Space Group Symmetry Classification of Energy Bands in Graphene and Destruction of Dirac Points by Supercell Potential

TL;DR

This paper extends the symmetry classification of graphene's energy bands from point groups to space groups and analyzes how supercell potentials can destroy Dirac points using group theory.

Contribution

It introduces a comprehensive space group symmetry classification for graphene's energy bands and explains Dirac point destruction via supercell potentials with group theoretical methods.

Findings

Space group symmetry classification of graphene bands

Destruction of Dirac points by supercell potential

Group theory explanation of band structure modifications

Abstract

In the previous publications (E. Kogan and V. U. Nazarov, Phys. Rev. B {\bf 85}, 115418 (2012) and E. Kogan, Graphene {\bf 2}, 74 (2013)) we presented point group symmetry classification of energy bands in graphene. In the present note we generalize classification by considering the space group symmetry. Also in the framework of group theory we describe destruction of the Dirac points in graphene by a supercell potential.