Edge states in Graphene: from gapped flat band to gapless chiral modes

TL;DR

This paper investigates how edge states in graphene can be manipulated through boundary potentials, revealing gapless valley-dependent modes linked to the material's topological properties.

Contribution

It demonstrates control over edge-state dispersion in graphene via boundary potentials, connecting these states to bulk topological characteristics.

Findings

Boundary potentials can tune edge-state dispersion.

Gapless valley-dependent edge states can be realized.

Edge states are connected to bulk topological properties.

Abstract

We study edge-states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge-bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under certain boundary potentials, gapless edge-states with valley-dependent velocity are found, exactly analogous to the spin-dependent gapless chiral edge-states in quantum spin Hall systems. The connection of the edge-states to bulk topological properties is revealed.