Opening of a Gap in Graphene Due to Supercell Potential: Group Theory Point of View

TL;DR

This paper uses group theory to analyze how a supercell potential with  periodicity affects the electronic dispersion near Dirac points in graphene, revealing a gap opening.

Contribution

It provides a group-theoretical analysis of the gap opening in graphene caused by a specific supercell potential, a novel approach in this context.

Findings

Supercell potential induces a gap at Dirac points.

Group theory explains the symmetry-driven gap opening.

Analysis applies  supercell periodicity to graphene.

Abstract

We analyze in the framework of the space group theory the change of the dispersion law in grapenein the vicinity of the (former) Dirac points due to application of supercell potential with the $\sqrt{3}\times\sqrt{3}$ space periodicity and the same point symmetry as graphene.