TY - GEN

T1 - Classification of topological insulators and superconductors

AU - Schnyder, Andreas P.

AU - Ryu, Shinsei

AU - Furusaki, Akira

AU - Ludwig, Andreas W.W.

PY - 2009

Y1 - 2009

N2 - 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 ind = 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 and Dyson" symmetry classes).

AB - 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 ind = 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 and Dyson" symmetry classes).

KW - Anderson localization

KW - Quantum hall effects

KW - Topological phase

UR - http://www.scopus.com/inward/record.url?scp=65649114938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65649114938&partnerID=8YFLogxK

U2 - 10.1063/1.3149481

DO - 10.1063/1.3149481

M3 - Conference contribution

AN - SCOPUS:65649114938

SN - 9780735406711

T3 - AIP Conference Proceedings

SP - 10

EP - 21

BT - Advances in Theoretical Physics - Landau Memorial Conference

T2 - Landau Memorial Conference on Advances in Theoretical Physics

Y2 - 22 June 2008 through 22 June 2008

ER -