Chiral Gauge Theory for Graphene Edge

TL;DR

This paper introduces a chiral gauge theory framework using an effective-mass approach to analyze graphene edges, revealing how mass and electromagnetic fields influence edge states and local density of states.

Contribution

It develops a novel gauge theory framework to model graphene edges, incorporating boundary conditions, mass, and electromagnetic effects within a unified effective-mass theory.

Findings

Mass term causes standing waves at the Dirac point to avoid zigzag edges.

Local density of states disappears at the Dirac point near zigzag edges.

Lowest and first Landau levels are affected by edge geometry and fields.

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.