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.
Highlights
Since graphene was first isolated experimentally [1], it is in the focus of attention of both theorists and experimenttalists
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
Though the idea of using the tight-binding approximation is by no means new, our mathematical approach is totally different, as one can see comparing the present work with [2], and, to our opinion, more convenient for applications. This statement is supported by the analysis of the symmetry of the energy band in silicene
Summary
Since graphene was first isolated experimentally [1], it is in the focus of attention of both theorists and experimenttalists. Though the idea of using the tight-binding approximation is by no means new (it was used already in the work by Lomer), our mathematical approach is totally different, as one can see comparing the present work with [2], and, to our opinion, more convenient for applications. This statement is supported by the analysis of the symmetry of the energy band in silicene. In this case the symmetry points are Γ—the center of the Brillouin zone, the points K which are corners of the Brillouin zone and the points M which are the centers of the edges of the Brillouin zone
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