Abstract
We discuss, for a two-dimensional Dirac Hamiltonian with a random scalar potential, the presence of a topological term in the nonlinear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. The 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 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 topological insulators in the symplectic symmetry class.
- Received 20 February 2007
DOI:https://doi.org/10.1103/PhysRevLett.99.116601
©2007 American Physical Society