Symmetry classification of energy bands in graphene and silicene

TL;DR

This paper uses group theory and tight-binding models to classify energy bands in graphene and silicene, analyzing effects of spin-orbit coupling and conditions for Dirac points formation.

Contribution

It provides a detailed symmetry classification of energy bands in graphene and silicene, including effects of spin-orbit coupling and band merging conditions.

Findings

Symmetry classification of energy bands in graphene and silicene.

Conditions for Dirac points in the Brillouin zone.

Impact of spin-orbit coupling on band structure.

Abstract

We present the results of the symmetry classification of the electron energy bands in graphene and silicene using group theory algebra and the tight--binding approximation. The analysis is performed both in the absence and in the presence of the spin-orbit coupling. We also discuss the bands merging in the Brillouin zone symmetry points and the conditions for the latter to become Dirac points.