Charles Kane’s world is filtered through a geometric lens. He calculates and stores information in a mental grid, sorting each bit away in pictures that blend together as beautifully as they do harmoniously.

Perhaps most notable about Kane’s perspective is that, with such clarity, he sees things that can’t actually be seen—by the naked eye, at least.

Kane, the Class of 1965 Endowed Term Chair Professor in Penn’s School of Arts & Sciences’ Department of Physics & Astronomy, studies the world’s biggest question marks on a microscopic scale.

It’s an interest Kane says dates back to his childhood, before he ever really understood that his frame of mind was that of a physicist.

“I was always interested in mathematics and science, and my first love was really mathematics,” Kane says. “When I went to college at the University of Chicago, though, I realized what I liked about mathematics was really what was important to the way a physicist thinks about things.”

One experience that guided him toward the theoretical branch of physics—in which he’s now renowned for his work on the theory of quantum electronic phenomena in solids—occurred while working in the laboratory of Thomas Rosenbaum, an experimental condensed matter physicist. Rosenbaum, who has since been named the president of the California Institute of Technology, put Kane to work building electronics and soldering wires.

“One thing I learned was that I wasn’t very good at soldering,” Kane says with a laugh. “I wasn’t really cut out to be an experimental physicist. But I feel that especially for a theoretical physicist, it’s really important to have experiences like that, where you actually see how it is that experimentalists operate. Certainly in my field, it’s really about what can be done in the lab. It’s not just about the abstract, pushing symbols around. It’s really about the physical world.”

After later earning his Ph.D. from the Massachusetts Institute of Technology and a two-year stint as a postdoc at IBM, a 28-year-old Kane landed a job as a junior professor at Penn, where he would go on to forge game-changing discoveries in the field of physics and earn honors as prestigious as a spot among the Thomson Reuters Citation Laureates.

The Current recently sat down with Kane in his office in the David Rittenhouse Laboratory to discuss how his work relates to the revolution of electronics technology, his teaching philosophy, the merits of pursuing the creation of a quantum computer, and what it was like to be in contention for the Nobel Prize.

Q: You mentioned your awakening to the differences between mathematics and physics. Could you talk about what makes them different?
A: I can tell you a little story about the difference between the way a mathematician thinks and the way a physicist thinks. A physicist tends to think about mathematics as being about something that exists in the concrete world. These still could be very abstract ideas, but it’s applied to something that is real. Mathematicians are not constrained by that. When I was working on this topological insulator theory that I developed, there was a particular point where I was trying to learn some mathematics that I didn’t know. I had this idea that there had to be something called a topological invariant that I was trying to formulate. So I went upstairs to talk to a mathematician—[Professor of Mathematics] Tony Pantev, who is a brilliant mathematician here at Penn—and I asked him if what I was saying was right. I was able to explain the math problem to him, and he did some math calculation that I still don’t completely understand, but his answer was, ‘Yes, there is a topological invariant.’ I said to him, ‘But Tony, I want to be able to calculate the topological invariant so I can tell what its value is.’ And he looked at me and said, ‘Why would you want to do that? You proved that it exists.’ That’s the thing with nontrivial mathematical content—calculating it, that’s not so interesting. [As a physicist], I can appreciate mathematical ideas if they’re about something in the physical world. And if it doesn’t have that, then math seems to me more dry nd academic.

Q: Have you found that a lot of your research has been informed by unofficial interactions with colleagues like that?
A: There are a lot of things that I don’t know that other people know. [Laughs.] And of course, the challenge is figuring out what, of that vast amount of stuff we don’t know, you need to assimilate to do something interesting. This was an example where what I needed to learn was something that was very well understood by mathematicians. From the point of view of a mathematician, it’s almost elementary. The challenge was a communications problem. That was hard to overcome. And it still remains a challenge. I do feel that there are still problems out there that we haven’t solved yet, and if we could improve the communication between the mathematicians and physicists, there would be more progress to be made.

