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 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.

4 pages, 4 figures

References in corpus (4)

• Electric Field Effect in Atomically Thin Carbon Films
• Topological Insulators with Inversion Symmetry
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Two-dimensional spin-filtered chiral network model for the Z_2 quantum spin-Hall effect

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• Theory of Anomalous Quantum Hall Effects in Graphene
• Observation of Anderson localization in ultrathin films of three-dimensional topological insulators
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• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
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