Electron density distribution and screening in rippled graphene sheets

Gibertini, Marco and Tomadin, Andrea and Polini, Marco and Fasolino, A. and Katsnelson, M. I. (2010) Electron density distribution and screening in rippled graphene sheets. Physical review B, 81: 125437. ISSN 1098-0121

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.