Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of anderson localization

Shinsei Ryu, Christopher Mudry, Hideaki Obuse, Akira Furusaki

Research output: Contribution to journalArticlepeer-review

Abstract

We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a Z2 topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The Z2 topological term realizes the sign of the Pfaffian of a family of Dirac operators. We compute the corresponding global anomaly, i.e., the change in the sign of the Pfaffian by studying a spectral flow numerically. This Z2 topological effect can be relevant to graphene when the impurity potential is long ranged and, also, to the two-dimensional boundaries of a three-dimensional lattice model of Z2 topological insulators in the symplectic symmetry class.

Original languageEnglish (US)
Article number116601
JournalPhysical review letters
Volume99
Issue number11
DOIs
StatePublished - Sep 11 2007

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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