be puny, you know. Who cares?” And there was a voice inside me saying that it’s going to be puny. Who cares? But, you know, I was thinking about it, and, so, this is where my background was fortuitous, because in addition to understanding graphene, I had spent a long time thinking about the quantum Hall effect. And, so, I recognized that this gap that opens up in graphene is actually related to the quantum Hall effect. And, so, in my mind, even though it was puny [laugh], it was interesting [laugh]. And it was interesting in a very sharp and precise kind of way. And that’s the kind of thing that motivates me as a theoretical physicist, and so I was excited about this. Now, at the time, I still had this voice inside my head saying, “But it’s puny [laugh], who”—you know. ZIERLER: [laugh] KANE: “You know, who cares?” [laugh] But I couldn’t let it go. I kept thinking about it. I realized that what this state that I had was, it was really two copies of the integer quantum hall effect, and that’s what we called the quantum spin Hall effect. And, so, that opened up this path of reasoning that I was able to follow. [laugh] And it’s remarkable where that path led to. I didn’t, at the beginning, I didn’t appreciate that the path would lead such a long way.
Did you coin the term “quantum spin Hall effect”?
Yes. Actually, it’s interesting. First of all, “spin Hall effect,” I did not coin. And, in fact, there was another thread that was happening at the same time, which was the theory of the spin Hall effect in semiconductor structures. And the names associated with that, there’s Allan MacDonald, and also Shou-Cheng Zhang. And they had been doing work on predicting a spin Hall effect. And, so, when I realized that this graphene, had these two copies of—and the reason we call it a spin Hall effect is because if you apply an electric field, then the up spins go in one direction, the down spins go the other direction, and so there’s no flow of charge, but there is a flow of spin. And, so, that’s the reason it’s a spin Hall effect. And, so, I originally was thinking of titling the paper spin Hall effect in graphene, and I remember—
It doesn’t quite have the same ring to it.
And I remember—there were caveats associated with whether it’s quantized. I wouldn’t call it a quantized spin Hall effect because the spin that flows is not quantized in the same way that the charge is quantized in the quantized Hall effect. So, I appreciated those caveats at the time. But I appreciated the sense in which it was a robust state. There was something special about it. But, in any case, I didn’t want to call it quantized spin Hall effect because there’s a sense in which that’s not true. But I remember one of my experimental colleagues, Jay Kikkawa, who I showed this paper to, and, he said, “Well, you should call it the quantum spin Hall effect. That would be much, much more exciting than just calling it the spin Hall effect.” [laugh] And, so, we ended up sticking with that, which is actually a good thing, yeah.
When does Duncan Haldane enter the scene for you on this research?
[laugh] Well, he entered the scene in probably 1987 when he wrote the [laugh]—when he wrote his paper pointing out that in a model of graphene you can get a quantum Hall effect without a magnetic field. And, so, he wrote that paper, and I knew about that paper for a long time. But it wasn’t, you know, in the front of my mind until I started thinking about graphene, and realized that this spin orbit interaction in graphene leads to two copies of Haldane’s model. So, we realized immediately when we were thinking about this puny energy gap in graphene that the model that we wrote down was exactly two copies of Haldane’s model. So, if you ask when did he enter, he did really enter, what is it, 15, 17 years before [laugh] I did [laugh].
When do you start to realize that all of this research is going to become quite prominent, that you are going to be honored so broadly for this?
Well, it wasn’t until the experiments, you know. I mean, if it wasn’t for the experiments, it would’ve been a, you know, novel idea.
A toy model?
But it would’ve been—yeah, yeah. And, you know, just like Haldane’s model, nobody paid any—it didn’t really get very much attention when he wrote it in 1987, because Haldane himself said in that paper, “It’s unlikely that this will ever be realized [laugh] experimentally.” [laugh]
So, are you—do you recognize this in real time? Are you champing at the bit for experiments to get underway? Are you not involved with these things?
