Sommaire:

Topological Insulators are new states of matter. At first sight, these are just ordinary band insulators : an energy gap separates the energy of states occupied by electrons from unoccupied states. However, the ensemble of occupied electronic states possesses a non-intuitive property, known in mathematics as a topological property. Its existence is at the origin of the main physical characteristics of topological insulators: the existence of metallic states at their surface. Hence from a phenomenological point of view the topological insulators are insulating materials surrounded by a metallic surface. Moreover these surface metals are rather unique: their electrons behave as if they were massless relativistic particles. More precisely their motion is described by a Dirac equation usually associated with relativistic particles. This leads to several unique physical properties, some of them reminiscent of those of graphene. Recently, this relation between relativistic excitations and topological property triggered a large amount of work to identify other phases with analogous properties. Excitations described by a Dirac or Weyl equation of motion have now been found in bulk materials and not only at the surface of insulators.

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