Charge inhomogeneities due to smooth ripples in graphene sheets

TL;DR

This paper investigates how smooth ripples in graphene sheets cause local charge inhomogeneities by altering the electronic structure, with potential observable effects in local probes like scanning tunneling microscopy.

Contribution

It models curved ripples as smooth bumps and calculates their impact on Dirac fermions' Green's function, revealing curvature-induced modifications in electronic properties.

Findings

Fermi velocity varies with position on the curved surface.

Energy-dependent oscillations appear in the local density of states.

Predicted effects are within a few percent of flat graphene density at typical energies.

Abstract

We study the effect of the curved ripples observed in the free standing graphene samples on the electronic structure of the system. We model the ripples as smooth curved bumps and compute the Green's function of the Dirac fermions in the curved surface. Curved regions modify the Fermi velocity that becomes a function of the point on the graphene surface and induce energy dependent oscillations in the local density of states around the position of the bump. The corrections are estimated to be of a few percent of the flat density at the typical energies explored in local probes such as scanning tunnel microscopy that should be able to observe the predicted correlation of the morphology with the electronics. We discuss the connection of the present work with the recent observation of charge anisotropy in graphene and propose that it can be used as an experimental test of the curvature effects.