To gap or not to gap? Mass distortions and edge modes in graphene armchair nanoribbons

TL;DR

This paper analyzes how different mass distortions affect edge modes, charge density, and conductivity in metallic armchair graphene nanoribbons, revealing conditions for gapless or gapped edge states with experimental implications.

Contribution

It provides a detailed theoretical analysis of edge modes in graphene nanoribbons under various mass terms, including the effects of Kekule distortions, using a macroscopic Dirac model.

Findings

Edge modes depend on mass terms and symmetries.

Kekule distortion leads to gapped edge modes.

Charge and conductivity traces can indicate edge mode presence.

Abstract

We investigate, in the framework of macroscopic Dirac model, the spectrum, charge density and conductivity of metallic armchair graphene nanoribbons in presence of different mass terms. We reveal the conditions and symmetries governing the presence of edge modes in the system. Depending on the mass terms present they are exponentially localized gapless or gapped modes. The latter situation is realized, in particular, for a full Kekule distortion. For this case, we calculate the mean charge and conductivity of the ribbon, and derive the traces of the presence of edge modes suitable for experimental verification.