Crystallization for a Brenner-like potential
Abstract
Graphene is a carbon molecule with the structure of a honeycomb lattice. We show how this structure can arise in two dimensions as the minimizer of an interaction energy with two-body and three-body terms. In the engineering literature, the Brenner potential is commonly used to describe the interactions between carbon atoms. We consider a potential of Stillinger-Weber type that incorporates certain characteristics of the Brenner potential: the preferred bond angles are 180 degrees and all interactions have finite range. We show that the thermodynamic limit of the ground state energy per particle is the same as that of a honeycomb lattice. We also prove that, subject to periodic boundary conditions, the minimizers are translated versions of the honeycomb lattice.
Keywords
Cite
@article{arxiv.1512.04489,
title = {Crystallization for a Brenner-like potential},
author = {Brittan Farmer and Selim Esedoglu and Peter Smereka},
journal= {arXiv preprint arXiv:1512.04489},
year = {2016}
}
Comments
Added references to Section 1, Commun. Math. Phys. (2016)