Dispersion relations in graphite intercalation compounds: Electronic energy bands

A phenomenological model based on staging periodicity and in-plane superlattice symmetry is developed for the electronic dispersion relations for graphite intercalation compounds. The formalism is applicable to arbitrary stage and intercalant, and is tractable for high-stage compounds where the first-principles calculations are prohibitively complex. In-plane and $k_z$-axis zone folding of the three-dimensional graphite effective-mass Hamiltonian forms the basis for studying the effect of the intercalant on the graphite host. To calculate energy bands for a stage-$n$ compound, matrix elements for every ($n+1\mathrm{}$) st graphite layer are replaced by those for intercalate layers in the Hamiltonian. The minimum number of parameters is used as required by symmetry. Specific application indicates that the transport properties and Fermi-surface topology can be explained approximately on the basis of our model using pristine-graphite parameters. A single additional parameter ${\mu }_0$ is introduced to account for the shift in potential of the graphite bounding layer, the shift being related to charge transfer to or from the graphite. Additional intercalate-graphite and intercalate-intercalate interaction parameters can serve to fine tune the electronic dispersion relations and to obtain intercalate-dependent properties. The model provides a very simple mathematical form for the calculation of optical properties, Landau-level quantization, and Fermi-surface topology.