Warren J. Elder, Eng Soon Tok, Dimitri D. Vvedensky, Jing Zhang
The electronic bands of graphene are examined within a tight-binding framework based on the method of invariants. Our method utilizes of the full point-group symmetry of the crystal for the construction of the Hamiltonian without the need for two- or three-center approximations. The method can accommodate electron spin, and the Hamiltonian is obtained for single- and double-group cases. Our analysis shows that the crystal symmetry ensures both a zero energy gap and linear dispersion from the $K$-point when the spin-orbit interaction is excluded from the Hamiltonian. When spin-orbit effects are included, the emergence of a small energy gap is predicted from the inter-site spin-induced mixing of the $\pi$ and $\sigma$ states and interactions due to second-nearest neighbor hopping.
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http://arxiv.org/abs/1306.2520
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