Periodic table for topological insulators and superconductors

Details Periodic table for topological insulators and superconductors Periodic table for topological insulators and superconductors

2009-01-18

arxiv.org/abs/0901.2686v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

To appear in the Proceedings of the L.D.Landau Memorial Conference "Advances in Theoretical Physics", June 22-26, 2008, Cherno

Scientific paper

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_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.

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