Possible Lattice Distortions in the Hubbard Model for Graphene

TL;DR

This paper investigates potential lattice distortions in the Hubbard model for graphene, revealing that only periodic, reflection-symmetric distortions with up to six atoms per unit cell are possible in the thermodynamic limit.

Contribution

It demonstrates that in the Hubbard model for graphene, only specific symmetric lattice distortions are allowed, expanding understanding of lattice stability and possible phases.

Findings

Only periodic, reflection-symmetric distortions are allowed.

Distortions involve at most six atoms per unit cell.

Undistorted lattice has two atoms per unit cell.

Abstract

The Hubbard model on the honeycomb lattice is a well known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of these two approximations we ask and answer the question of the possible lattice distortions for graphene in zero magnetic field. The answer is that in the thermodynamic limit only periodic, reflection-symmetric distortions are allowed and these have at most six atoms per unit cell as compared to two atoms for the undistorted lattice.