Graphene ground states

TL;DR

This paper classifies all stable deformations of graphene's hexagonal lattice, showing they are either rippled or rolled-up structures, based on energetic considerations.

Contribution

It provides a comprehensive classification of graphene ground states, linking geometric configurations to energetic stability, and proves that all ground states are either periodic ripples or nanotubes.

Findings

Ground states are either periodic ripples or rolled nanotubes.

All stable deformations can be characterized by configurational energies.

The classification covers all possible ground-state geometries.

Abstract

Graphene is locally two-dimensional but not flat. Nanoscale ripples appear in suspended samples and rolling-up often occurs when boundaries are not fixed. We address this variety of graphene geometries by classifying all ground-state deformations of the hexagonal lattice with respect to configurational energies including two- and three-body terms. As a consequence, we prove that all ground-state deformations are either periodic in one direction, as in the case of ripples, or rolled up, as in the case of nanotubes.