Berry's Phase for Standing Wave Near Graphene Edge

TL;DR

This paper investigates the Berry's phases of standing waves near graphene edges, revealing trivial phases near zigzag edges and non-trivial phases near armchair edges, with implications for local density of states and transport properties.

Contribution

It provides a detailed analysis of Berry's phases for standing waves at different graphene edges, highlighting the presence or absence of Dirac singularities and their effects.

Findings

Berry's phase near zigzag edge is trivial

Berry's phase near armchair edge is non-trivial

Absence of Dirac singularity near zigzag edge

Abstract

Standing waves near the zigzag and armchair edges, and their Berry's phases are investigated. It is suggested that the Berry's phase for the standing wave near the zigzag edge is trivial, while that near the armchair edge is non-trivial. A non-trivial Berry's phase implies the presence of a singularity in parameter space. We have confirmed that the Dirac singularity is absent (present) in the parameter space for the standing wave near the zigzag (armchair) edge. The absence of the Dirac singularity has a direct consequence in the local density of states near the zigzag edge. The transport properties of graphene nanoribbons observed by recent numerical simulations and experiments are discussed from the point of view of the Berry's phases for the standing waves.