Crystal structure and chemistry of topological insulators

Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states are crystal symmetry, the presence of strong spin-orbit coupling, and an inversion of the energies of the bulk electronic states that normally contribute to the valence and conduction bands. The goals of this review are to briefly introduce the physics of topological insulators to a chemical audience and to describe the chemistry, defect chemistry, and crystal structures of the compounds in this emergent field.