The valence bands in two-dimensional graphite

Abstract
A group-theoretical treatment of the spatial symmetry of two-dimensional graphite leads to a classification of the one-electron eigenstates. The method of idempotent operators is used to derive Bloch orbitals for the crystal valence bands as linear combinations of the atomic orbitals 2p$_{x}$, 2p$_{y}$ and 2s. The functions 2p$_{z}$ form the conduction band. The energy of the electrons in such orbitals is estimated in terms of four overlap integrals between nearest neighbour atoms, and four corresponding Hamiltonian integrals. The deduced band structure is not sensitive to the precise values of these integrals, and cannot be changed materially by the inclusion of further neighbours. The states form three touching bands, all fully occupied by electrons in the normal structure. The large band width of some 10 eV affects previous discussions of soft X-ray experiments.

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