Symmetry classification of energy bands in graphene in the framework of the tight-binding approximation

Details Symmetry classification of energy bands in graphene in the framework of the tight-binding approximation Symmetry classification of energy bands in graphene in the framework of the tight-binding approximation

2012-03-20

arxiv.org/abs/1203.4492v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

LaTeX, 3 pages

Scientific paper

In our previous paper (E. Kogan and V. U. Nazarov, Phys. Rev. B {\bf 85}, 115418 (2012)) we presented the results of the symmetry classification of the electron energy bands in graphene. The labeling of the bands was based on compatibility relations and guesses. In the present work we show that in the framework of the tight-binding approximation the representations of the small group in the symmetry points can be rigorously found in the framework of the group theory algebra. One of the results of the proposed analysis is the explanation of the merging of the $\sigma$ bands at the $K$ point, which, though obtained previously in many band calculations for graphene, has attracted much less attention then merging of the $\pi$ bands.

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