Q: Could you give an example of one such problem?
A: One direction my field is going in is trying to understand the fundamental electronic phases that matter can exist in. There are some areas in which this problem has been solved, in particular states where you can understand them by thinking about one particle at a time. That, we have a fairly good understanding of. But in general, one has to worry about the interactions between all the particles, and it becomes a many-body problem, and the many-body problem is very hard. This many-body problem brings in levels of mathematics that are much more sophisticated than the single-particle problem. This is an example of an area where I think mathematicians can help physicists.

Q: Your research is focused on the theory of quantum electronic phenomena in solids. What does this encompass?
A: The theory of quantum electronic phenomena in solids underlies the information technology revolution that we’ve all experienced over the last few decades. In your pocket, you have a cell phone that has semiconductors in it. A lot of the revolution of electronics technology came about because of quantum electronic phenomena in solids. It’s first understanding how the materials behave, how a semiconductor behaves, and then it’s learning what you can do with that information. Semiconductor technology is something that is very highly developed. In a sense, what I’m trying to do is to complete that task of understanding what kinds of behaviors materials can have and what you can do with them.

Q: You’ve said before that this is an ‘exciting’ branch of physics because ‘the technology for manipulating and controlling matter on a microscopic scale continues to advance in fascinating directions.’ Can you talk about these advancements and what makes them so exciting?
A: It’s true that technological advances have allowed people to control and manipulate matter in unprecedented ways so that they can create materials that are virtually perfect, in terms of their crystalline order. They can create materials that are extremely small, and control them on an extremely small scale. They can make materials, for instance, that [have] reduced dimensionality. You can have a material that is two-dimensional. An example of that is graphene, which is a very exciting material these days. In addition, one can combine materials in various ways and make structures out of them, and by doing that, one can make things that you weren’t able to make before. One of the directions I’m interested in is learning how to control the quantum mechanical behavior of electrons in various types of materials. One of the things that one might hope to be able to do with that is to make a new kind of computer, which is a quantum computer. That’s one of the holy grails of our time—learning how to make a quantum computer.

Q: Why is the quantum computer such a focus in the scientific community right now?
A: There are two reasons. One is that as a computer, a quantum computer can do certain kinds of problems in a qualitatively faster way than an ordinary computer can. There’s a classic problem that is, if you have some huge hundred-digit number, can you find its factors? This is a very practically important problem because this is the way the codes that store your credit card information are kept. It turns out that if you have a quantum computer, you can factor large numbers much more quickly. From my perspective, the idea of having a quantum computer is a tool for probing what is strangest about quantum mechanics in a fundamental way. Quantum mechanics has some very, very strange features, which to this day are not completely understood. What happens when you measure something in quantum mechanics? That’s a very deep and fundamental problem. Getting control of the types of physics that we need in order to make a quantum computer moves us in the direction of understanding those fundamental problems in a better way. Making a quantum computer is a very difficult problem. I don’t know if it will happen in my timescale or not, but the quest for making a quantum computer has created interesting science problems along the way. Making a quantum computer is a motivation, but the fun is the route that you take toward getting there. I think that there’s much that we have to learn about the electronic properties of materials.

