Gauge field for edge state in graphene

TL;DR

This paper analytically investigates a special gauge field in the continuous model of graphene, elucidating the properties and robustness of edge states, especially on zigzag edges, and their stabilization mechanisms.

Contribution

It introduces a gauge field framework to explain edge state properties and their stability against surface reconstruction and particle-hole symmetry breaking.

Findings

Edge states exist only on zigzag edges.

The gauge field explains the partial k-space appearance of edge states.

Next nearest-neighbor interactions stabilize edge states.

Abstract

By considering the continuous model for graphene, we analytically study a special gauge field for the edge state. The gauge field explains the properties of the edge state such as the existence only on the zigzag edge, the partial appearance in the $k$-space, and the energy position around the Fermi energy. It is demonstrated utilizing the gauge field that the edge state is robust for surface reconstruction, and the next nearest-neighbor interaction which breaks the particle-hole symmetry stabilizes the edge state.