Graphene, Dirac equation and analogue gravity

TL;DR

This paper investigates the electronic properties of graphene nanoscrolls using a curved space Dirac equation, deriving optical conductivity and performing simulations for cylindrical geometries.

Contribution

It introduces an explicit cylindrical parametrization and analytical solutions for charge carriers, advancing the understanding of graphene nanoscrolls' electronic behavior.

Findings

Derived a compact optical conductivity expression for graphene nanoscrolls.

Provided analytical solutions for pseudoparticle modes on curved backgrounds.

Performed simulations demonstrating the applicability of the curved space Dirac model.

Abstract

We provide an updated study of some electronic properties of graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider an explicit parametrization in cylindrical coordinates, together with analytical solutions for the pseudoparticle modes living on the two--dimensional background. These results are then used to obtain a compact expression for the sample optical conductivity, deriving from a Kubo formula adapted to the 1+2 dimensional curved space. The latter formulation is then adopted to perform some simulations for a cylindrical nanoscroll geometry.