A cosmological model for corrugated graphene sheets

TL;DR

This paper introduces a formalism coupling the Dirac equation to curved space to model the electronic effects of topological defects and corrugations in graphene sheets, providing insights into their local density of states.

Contribution

It proposes a novel theoretical approach using a cosmic string analogy to analyze electronic properties of corrugated graphene with multiple topological defects.

Findings

Local density of states shows characteristic modulations near defects

The formalism can handle arbitrary defect configurations

Predictions are relevant for scanning tunneling microscopy observations

Abstract

Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. 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.