Well, I—well, yes and no. I was hopeful, though—so, I was not so optimistic about graphene, simply because it’s so puny, and—but there was a parallel development by Shou-Cheng Zhang and Laurens Molenkamp, where they were—Shou-Cheng realized that the same physics arises in mercury cadmium telluride quantum wells. And, so, when they did that, and there was some understanding that Molenkamp was actually going to be able to pull it off, that was when I realized that things were going to, you know, get to the next level.
What were you looking for?
Around the time that that was happening, I was thinking about the three-dimensional version of this effect. And when I realized that there could be such a thing as a three-dimensional topological insulator, then I was primed to think about materials where this could happen. And, so then, at that point, I sort of realized that, hey, maybe this is something that really could happen experimentally in materials that have strong spin orbit interactions. And, so, I put a lot of effort into trying to find real materials where this would come about, and I was fortunate enough to find one, which is this alloy of bismuth and antimony.
And, so, with these experiments, what were you looking for specifically? What was the feedback mechanism to give you solid grounding for the theoretical work you were doing?
Well, so, one had to make a solid prediction for what one observed. And, so, in the three-dimensional case we made a prediction for angle-resolved photoemission spectroscopy. So, photoemission is a way you can measure basically the electronic structure of the surface, and there was a sharp prediction for what the signature of a topological insulator would be. Basically, you count some number of crossings, and the question is whether that number is even or odd. And the prediction is that in a topological insulator, it would be odd. Actually, I wasn’t really in contact with the experimentalists before they did the experiment. I was very hopeful, though, when we wrote the paper predicting that bismuth antimony would be a three-dimensional topological insulator. At that time, I didn’t know Zahid Hasan, who was the professor at Princeton who did the experiments that first observed this. So, it’s interesting, my first interaction with Zahid Hasan was actually mediated by my PhD student, Liang Fu, who, on his own initiative, took it upon himself to go up to Princeton to take a class. And, in the process of doing that, he got to know the graduate students at Princeton, and in particular got to know David Hsieh, who was one of Zahid Hasan’s students. And, so, they got to know each other, became good friends, and made this connection. And, so, through that, I got to know Zahid Hasan. Zahid was interested in bismuth antimony for other reasons, but then realized that there was actually something more interesting than the other reasons [laugh] that he had for looking at these materials.
And what was your point of contact on the research side? What did you work on with Zahid?
Well, so, Zahid does—you know, did these experiments, and so there were various contacts that we made for other materials. He was interested in antimony and bismuth. There was one paper that I wrote with Zahid, which was about understanding the electronic structure of antimony and bismuth together and understanding what those do. So, but, certainly, we had a lot of conversations. But, you know, I wouldn’t say that my interaction has been—was that close with the experimentalists. But certainly, there’s motivation going in both directions on that.
Charlie, I wonder if you might compare and contrast the experience and what it felt like in the same year to win the Buckley and the Dirac prizes.
[laugh] Well, yeah, I mean, first off, I mean—
I mean, with Buckley maybe it’s more near and dear as condensed matter, but Dirac for theory?
Well, look. So, first off, I didn’t start off in my career ever imagining myself that I was Buckley Prize or Dirac Prize material. That was not my self-image or view of myself.
But if you love the science, and you work hard, that’s how these things happen.
Well, I feel very fortunate. You know, for me, the Buckley Prize was the most meaningful and moving thing for me, just because it’s a recognition coming from the people whose opinions I value the most. And it was also—it was just a wonderful experience. One of the highlights was a dinner after the Buckley Prize celebration. And then after the dinner, I went out and drank beer with my good friends, and it was just a—it was one of the happiest times I’ve had. So, it was a wonderful thing, yeah.
Now, that same year, I’m very interested in this, you were a Simons investigator. What does that mean? What’s the point of contact with the Simons Foundation? What do they offer you, and what are their expectations in terms of your research?
