TY - JOUR
T1 - Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of anderson localization
AU - Ryu, Shinsei
AU - Mudry, Christopher
AU - Obuse, Hideaki
AU - Furusaki, Akira
PY - 2007/9/11
Y1 - 2007/9/11
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevLett.99.116601
DO - 10.1103/PhysRevLett.99.116601
M3 - Article
C2 - 17930456
AN - SCOPUS:34548707028
SN - 0031-9007
VL - 99
JO - Physical review letters
JF - Physical review letters
IS - 11
M1 - 116601
ER -