2013/10/31 by Michel Fruchart, David Carpentier · 1 voice
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.mtrl-sci
paper · pdf · doi:10.1016/j.crhy.2013.09.013
published as Comptes Rendus Physique 14 (2013) 779-815 · 46 pages, 29 figures. This papers aims to be a pedagogical review on topological insulators. It was written for the topical issue of "Comptes Rendus de l'Académie des Sciences - Physique" devoted to topological insulators and Dirac matter
arxiv created 2013/11/03 · arxiv updated 2013/12/06
Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates valence bands from conduction bands. The ensemble of valence bands is then a well defined object, which can possess non-trivial or twisted topological properties. In the case of a twisted topology, the insulator is called a topological insulator. We introduce this notion of topological order in insulators as an obstruction to define the Bloch wave functions over the whole Brillouin Zone using a single phase convention. Several simple historical models displaying a topological order in dimension two are considered. Various expressions of the corresponding topological index are finally discussed.