Well, prior to learning that I was getting the Simons award, I didn’t have any contact [laugh] with them. So, this was an out-of-the-blue thing, which I’m extremely grateful for, and has given me, a sort of a freedom to work on things where I’m not as focused on every moment, trying to justify them. And, so, that has been a wonderful experience for me, and they’ve been very supportive, and, yeah, I’m extremely grateful.
So, around this time and in the years since, just sort of set the stage for some of the big, exciting things that were happening with topological insulators.
Well, over what period?
From, you know, like the early 2010s all the way to now.
Well, OK, so after 2010, the basic phenomenology of topological insulators had been established. So, in terms of developments since then, there have been a couple of—there have been several things. One has been the development of topological superconductivity. And, again, this was—so, there was a theoretical idea that Liang Fu and I had, around 2008, 2007 that if you combine a topological insulator with an ordinary superconductor that you can realize a kind of topological superconductivity. And, so, this led to the idea that you can use the superconducting proximity effect to create topological superconductivity. So, you have one material, which sort of has the topological in it, and you have another material that has the superconductivity in it, and you put them together, and then you get something new. And so I think this paper that Liang that I wrote was the first version of that. And then, it turned out that there are many other versions, and you don’t actually even really need a topological insulator. You can have another kind of material that can—that is topological enough that you can do it. And this led to, a whole wide variety of people trying to engineer topological superconductivity in various platforms. And this has been one of the developments where there’s been—it’s been [laugh] a little bit of a roller coaster ride for how things are going. But, you know, there’s a promising development, which is these semiconductor nanowires where they’re, famous experiments which see something that looks like a Majorana and—but there’s controversy, and, you know, so that’s—
Yeah, what is that? What is the controversy with Majorana? Can you explain that a little bit?
Well, I think the controversy is whether the signature that is observed is unambiguously demonstrating that you have Majorana modes. That’s the controversy, because the—and, again, this is an example where the [laugh] devil is in the details and the weeds. Can you experimentally rule out all of the less interesting explanations for what is observed? And I think that has been the challenge for that. And, so, there’s a very sharp prediction, which I think was actually made by Patrick Lee and his collaborators which is that if you can tunnel into the end of this single unpaired Majorana mode, then, at low energy, it should have a perfectly quantized conductance. And so, there was some controversy about whether or not that was observed or not, and I guess they took it back. But— ZIERLER: [laugh]
So, you know, look, my feeling on this is that it should work, and eventually it’s going to. That’s my hope on this. Now, whether or not the nanowires are the best way or not, that I don’t know. Maybe there are other ways that one can do this as well. But, that’s been one of the developments over the last, you know, sort of eight or ten years. Another development that has happened is that there’s been a realization that there are many, many more flavors of topological phenomenon in electronic materials, because crystals can have many, many more kinds of symmetries. And, so, there’s become an industry of understanding the different kinds of symmetry protected topological phenomenon that one can have. And, so, as an example of that, one of the early examples that I was involved with my colleagues here at University of Pennsylvania is the idea of topological semimetals. And, so, I told you that graphene is special because the conduction and valence band exactly touch each other. So, it’s right on the boundary between being a metal and an insulator. So, graphene is a two-dimensional material, and so you could ask the question, could that happen in three dimensions? Could there be a three-dimensional material that is right on the boundary between being a metal and an insulator? So, could there be a three-dimensional version of graphene? There was some earlier work where it was realized that if you have what’s called a Weyl semimetal, that that is a very interesting thing where somehow the Weyl point is protected: you can’t get rid of it. But the question is whether you can have a Dirac point which is two Weyl points on top of each other. They wouldn’t be protected, unless there is some extra symmetry. And, so, we posed this question of whether—is it possible to have this three-dimensional what we call Dirac semimetal? And, so, this is again the kind of thing that I like. It’s a sharp question you can ask, and so I started thinking about this, and realized that that is precisely what happened in the first model that I wrote down of the three-dimensional topological insulator. So, if you go to the point where the topological insulator becomes a trivial insulator, there’s a transition point, and that transition point is at a high symmetry point. And, so, if you have that symmetry, then you’re guaranteed to be at that transition. And, so, this is a new phenomenon in which there’s a sense in which it’s less interesting than a topological insulator because it is—because it’s not as robust. So, if you make things dirty, so that you no longer have the perfect symmetry, then there’s a sense in which you lose this effect. So, it’s a little bit less interesting than the topological insulator, but it’s still interesting. And this is one of my—one of my things is that the way you get ahead in theoretical physics is you’ve got to think of the least interesting thing [laugh] that you can think of that’s still a little bit interesting because all the really interesting things are already taken. And, oftentimes, the less interesting things turn out to be more interesting than you first would’ve thought.
