2009/05/13 by Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki +1 · 2 citations
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1063/1.3149481
published as AIP Conf. Proc. 1134, 10 (2009) · 12 pages, 5 figures; Proceedings of the L.D. Landau Memorial Conference, 2008
arxiv created 2009/05/13 · arxiv updated 2015/05/13
An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a topologically trivial and a topologically non-trivial state. Our approach consists in reducing the problem of classifying topological insulators (superconductors) in d spatial dimensions to the problem of Anderson localization at a (d-1) dimensional boundary of the system. We find that in each spatial dimension there are precisely five distinct classes of topological insulators (superconductors). The different topological sectors within a given topological insulator (superconductor) can be labeled by an integer winding number or a Z2 quantity. One of the five topological insulators is the 'quantum spin Hall' (or: Z2 topological) insulator in d=2, and its generalization in d=3 dimensions. For each dimension d, the five topological insulators correspond to a certain subset of five of the ten generic symmetry classes of Hamiltonians introduced more than a decade ago by Altland and Zirnbauer in the context of disordered systems (which generalizes the three well known "Wigner-Dyson'' symmetry classes).