Focus on materials science of topological insulators and superconductors

Akihiro Tanaka and Taizo Sasaki National Institute for Materials Science, Japan In a March 1997 article in Physics Today [1], Gerald Mahan, Brian Sales and Jeff Sharp write on what they deem a ‘new approach to an old problem’. The subject is thermoelectric materials, which is indeed an old problem, predating the inception of modern solid state physics itself: thermoelectric refrigeration using wires made of bismuth and antimony, the article points out, dates back to 1838. A major pivotal point came in the 1950s with the recognition that semiconductor-based home refrigerators may well become a reality, and the flurry of R&D activities that ensued turned up among other findings a prominent material, the Bi2Te3/Sb2Te3 alloy which operates well at room temperatures. Mahan et al make the case that the time is ripe to take another stab at such materials, what with the growing concerns on environmental issues, not to mention the considerable advance in synthesis techniques and theoretical methods now at the researcher’s disposal. They assert that by enlisting the full force of these latest know-hows, the ‘old problem’ can be turned into a promising playground for new applications. As much as these views are farsighted, it turns out that history had yet another twist in store for these and closely related materials, coming from a totally different field and in a manner completely unanticipated at the turn of the century. Semiconductors with strong spin–orbit interactions came into focus among condensed matter physicists seeking new guiding principles in their quest for materials with spintronic applications. This line of effort culminated in a number of important theoretical papers published around the year 2005 on the spin quantum Hall state, a new state of matter predicted to transport spin (but not charge), which can form in electron systems residing in a two-dimensional environment such as graphene. This was quickly followed by an experimental verification of the state in quantum dots, as well as the proposal of a 3d counterpart which is now commonly called a topological insulator—actually, there are several other classes of topological insulators, but here we shall adhere to popular usage. As far as material properties go, these insulators are basically featureless in the bulk, yet they have a highly unusual surface metallic state, featuring a Dirac fermion-like mode (or an odd number of them) and an assortment of novel quantum effects which cannot occur in the bulk of a detached 2d system. Interestingly, much of the experimental premises in this development cover common grounds with the materials related to in the opening paragraph—and for good reasons. While our focus in this issue is not on thermoelectric properties, it is nevertheless instructive to ponder a bit on this point. First of all, from a materials design point of view, both purposes tend to favor a modest energy gap and heavy elements. However it is perhaps even more essential here to note the distinguishing feature of topological insulators: they are symmetry-protected and topology-protected. They are symmetry-protected because unless time reversal symmetry is broken (e.g. by turning on a magnetic field), this quantum state cannot be destroyed by perturbations. They are topologyprotected since this symmetry-protection owes to the presence of a topological