Analytic calculation of the optical properties of graphite

We present an analytic calculation of the dielectric constant of graphite valid in the spectral range dominated by {π}-electron transitions. An orthogonal, nearest-neighbor tight-binding description of electron bands is applied and interaction between different graphite layers is ignored. In addition to the optical response, a simple closed-form expression for the density of states is obtained. The only free parameter is the {π}-electron transfer integral, which we determine from a comparison with experiments. The analytic result agrees reasonably with measured spectra and the agreement is further improved by the inclusion of broadening. To the best of our knowledge, the present analytic calculation is the first for any real material.