Modeling disorder in graphene

TL;DR

This paper investigates various models of local disorder in graphene, revealing how vacancies and impurities significantly alter its electronic properties, including zero modes, resonances, and energy gaps.

Contribution

It systematically analyzes different disorder types in graphene and their effects on electronic structure, highlighting their connections and resulting spectral phenomena.

Findings

Vacancies induce localized zero modes and resonances.

Impurities cause gap and pseudogap formations.

Disorder leads to non-dispersive midgap zero modes.

Abstract

We present a study of different models of local disorder in graphene. Our focus is on the main effects that vacancies -- random, compensated and uncompensated --, local impurities and substitutional impurities bring into the electronic structure of graphene. By exploring these types of disorder and their connections, we show that they introduce dramatic changes in the low energy spectrum of graphene, viz. localized zero modes, strong resonances, gap and pseudogap behavior, and non-dispersive midgap zero modes.