Zero Modes on Zero-Angle Grain Boundaries in Graphene

TL;DR

This paper investigates the topological electronic states at zero-angle grain boundaries in graphene, revealing symmetry-protected zero modes and topological transitions through theoretical analysis and numerical calculations.

Contribution

It introduces a hidden chiral symmetry that supports zero modes and links topological transitions to bulk gap closures in graphene grain boundaries.

Findings

Zero modes are supported by a hidden chiral symmetry.

Zero modes occupy a finite part of the interface Brillouin zone.

Topological transitions occur at bulk gap closures.

Abstract

Electronic states confined to zero angle grain boundaries in single layer graphene are analyzed using topological band theoretic arguments. We identify a hidden chiral symmetry which supports symmetry protected zero modes in projected bulk gaps. These branches occupy a finite fraction of the interface-projected Brillouin zone and terminate at bulk gap closures, manifesting topological transitions in the occupied manifolds of the bulk systems that are joined at an interface. These features are studied by numerical calculations on a tight binding lattice and by analysis of the geometric phases of the bulk ground states.