Quantum transport of non-interacting 2D Dirac fermions

Shinsei Ryu, KITP

Abstract: We discuss the quantum transport of the 2D non-interacting Dirac Hamiltonian, which, e.g., underlies theoretical descriptions of graphene and a surface state of 3D Z_2 topological insulators. For a random scalar potential type disorder, a Z_2 topological term is derived in the non-linear sigma model encoding the physics of Anderson localization in the symplectic symmetry class. Unlike the Pruisken term (Chern integer) in the IQHE, the Z_2 topological term cannot be expressed, in general, as an integral of a local quantity, but as a sign of the Pfaffian of a family of Dirac operators. The Z_2 topological term has a significant effect on the renomalization group flow of the conductance.