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

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

2007-02-22

arxiv.org/abs/cond-mat/0702529v4

Phys. Rev. Lett. 99, 116601 (2007)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.99.116601

We discuss, for a two-dimensional Dirac Hamiltonian with random scalar potential, the presence of a $Z_2$ topological term in the non-linear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The $Z_2$ 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 $Z_2$ 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 $Z_2$ topological insulators in the symplectic symmetry class.

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