title: Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization.
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.
authors.affiliation: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Shinsei
authors.initials: S
authors.lastname: Ryu
authors.forename: Christopher
authors.initials: C
authors.lastname: Mudry
authors.forename: Hideaki
authors.initials: H
authors.lastname: Obuse
authors.forename: Akira
authors.initials: A
authors.lastname: Furusaki