Topological Insulators, or Gold Plated Bowling Balls

A bizarre new phase of materials only recently theorized to exist are now being experimentally identified and driving new condensed-matter research in labs around the world. It is well known that there are three so-called thermodynamic phases of matter – solid, liquid and gas. Similarly, there are three well known electronic phases of matter – insulators such as air, conductors such as copper, and semiconductors; the slightly more exotic materials which are the foundation of current computer technologies. Materials constituting a new electronic phase of matter, termed strong topological insulators (or TIs) are seemingly commonplace semiconductors with remarkable properties: Pure, unaltered TIs exhibit insulating properties in their bulk and conducting properties on their surface. At first glance, a material with the electronic properties of a gold-plated bowling ball seem of little more than academic interest, but recent developments in theory and experiment have turned TIs into one of the hottest fields in physics.

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The discovery of TIs is rather curious because unlike almost every other phase of matter, they were characterized theoretically before being discovered experimentally. This theoretical breakthrough occurred in 2008 by Fu et al. with an innovative application of the mathematics of topology to the arrangements of electrons in solids. The atomic structure of a material dictates the energies and spins of its electrons, and in most materials there is an arrangement of specific levels that are “allowed”. Known arrangements of these allowed levels leads to the well-understood properties of conductors, insulators and semiconductors. Meanwhile topology concerns itself with the “connectedness” of a shape, and it can describe the differences between a complex Celtic knot and a simple loop – though these are both closed loops, the first cannot be deformed into the second without being cut open and untangled. When these topological ideas were applied to the arrangements of electronic levels in a solid, it was discovered that there are complex insulating arrangements that cannot be transformed into the arrangement of normal insulators, much like a knot that cannot be pulled or twisted into a loop without being cut open. However, at an interface between a material with a knotted electronic structure and its normal insulating surroundings (like air or vacuum), this changeover must occur. Since there is a change in topology at this boundary, the interface cannot remain insulating, which is analogous to cutting open the knot. Theory predicts that this boundary with an “open” topology surrounding the TI would necessarily demonstrate conductivity. Intriguingly, this conductivity would not depend on the composition or structure of the surface, but instead would be topologically protected, meaning no matter its purity, the surface of a TI must be a continuous and perfect conductor.

This theoretical prediction began a race to synthesize and characterize this type of material, and recently groups led by Zhang in 2009 and Felser in 2013 have had remarkable success. They discovered that to achieve the required knotted electronic structure, heavy elements with high atomic numbers were best at pulling strongly on electrons and controlling their allowed states. Entirely new characterization methods designed to probe only the atomically thin surface of a material showed that indeed the surface conductivity of TIs exhibit all the properties predicted by theory, and strongly resemble those of another popular atomically thin material – graphene. The thinness of graphene makes it difficult to synthesize and process, but makes it perfectly suited for applications in spintronics – a new way of information processing that works with electron spin instead of charge and promises much higher processing speed combined with lower power consumption. Unlike graphene, TIs are extremely easy to produce out of common semiconductor materials already used in the computer industry, and are completely insensitive to contamination. Indeed, since the conductivity of the surface is topologically protected, Felser et al. have shown that the dissipation of electrons which normally occurs even in good conductors like graphene is absent in TIs, allowing the type of very long-lived coherent electronic signals required for advancements in next generation spintronic computing. The discovery and characterization of TIs has had a far-reaching effect on our understanding of electronic structure, and has opened the door to amazing new applications in information processing and computing.