Higher-order topology in monolayer graphene

TL;DR

This paper demonstrates that monolayer graphene inherently supports higher-order topological corner states, which are localized at atomic scales due to a nontrivial Zak phase product, expanding the understanding of topological phases in 2D materials.

Contribution

It introduces a method to identify higher-order topological corner states in graphene through Zak phase analysis and provides explicit conditions for their existence across different geometries.

Findings

Topological corner states are present in monolayer graphene.

Zak phase product determines the existence of corner states.

Corner states exhibit nontrivial localization properties.

Abstract

We show that monolayer graphene intrinsically hosts higher-order topological corner states, in which electrons are localized topologically at atomic sizes. The emergence of the topological corner states in graphene is due to a nontrivial product of the Zak phases for two independent directions, which can be handily calculated graphically by using the bulk wavefunctions. We give an explicit expression that indicates the existence of topological corner states for various geometric edges and corner angles. We also demonstrate the nontrivial localization nature of the topological corner states in graphene by putting an imaginary onsite potential mask.