In science, the usual order is that experiments reveal something and then theorists explain it afterward, if at all. A classic example is superconductivity. It was first noticed in 1911, but it took theorists nearly 50 years to come up with an explanation, and even that explanation does not apply to every superconducting material. But once in a while, we theorists hit on things all by ourselves. And once in a long while, that something turns out to be technologically useful.
Now is one of those times. This is the story of a remarkable theory, hatched in the middle of the past decade, that experimentalists have been pursuing ever since. It is particularly sweet because it is linked to a branch of mathematics—topology—that had until now been mostly beyond any hope of practical application. And the discovery is about as straightforward as it gets: It is possible to produce materials that are insulators on the inside but conductors on the outside.
This is heady stuff, for engineers and physicists alike. The mobility, or speed, of the surface electrons in these materials is increasing dramatically every year. Just as important is their intrinsic stability, a quality that suggests they'd be robust enough to work in practical devices, such as extremely high-capacity interconnects and, one day, maybe even practical quantum computers. Physicists, meanwhile, are deeply intrigued by the possibility of using such materials to simulate new particles and other items of theoretical interest.
Topology is the branch of mathematics concerned with aspects of form that can't be fundamentally altered by stretching. A typical example is the hole of a doughnut: Let's say you deform the doughnut into the shape of a coffee cup. What had been the hole in the doughnut is now the "hole" in the cup's handle. Mathematicians call such features topologically invariant. They can, paradoxically, appear even in a seemingly formless substance such as an electron gas, produced when electrons are confined so that they move in only two dimensions.
In fact, the ability of such a gas to be topologically complex is what led to these new materials. Until recently, electron gases had been found only at the junction of two semiconductors having different electronic properties. These gases are crucial for high electron mobility transistors (HEMTs), a form of field-effect transistor used in radar, imaging, and other applications that require high gain at high frequencies. However, the idea of a 2-D electron gas that exists at the surface of an insulator—and is topologically protected from disorder—was a revelation that emerged from theoretical work done in 2005 and 2006.
Working independently, my group at the University of California (Berkeley and Santa Barbara) and researchers at the University of Pennsylvania and the University of Illinois predicted the existence of "topological insulators," which have insulating interiors but metallic surfaces. We also predicted that though these surfaces would be atomically thin, they would nevertheless be remarkably impervious to disorder and other effects that would tend to destroy their conductivity. That is, they would resist fundamental change, much as the hole does in a stretching, twisting doughnut.
Experimentalists confirmed these predictions in 2008, working with compounds of bismuth. This success triggered an explosion of experimental and theoretical work that continues to this day.
Because of their unique conductive properties, topological insulators will extend the bag of tricks available with electronic devices. There is reason to hope that these topological tricks will transform electronics by making it possible to create robust 2-D electronic gases of arbitrary shape and by allowing the simple manipulation of the spin of an electron. Electron spin is already a crucial property for magnetic storage in your hard drive; topological insulators may also allow it to be used for logic, replacing the microprocessor in your computer with a more energy-efficient and potentially faster design.