Q: You were the first to propose the existence of the quantum spin Hall effect. Can you talk a little bit about this discovery and its significance in the field of physics?
A: It was a little bit of a serendipitous thing. I’ll tell you the story of how we stumbled upon this idea. This really was something that wasn’t just me—it was also [Professor of Physics] Gene Mele, my colleague. Just about 10 years ago this fall, we were very excited about the discovery of graphene. Graphene is a two-dimensional material—it’s basically a single plane of pencil lead. What people had learned how to do was to isolate a single atomically thin layer of graphene and do very interesting electronic experiments on it. This is something that Gene and I had been thinking about for a long time because we had been doing other research about materials related to graphene. We thought, this is going to be big—and it was big and still is. The Nobel Prize was awarded a couple years ago for the discovery of graphene. So we thought to ourselves, ‘We have to do something interesting on this because if we wait too long the whole world is going to descend on this problem and take all of the easy problems away.’ [Laughs.] I started thinking, ‘What is it that’s interesting about graphene?’ And the thing that is most striking about the electronic properties of graphene is that it’s right on the boundary of being an electrical conductor and being an electrical insulator. It’s right at the transition between those two. Then I asked myself the question, ‘Why is that? Why is it on the boundary between being an electrical conductor and an electrical insulator?’ When I thought about it, what I realized was that, actually, it shouldn’t be on the boundary. It should actually be an insulator. When [classifying graphene as] an insulator, there’s a sharply defined criterion, which is the existence of what we call an energy gap. I realized there should be an energy gap in graphene, provided one accounts for a property of electrons one doesn’t usually account for when thinking of graphene, which is something called a spin-orbit interaction. If you take this into account, then graphene should be an insulator. I started thinking about this insulator, and it turned out it was interesting because it related to something else I had studied for years, which is the quantum Hall effect. What I was able to understand by thinking about this connection between graphene and the quantum Hall effect is, yes, graphene is an insulator, but it’s a conductor on its boundary. The nature of this insulating state that graphene should have is such that it should conduct electricity not on the inside of the material but on the boundary. This is something I realized I hadn’t  seen before. This was something that was new. Of course when I noticed this, even more questions posed themselves. How could it be? Usually the boundary of a two-dimensional system is one dimensional, and usually when I think about conductors in one dimension, they should turn into insulators if there are any dirt or impurities. I suspected that [would] be the case [with graphene] as well, but when I thought about it and investigated, I realized that, no, actually, this conductor is insensitive to how dirty it is. There’s something deep protecting this conducting edge of this insulator interior. That’s really the significance of the quantum spin Hall effect—it’s that you have something that doesn’t conduct electricity on the interior, but it does conduct electricity in a very special way on its boundary. When I realized that these edge states—at the time I was thinking about graphene—were protected in a sense, that’s when I realized there was something that was new.

Q: That must have been extremely exciting.
A: It is an exciting discovery. Though at the time it didn’t seem as exciting because the reason people didn’t think about this for graphene before is because this effect it relies on—the spin-orbit effect I mentioned—is a very weak effect. What that means is that while graphene in principle should be an insulator, in practice it is not because this energy gap that makes it an insulator is really, really small. The energy gap in graphene, in fact, is so small that nobody has measured it. Graphene as a model system for a theoretical physicist was very nice because I could make a model that I could understand, but as a material for observing this [quantum spin Hall effect] in the real world, it’s not the best material. While I was excited because it was very interesting, I was not completely happy because we had not found a material that would be for practical purposes a quantum spin Hall insulator.

Q: How does that discovery relate to your work with topological insulators?
A: An important development that had to happen—this was [discovered by] colleagues at other institutions—was the realization that there are other venues that can host this topological insulator. A very important development was a realization by Shoucheng Zhang from Stanford and his collaborators that mercury cadmium telluride quantum walls can give this effect, and it has a big spin-orbit interaction. One other important development that was again back here with Gene Mele and [former Ph.D. student] Liang Fu, who played a very key role, was the realization that there’s a three-dimensional version of this effect. You can have a three-dimensional crystal, which on its interior is an insulator, but now on its surface, which is a 2-D surface, it can be an electrical conductor. We realized this first in a model, but then we were also able to come up with predictions for real material candidates that this would occur in. Those predictions were then verified experimentally. It was with the discovery of these three-dimensional topological insulators that this field really took off.

Q: What are some of the potential applications for topological insulators?
A: One application is taking advantage of this very special conducting state that can take place at the edge of a two-dimensional topological insulator or on the surface of a three-dimensional topological insulator. The thing that’s very nice about these states is that they are less sensitive to scattering of electrons by impurities. So in a sense, they are better conductors. That may be something that is useful for designing electronics where the electrons don’t lose their energy to heat as much. The more ambitious class of applications, which is one thing I’ve been interested in a lot recently, is using the special properties that these edge and surface states have as a route to making a new quantum computer. What we were able to show was the realization that if you combine a topological insulator with another fascinating material—a superconductor—this allows you to create a very interesting quantum state, which we call a topological superconductor. This topological superconductor offers a new way of storing and manipulating quantum information.

