Electron density distribution and screening in rippled graphene sheets

TL;DR

This study uses a self-consistent density-functional approach to analyze how ripples in graphene influence electron density distribution and screening, revealing the dominance of scalar potentials and the complex nature of electron-hole puddles.

Contribution

It provides a detailed microscopic analysis of ripple-induced electron density fluctuations in graphene, highlighting the roles of scalar potentials and atomic displacements.

Findings

Density fluctuations are mainly controlled by scalar potentials.

In-plane atomic displacements significantly affect electron distribution.

Electron-hole puddles are spatially complex and not directly correlated with topography.

Abstract

Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.