Yeah, yeah, that’s a truism in science, no doubt.
So, in any case, so, yeah, so this Dirac semimetal turned into something, and now there are many different versions of that, and they show up in experiments, and that’s a very exciting interplay. Where that has become is an endeavor where there’s this very, very fruitful interplay between the kind of theoretical physics that I do but also computational theoretical physics where people do first principle computations of the band structures of real materials and then identify these topological features in the band structure, and then experiments on real materials. And, so, that sort of identified a very fruitful interplay. And one of the things that we have developed at Penn is—so, I have colleagues—I have a colleague, Andrew Rappe, who’s one of the experts in computational condensed matter, and so I very much enjoy interacting with him about these things.
Charlie, I’ll corner you on only one more prize, since I know it’s not the easiest thing— KANE: [laugh]
—for you to talk about. The Breakthrough Prize, what was that like, and in what ways was that different than the others?
Well, yeah, I mean, [laugh] in what ways it was different, it was a lot more money [laugh], and it was an experience unlike any that I’ve ever had.
Did if feel like—I mean, not that you know personally—but did it feel like a 21st century update for the original intentions of the Nobel Prize?
It’s different. It’s different from the Nobel Prize in that it doesn’t have this long history. I think time will tell whether it becomes a 21st century update. I think it’s too early [laugh] to be able to say that. Certainly, I think that is the intention. I think that’s what the people who endow this prize have in mind. But I think it’s still early in that, and it’s—I think one has to wait for the historical record to establish that.
As the citation says, it delineates or it complements with both topology and symmetry in physics. So, I wonder if you can—in what ways that you sus these things out separately, or are they totally interwoven in terms of thinking of your overall research achievements?
Well, yeah, so, look, both symmetry and topology, they’ve been around for a long time, and they’ve been appreciated as key ingredients for how we think about matter for a long time. So, I don’t feel like I invented any of that. I think my contribution has been to identify a way in which the two of them work together to give you something that wasn’t appreciated before, and to recognize that that was hiding in plain sight in the electronic structure of real materials. I mean, in a sense, the features of the electronic structures of materials that we identified, they are features that could’ve been known about much earlier, because the band theory of solids, which is basically understanding the way we understand the electronic structure of materials, that was sort of set out before I was born. And the role of symmetry in that was very, very highly developed and highly understood. And there was also some understanding of the role of topology in that. But I think what I was able to contribute was sort of an appreciation of the way that symmetry and topology interact with each other in order to inform us about a way of classifying the electronic phenomena that occurs in the materials.
Charlie, to bring the conversation up to the present, I asked you initially when you joined the faculty at Penn, where condensed matter was in terms of building states[?] and things like that. Can you reflect a little on your many decades at Penn, particularly in terms of condensed matter, and its role as a center for condensed matter?
Yeah. Well, so, Penn, you know, has done a lot of work building condensed matter, and in different directions. So, one direction that has been built a lot is in soft condensed matter. And, really, Tom Lubensky deserves a lot of credit for having that vision of soft matter. And then—and in quantum matter, we also have been developing—over the last couple of years, we’ve hired a bunch of junior people, and I’m very bullish on that as well. And, so, I feel like we’ve been supported in the department, and that’s something that—that’s a good thing. You know, there’s always tugs in different directions. And, frankly, I’m probably the most apolitical person you would’ve ever met. And, so, I’m not as effective at—as an advocate for building things in my own direction. But certainly I feel good about where I am, and that’s a good thing.
