Valley-Hall Kink and Edge States in Multilayer Graphene

TL;DR

This paper theoretically investigates topologically protected 1D edge and interface states in multilayer graphene, focusing on their dependence on stacking, interface structure, and external electric fields, revealing conditions for their presence or absence.

Contribution

It introduces a detailed theoretical analysis of valley-Hall edge and interface states in multilayer graphene, highlighting their dependence on stacking and external fields, which was not previously characterized.

Findings

1D states are absent at multilayer ribbon armchair edges.

1D states are present at internal valley-Hall interfaces in ABC stacked multilayers.

External electric fields influence the properties of these topological states.

Abstract

We report on a theoretical study of one-dimensional (1D) states localized at few-layer graphene system ribbon edges, and at interfaces between few-layer graphene systems with different valley Hall conductivities. These 1D states are topologically protected when valley mixing is neglected. We address the influence on their properties of stacking arrangement, interface structure, and external electric field perpendicular to the layers. We find that 1D states are generally absent at multilayer ribbon armchair direction edges, but present irrespective of crystallographic orientation at any internal valley-Hall interface of an ABC stacked multilayer.