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

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dc.creatorRyu, Shinsei
dc.creatorMudry, Christopher
dc.creatorObuse, Hideaki
dc.creatorFurusaki, Akira
dc.date2007-02-22
dc.date2007-09-11
dc.date.accessioned2026-07-07T08:28:36Z
dc.date.available2026-07-07T08:28:36Z
dc.descriptionWe 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.
dc.description4 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0702529
dc.identifierhttp://arxiv.org/abs/cond-mat/0702529
dc.identifierPhys. Rev. Lett. 99, 116601 (2007)
dc.identifierdoi:10.1103/PhysRevLett.99.116601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137675
dc.subjectMesoscale and Nanoscale Physics
dc.subjectDisordered Systems and Neural Networks
dc.titleZ2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
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