Universal geometric classification of armchair graphene nanoribbons by their properties in a staggered sublattice potential

TL;DR

This paper explores the topological and electronic properties of armchair graphene nanoribbons under a staggered sublattice potential, revealing three classes of behavior and providing an effective theory for their band-gap variations.

Contribution

It introduces a classification scheme for armchair graphene nanoribbons based on their width and potential, supported by an effective theory that explains the observed scaling laws.

Findings

Identified three distinct classes of armchair nanoribbons based on their width.

Derived scaling laws for band gap variation in these nanoribbons.

Proposed experimental systems where these theoretical results are applicable.

Abstract

We demonstrate the topological properties of the band-gap of armchair graphene nanoribbons in a spatially varying staggered sublattice potential. Several general scaling laws are presented to quantify the band gap variation. It is found that all armchair nanoribbons are described by one of three distinct classes depending on their width, one of which is the well known massless Dirac condition, and the other two we call potentially gapless, and gapless-superlattice. We construct an effective theory which faithfully reproduces these results, and makes explicit the nature of the competing masses and overlap integrals across a particular sample. Finally we propose several systems on which these results should shed considerable light, and which have all already been experimentally realized.