Topological insulators are paradoxical materials: they have an electrically insulating interior and a conductive exterior, yet they have the same composition throughout. In addition, the direction in which the electrons travel through the conductive layer is determined by their spin, a quantum property with two states (up and down), such that spin-up electrons move in one direction and spin-down electrons move in the other. These properties make topological insulators very interesting materials for researchers developing spintronics devices, which encode information based on electron spin (rather than electron charge) for electronics and quantum-computing applications. See also: Electrical conductivity of metal; Electrical insulation; Electron; Electron spin; Quantum computation; Spintronics

In mathematics, topological spaces are ones that retain the same properties even when stretched or deformed. The physics behind the topological insulators’ behavior is complicated, but to oversimplify, imagine that the electronic states of molecules on the surface of the topological insulators cannot change. The large energy difference (also known as band structure) between the surface and insulating states therefore does not change if the material is stretched or folded. Consequently, the band structure continues to prevent the surface electrons from entering the insulating region. See also: Band theory of solids; Topology

Since the discovery of topological insulators in 2007, researchers have found ones that function at room temperature, such as bismuth selenide (Bi₂Se₃) and bismuth telluride (Bi₂Te₃). They have also added small amounts of impurities to materials to create topological insulators with tailored properties, and in 2013 reported that the mineral kawazulite [Bi₂(Te,Se)₂(Se,S)] is a naturally occurring topological insulator.