Topological Insulator Materials

Topological insulators represent a new quantum state of matter which is\ncharacterized by peculiar edge or surface states that show up due to a\ntopological character of the bulk wave functions. This review presents a\npedagogical account on topological insulator materials with an emphasis on\nbasic theory and materials properties. After presenting a historical\nperspective and basic theories of topological insulators, it discusses all the\ntopological insulator materials discovered as of May 2013, with some\nillustrative descriptions of the developments in materials discoveries in which\nthe author was involved. A summary is given for possible ways to confirm the\ntopological nature in a candidate material. Various synthesis techniques as\nwell as the defect chemistry that are important for realizing bulk-insulating\nsamples are discussed. Characteristic properties of topological insulators are\ndiscussed with an emphasis on transport properties. In particular, the Dirac\nfermion physics and the resulting peculiar quantum oscillation patterns are\ndiscussed in detail. It is emphasized that proper analyses of quantum\noscillations make it possible to unambiguously identify surface Dirac fermions\nthrough transport measurements. The prospects of topological insulator\nmaterials for elucidating novel quantum phenomena that await discovery conclude\nthe review.\n