Q: It sounds like your earlier background in experimental physics played a role in these discoveries.
A: It certainly instilled in me the desire to make these abstract ideas that I was coming up with happen in the real world. That’s the satisfying thing. The ideas we develop, they have sort of an aesthetic beauty to them, which is, in a way, independent of the practical applications. But for me it’s the combination of the beauty of the ideas, and having these beautiful ideas come to live in the real world. That’s what really drives me.

Q: You were recently named one of this year’s Thomson Reuters Citation Laureates, which is an honor designed to recognize researchers whose body of work puts them in contention for a Nobel Prize. Earlier this year, you were also elected by your peers to the National Academy of Sciences, which is one of the highest honors a U.S. scientist or engineer can receive. What have these experiences been like for you?
A: I have received a level of recognition that is far beyond what I ever imagined could have been possible 10 years ago when I was just starting out with this. I had no idea that things would turn out like this. I feel tremendously honored, and to be frank, I feel very fortunate. There’s a certain amount of perseverance that comes into it, but there’s also a certain amount of luck in that what I stumbled onto turned out to be something that was a path leading somewhere very interesting.

Q: You were also named as one of the 2014 winners of the Lindback Award for Distinguished Teaching at Penn. What is your teaching philosophy?
A: My approach is to try to explain things as clearly and transparently as I can. You know, I’m never going to win people over by telling good jokes or being a flamboyant personality. [Laughs] My strength, if I have one, is being able to take things that are hard to understand and make them easier to understand by explaining them very clearly. Many of these ideas, if you know how to think about them in the right way—they’re not hard. You just need to be shown the right way to think about them and get used to thinking in the right way. So for me, showing people the simple way to think about difficult concepts is what I try to do.

Q: I’m sure that’s easier said than done. How do you do that?
A: Part of it is figuring out for myself what the simple way of thinking about things is. The first person I have to explain things to is myself. You have to really understand what you’re talking about, and then it’s a matter of coming up with a very clear argument.

Q: When you launched your research career, did you envision yourself eventually teaching?
A: I think I did. My father was a professor of civil engineering, so certainly I had a little bit of an idea what it was like. And I think I had an idea that I wanted to do research, but at the time, when I was young, I didn’t really know what that meant. I knew that I liked sitting and thinking about stuff and doing calculations—that’s what I enjoy doing. It’s pretty amazing that I’ve gotten a job that I get paid for doing that.

Q: Are there any problems within your scope of work that are currently keeping you up at night?
A: We have a very good understanding about the electronic phases of matter that you can understand by thinking about one particle at a time. Topological insulators are an example of that. What’s been keeping me up at night lately is trying to come up with ways of thinking about the many-electron problem. In other words, I’ve been trying to identify the simplest version of the really hard problem. I have some ideas, though a lot of my ideas turn out to be wrong, and I have to start over again.

Q: You mentioned before that the creation of the quantum computer is a major goal in the scientific community. Are there any other major goals you have your sights set on?
A: There’s this big problem of understanding what the kinds of phases of matter are that can exist. That’s a problem that is bigger than making a quantum computer. Who knows what else one could make if we could understand the different ways that electrons can behave? This could get at deeper issues in quantum mechanics, and so that’s the sort of big problem I see myself focusing on.

Q: There’s a section of your website devoted to your interest in classical guitar music. When did you become interested in guitar?
A: I think I was about 16 years old, and I wanted to learn how to play ‘Stairway to Heaven.’ That’s how it started, and I realized I liked classical music. I took classical guitar lessons when I was young for several years, and I’ve managed to keep it up over time. Lately it’s been getting harder. There’s always been a tug between doing physics and playing guitar, and lately the physics has been winning. Though I’ve gotten to the point where I can enjoy it.

Q What’s the most rewarding part of your work?
A: The most rewarding part is the rare ‘a-ha’ moment that you get, and they don’t come that often. But the moment when you realized you figured something out that you didn’t know before, that’s a very rewarding thing.