Effects of topological defects and local curvature on the electronic properties of planar graphene

TL;DR

This paper introduces a formalism coupling the Dirac equation to curved space to analyze how topological defects and curvature influence the electronic properties of graphene, providing a new approach to understanding defect effects.

Contribution

It presents a novel formalism using a cosmic string analogy to model arbitrary topological defects and curvature in graphene, advancing the analysis of their electronic impacts.

Findings

Local density of states shows characteristic modulations near defects

Defects such as pentagon-heptagon pairs significantly affect electronic properties

The formalism can be applied to various defect configurations

Abstract

A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon-heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.