Graphene properties from curved space Dirac equation

TL;DR

This paper develops a mathematical framework using the curved space Dirac equation to analyze the electronic properties of curved graphene sheets, including conductivity, with a focus on cylindrical geometries.

Contribution

It introduces a novel formulation for modeling charge carriers in curved graphene using the Dirac spectrum, extending the understanding of electronic behavior in non-flat geometries.

Findings

Derived a conductivity Kubo formula for curved graphene

Analyzed electronic properties of cylindrical graphene samples

Provided theoretical insights into curvature effects on graphene

Abstract

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.