It is well established that symmetry has an important influence on the properties of materials, but the topology of electronic states might be an even more fundamental property. Topological insulators (TIs) are new states of matter based on the topology in the electronic band structure. Relativistic effects are the origin of the topologically non-trivial electronic structure, and the new state of matter has been realized in two-dimensional quantum well structures and three-dimensional bulk crystals of heavy elements and compounds. TI materials have an insulating gap in the bulk, and robust metallic edge/surface states on the boundary, which is robust against disorder and leads to unique spin and charge transport properties. Examples of TIs include HgTe/CdTe quantum wells, Bi-Sb-alloys, Bi2Se3, and half-Heusler compounds.
