Negative-curvature spacetime solutions for graphene

TL;DR

This paper investigates the electronic properties of graphene-like materials on negatively curved surfaces, providing explicit solutions and analyzing how curvature influences local density of states.

Contribution

It offers a detailed analysis of charge carriers on negatively curved graphene surfaces, including explicit parametrization and analytic solutions for pseudoparticle modes.

Findings

Explicit solutions for pseudoparticles on Beltrami geometry

Curvature significantly affects local density of states

Analytic description of charge carriers on curved surfaces

Abstract

We provide a detailed analysis of the electronic properties of graphene-like materials with charge carriers living on a curved substrate, focusing in particular on constant negative-curvature spacetime. An explicit parametrization is also worked out in the remarkable case of Beltrami geometry, with an analytic solution for the pseudoparticles modes living on the curved bidimensional surface. We will then exploit the correspondent massless Dirac description, to determine how it affects the sample local density of states.