I was excited to hear that Charlie Kane, Laurens Molenkamp and Shoucheng Zhang were among the recipients of the 2013 Physics Frontiers Prize. Their seminal works both theoretically predicting and experimentally discovering the topological insulator have profoundly influenced the direction of condensed matter physics over the past few years and have shaped my own research agenda at Caltech.
I first learned about the topological insulator from a talk Charlie Kane delivered at the 2006 American Physical Society March Meeting. It was around this time that graphene was exploding onto the scene following Andre Geim and Konstantin Novoselov’s demonstration that single sheets of it could be peeled from graphite using Scotch tape. Inspired by the highly unconventional charge transport properties that were being measured from graphene, Charlie had begun to think about whether its spin transport properties might also yield surprises. The huge surprise, as Charlie would reveal in his talk, was that graphene could theoretically exhibit a quantum spin Hall effect in which spin-polarized charge carriers flow without dissipation along the edges of an electrically insulating material. Such quantum spin Hall insulators (later renamed the 2D topological insulator), as Charlie and his colleague Eugene Mele proved, are a phase of matter distinct from ordinary electrical insulators by virtue of a quantum entanglement of its electrons.
As a junior graduate student at the time, I found it fascinating that something as basic as the electrical insulator still had such fundamentally new physics to offer. Finding out how to experimentally detect these new phases of matter seemed like a very exciting Ph.D. research direction. However there was an issue with Charlie’s graphene proposal. The quantum spin Hall effect relies on a coupling between the spin of a delocalized electron and its motion through the lattice of nuclei that make up the crystal. The larger the nuclei, the stronger the coupling. The problem with graphene, at least for experimentalists like myself, is that the carbon nucleus is so light that any quantum spin Hall effect would be unmeasurably weak.
Shoucheng Zhang was ahead of everyone in recognizing this problem and conceived of a system that might exhibit a measurable quantum spin Hall effect. Rather than use an inherently 2D material like graphene, Shoucheng and his students Andrei Bernevig and Taylor Hughes proposed a structure in which electrons are confined to a thin layer of HgTe sandwiched between CdTe barriers, rendering them effectively two-dimensional. Owing to the heavy nuclei of both mercury and tellurium, he predicted a quantum spin Hall effect that could be realized in experimentally accessible regimes and even described the exact measurements that were needed to prove its existence.
Laurens Molenkamp had started to work on CdTe/HgTe/CdTe heterostructures years before the quantum spin Hall effect was predicted. He was interested in growing samples of the highest quality (i.e. containing a minimal amount of impurities and lattice defects) in effort to study the intrinsic characteristics of charge and spin flow through their interior. This expertise put him in a unique position to test Shoucheng’s idea. In 2007, his team published a remarkable result showing the first experimental signature of a quantum spin Hall effect. In a nutshell, the observation was that once prepared in a bulk electrically insulating state, the sample exhibits a quantized electrical conductance that is independent of the sample width, which proves that current is carried only along the edges as expected in the quantum spin Hall phase.
At the time these early breakthroughs in quantum spin Hall physics were occurring, I had been working on studying the electronic structure of thermoelectric materials in Zahid Hasan’s group at Princeton. These are materials across which a voltage can be induced by a temperature gradient, which makes them promising as waste heat to electricity converters. Good thermoelectric performance requires a low thermal conductivity, which is typically the case for compounds made of heavy elements. Coincidentally, heavy elements are also conducive to the quantum spin Hall effect and therefore it was interesting to consider whether new phases of matter might also lurk in these thermoelectric materials. However, the problem was that thermoelectric compounds are bulk 3D materials whereas the quantum spin Hall effect is an exclusively 2D phenomenon.
Once again Charlie Kane delivered the answer. During a seminar at Princeton in 2007, he introduced the idea of a 3D topological insulator that he had developed with his student Liang Fu. This was a new phase of matter that, like the quantum spin Hall phase, is distinguished from ordinary 3D insulating phases by virtue of quantum entanglement. But unlike the quantum spin Hall phase, a 3D entangled phase was previously not believed possible. Credit for this discovery also belongs to Joel Moore (who in fact coined the term topological insulator), Leon Balents and Rahul Roy. However, it was Charlie and Liang who showed that the 2D surfaces of a 3D topological insulator form a special type of metal that is unusually robust against impurities, and who were the first to propose real compounds that might realize this phase of matter.
Among the compounds predicted was Bi1-xSbx, a thermoelectric material that Zahid and I happened to be working on with Bob Cava at the time. The technique that we specialized in was angle-resolved photoemission spectroscopy, which is highly sensitive to the surface electronic structure of a material. Following Charlie and Liang’s prescription, we began an intensive cycle of sample growth and measurement in search of the 3D topological insulator. While this was definitely one of the most physically exhausting periods of my life it was also one of the most fun, and I look back fondly upon that opportunity of being engaged in an exciting intellectual pursuit. The all nighters paid off because we finally did discover the first 3D topological insulator in nature.
Like me, numerous scientists around the world have re-directed their focus to topological insulators following the seminal works of Charlie, Shoucheng and Laurens. Improved material quality and device fabrication are continually inching topological insulators towards technological applications. However, in my opinion, the even greater contribution that these three prize recipients have made is to bring topological materials to the forefront of condensed matter physics. Beyond topological insulators, they have inspired scientists to reconsider whether other well known phases such as superconductors or Mott insulators can also have topological counterparts. What applications these new generations of topological materials might have is probably beyond our current imagination. That being said, there is recent experimental evidence that a 1D topological superconductor can support Majorana bound states, which may be the building blocks of a fault-tolerant quantum computer. This work was in fact Science Magazine’s runner-up for the 2012 scientific breakthrough of the year, trailing only the discovery of the Higgs boson. Let’s hope this is the start of a trend!