And you’ve firmly been, are, and will continue to be, I’m sure, rooted in the world of basic science. But in the way that you’ve done your work at the interface with experimentation, involved with new materials, what are some of the applications either in train or hypothetically in the future in terms of the ways we might see these materials be put to industrial or societal use?
Well, yeah, OK, so, look, that’s on some level, that’s the most important question [laugh]—what is it all good for? And, to be honest, that’s not what I spend most of my time being excited about.
No. But, I mean, just as a spectator.
But let me just say as—so, the biggest dream that I have is to be able to develop ways of harnessing quantum mechanics to do the things that quantum mechanics can do, and I think this is—one of the great challenges for the coming century is figuring out the best way of doing that. And, so, this could be, you know, making a quantum computer or, you know, having quantum communication, because quantum mechanics has fundamental features that allow it to do things that you can’t do without quantum mechanics.
Charlie, just to interject at this point, is what you’re saying—does it require first a better understanding of quantum mechanics itself, or a better understanding of how quantum mechanics can be applied?
Well, I think those two go together, because, in a sense, you know, the rules of quantum mechanics that we understand now are basically the same as the rules of quantum mechanics that were laid out in the beginning of the 20th century. It’s not like there’s a new theory. I mean, look, there’s string theory and, you know, things like that. But that’s not really relevant. You know, the Schrödinger equation and all that, that is firmly established. But the thing is that the question is not what the fundamental theory is. The question is: how does matter that obeys the rules of quantum mechanics behave?
So, then, let me ask—
And what are the principles for how you understand that, OK? So, let me give you an analogy, which I kind of like. This is an analogy that Piers Coleman told me about, and which I think is good, which is Newton. So, Newton developed the laws of mechanics, and they’re the same Newton’s laws today are the laws that Newton developed. But the [laugh], the deep question is how does matter that obeys Newton laws behave? That’s a much larger question than just writing Newton’s laws.
OK, and, so, that requires the introduction of concepts and ways of thinking. It’s like, for instance, the concept of energy. Newton didn’t invent the concept of energy. That’s something that developed much later, but it’s a very powerful organizing principle for thinking about the way that matter that obeys Newton’s laws behaves. And, so, my feeling about quantum mechanics is it’s the same sort of deal where, you know, we have the theory of quantum mechanics, and it’s—on a certain level, it is as right as Newton was. Now, I mean, Newton’s right, and quantum mechanics is right. It describes the physical world. But the interesting question is how does matter that obeys quantum mechanics behave, and how can we use that in order to do something that is interesting? And that’s where the developments in recent years have led to something that’s new and equally fundamental, I would say.
So, then, let me ask, Charlie, a really fun and foundational question, given what you just said. From your perspective, you know, the famous disagreement between Einstein and Niels Bohr, right, about quantum mechanics, what to your mind remains provisional, and what is settled, from those disagreements or debates?
Well, it is settled that quantum mechanics—that every experiment and measurement that has been done agrees with the predictions of quantum mechanics. Now, what is not settled is what is the implication of quantum mechanics in the macroscopic realm? And that’s where the disagreement becomes most glaring, you know, the argument that you referred to. And is there something fundamental that prevents that glaring disagreement from being something we have to worry about. So, yeah, so, I don’t know the answer to that. I mean, look, there are deep questions about how do you, understand quantum mechanics at the smallest length scales, right, and the connection between quantum mechanics and gravity. And it could be that those ideas actually—and those issues are able to make contact with things that one can actually measure. I mean, that would be—to me—that would be what would make those things interesting and exciting, as opposed to sort of a philosophical question. And, in a way, you know, the things that excite me most about physics, theoretical physics and physics in general, are if you can get at issues, deep issues like that, and yet make them into a realm where you can make contact with them in real experiments, real measurements, and actually make predictions. And, so it could be that, as we come to understand the way quantum mechanics works, that there are things yet to be uncovered about that, that could well be things that one can, you know, make contact with in experiments.
