Graphite intercalation compounds: Electronic properties in the dilute limit

A model is presented for the electronic properties of graphite intercalation compounds in the dilute limit, corresponding to intercalate concentrations more dilute than a stage-4 or -5 compound. In this limit, the electronic effect of intercalation in donor and acceptor compounds is modeled, respectively, as a raising or lowering of the Fermi level within the $\pi$ bands of pure graphite, as represented by the Slonczewski-Weiss-McClure dispersion relations for $E\left(\overrightarrow{\mathrm{k}}\right)$. Within this framework we calculate the dependence on Fermi level of the following quantities: (i) the electron and hole carrier densities, (ii) the electron and hole density of states, (iii) the de Haas-van Alphen extremal areas, (iv) the Hall constant in the low-magnetic-field limit, and (v) the in-plane electrical conductivity ${\sigma }_{\mathrm{a}}$ with several different assumptions for the energy dependence of the relaxation time. Distinctive features in the energy dependence for each of these quantities are identified in order to suggest experiments designed to determine the fractional number of carriers introduced per intercalate atom or molecule.