On the edge energy of graphene

TL;DR

This paper challenges the traditional continuous model of surface/edge energy by showing that in graphene, edge energy can be discontinuous and multi-valued for certain orientations due to its non-Bravais lattice structure.

Contribution

It introduces a geometric argument demonstrating the inadequacy of continuous models for edge energy in non-Bravais lattices like graphene.

Findings

Edge energy can be discontinuous for certain orientations.

Edge energy can be multi-valued for specific orientations.

Traditional continuous models may not accurately describe edge energies in graphene.

Abstract

Surface/edge energy is typically modeled as a continuous function of orientation, $\gamma({\bf n})$. We put forward a simple geometric argument that suggests this picture is inadequate for crystals with a non-Bravais lattice structure. In the case of the idealized graphene/hexagonal lattice, our arguments indicate that the edge energy can be viewed as both discontinuous and multi-valued for a subset of orientations that are commensurate with the crystal structure.