So, that’s what—you know, I’m very hopeful, and I suspect that it’s going to be the generations that come after me that are going to be the ones that make those breakthroughs.
Given your emphasis of Patrick Lee’s wisdom and his foresight, are there any developments that have happened in recent years that that generation of physicists might not have seen coming?
Well, yeah, I mean, certainly, the sort of quantum information side of things and, you know, there’s very—you know, understanding the sort of structure of quantum entanglement is—and how that then informs the structure of quantum states of real materials and, you know, things that one can access experimentally. I think that’s a new direction, which I think was not in the front of people’s minds in the 1970s and ’80s. And that is a very powerful direction that we’re moving in in the present century.
Charlie, just to bring our conversation right up to the present, recent months this year, what have you been working on? What’s been interesting to you?
Well, so, a couple of things. In the last couple of years, I’ve been interested in trying to understand the effects of strong interactions on topological phases of matter. And the challenge there is developing theories which are close enough to real materials that you could make contact to experiments. And that’s a hard—it’s much harder for strongly interacting systems than it is in band theory where I was so fortunate to be able to do that. But, so, that’s one of the directions that I’ve been going in. You know, another direction I’ve been thinking a lot about is just within the context of band theory. Is there anything left in terms of understanding the topological structure, topological structures in band theory? And, so, I’ve [laugh] actually been going back and thinking about some very simple things just trying to understand the topological structure of metals. And, you know, we’ll see if that’s something that turns into something interesting or not. I’m not sure. But, you know, it’s been—it’s a lot of fun. I like thinking about things which are a little bit off the beaten track. I’m not one that excels at sort of following the most trendy, exciting things that everybody else is thinking about because I’m kind of slow, and I like having things to myself a little bit. But, you know, I think there are many, many, many exciting directions to think about, and, you know, those are a couple of them.
Charlie, I’ll ask one final question that will link retrospective questions about your career, where you are currently, and where you and the field is headed next. And that is I’ll return to my initial question about nomenclature, and the distinctions where we have this transition from solid-state to condensed matter, where soft matter fits in with this, and, as you emphasized in your answer right off the bat, that condensed matter theory and experiment, it’s a huge field, and it has many, many aspects to it. So, with all of that in mind, at some point does the nomenclature need a refresh or an update, given all the areas that condensed matter goes into from everything from quantum information to the deepest questions in cosmology? What do you think in terms of the way the field defines itself, and where that might be headed into the future?
Yeah, well, that’s a very big question you’re asking, and, you know, maybe—
That’s why I save it for the last one [laugh].
Yeah, well, and, you know, and maybe it’s the same question that people could’ve asked back in the beginning of the [laugh] 20th century where it was just physics—
—right? And, you know, that was before there was like nuclear physics and particle physics and solid-state physics and just—
I forget who it was. But somebody told me that if you were to ask Fermi if he were a theorist or an experimenter, he wouldn’t know what you were talking about.
Well, OK, that’s probably true, right. I mean, he was [laugh] better than most at both of those, right?
Yeah, [laugh] right.
So, yeah, look, I don’t know how this is going to evolve. But it certainly is the case that the field is growing increasingly diverse in such a way that people at different ends of the field are really thinking about very different things. And while there are, overarching concepts that unite things, the day-to-day is very different. Somebody doing biological physics, and somebody doing, you know, hardcore, quantum electronic structure, those are very different—very, very different endeavors. And, so, the challenge I think is how do you keep people learning? How do you keep people interacting with each other in a way that they get the benefit from that interaction without spreading everybody too thin? That, I think, is the challenge that we face as a field.
Charlie, it’s been so much fun spending this time with you. I’m so happy we connected, and you were able to share all of your perspective and insight. I really appreciate this, so thank you so much.
OK. Well, it’s been a pleasure. Thank you.