Chiral Gauge Theory for Graphene Edge

Abstract

An effective-mass theory with a deformation-induced (an axial) gauge field is proposed as a theoretical framework to study graphene edge. Though the gauge field is singular at edge, it can represent the boundary condition and this framework is adopted to solve the scattering problems for the zigzag and armchair edges. Furthermore, we solve the scattering problem in the presence of a mass term and an electromagnetic field. It is shown that the mass term makes the standing wave at the Dirac point avoid the zigzag edge, by which the local density of states disappears, and the lowest and first Landau states are special near the zigzag edge. The (chiral) gauge theory framework provides a useful description of graphene edge.