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Title: Periodic table for topological insulators and superconductors

Abstract

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z{sub 2}. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.

Authors:
 [1]
  1. California Institute of Technology, Pasadena, CA 91125 (United States)
Publication Date:
OSTI Identifier:
21304870
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1134; Journal Issue: 1; Conference: Landau memorial conference on advances in theoretical physics, Chernogolovka (Russian Federation), 22-26 Jun 2008; Other Information: DOI: 10.1063/1.3149495; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; CHARGE CONSERVATION; CLASSIFICATION; CLIFFORD ALGEBRA; DIELECTRIC MATERIALS; ELECTRONS; FERMI LEVEL; HALL EFFECT; INTERFACES; MATRICES; PERIODICITY; PHASE TRANSFORMATIONS; SUPERCONDUCTORS; SYMMETRY; TOPOLOGY

Citation Formats

Kitaev, Alexei. Periodic table for topological insulators and superconductors. United States: N. p., 2009. Web. doi:10.1063/1.3149495.
Kitaev, Alexei. Periodic table for topological insulators and superconductors. United States. doi:10.1063/1.3149495.
Kitaev, Alexei. Thu . "Periodic table for topological insulators and superconductors". United States. doi:10.1063/1.3149495.
@article{osti_21304870,
title = {Periodic table for topological insulators and superconductors},
author = {Kitaev, Alexei},
abstractNote = {Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z{sub 2}. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.},
doi = {10.1063/1.3149495},
journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1134,
place = {United States},
year = {2009},
month = {5}
}