Symmetry of electron bands in graphene: (nearly) free electron vs. tight-binding

TL;DR

This paper analyzes the symmetry properties of electron bands in graphene using both free electron and tight-binding models, combining numerical calculations with group theory to provide comprehensive band labeling.

Contribution

It offers a detailed symmetry labeling of graphene's electron bands by integrating numerical and analytical group theory approaches in both models.

Findings

Symmetry labels are consistent across models.

Complementary predictions from free electron and tight-binding models.

Enhanced understanding of band structure symmetries in graphene.

Abstract

We present the symmetry labelling of all electron bands in graphene obtained by combining numerical band calculations and analytical analysis based on group theory. The latter was performed both in the framework of the (nearly) free electron model, or in the framework of the tight-binding model. The predictions about relative positions of the bands which can be made on the basis of each of the models just using the group theory (and additional simple qualitative arguments, if necessary) are complimentary.