Gaussian curvature energy of graphene sheets

Abstract

The energy density of an elastic sheet is the sum of a mean curvature H term, 2kcH2, and a Gaussian curvature K term, k̄K, where kc, k̄ are constants. The sign of kc is commonly understood to be positive, but the sign of k̄ and even the role of K are subject to debate. We give reasons for the Gaussian contribution to be k̄|K| instead, with k̄ positive. This is used to obtain the mean amplitude of thermal fluctuations of a graphene sheet. © 2011 Elsevier B.V. All rights reserved.