Optical Properies of Graphite

A three-dimensional Fourier expansion has been developed to describe the dispersion relations $E\left(\overrightarrow{\mathrm{k}}\right)$ for the $\pi$ bands of graphite throughout the Brillouin zone. The coefficients of the Fourier expansion are evaluated by a fit to the experimentally determined parameters of the Slonczewski-Weiss model, as well as to the optical data. Using this energy-band model, the interband contribution to the frequency-dependent dielectric constant has been calculated in the energy range $0.5<\mathrm{}\hslash \omega <6\mathrm{}$ eV for both $\overrightarrow{\mathrm{E}}\perp \overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{E}}\parallel \overrightarrow{\mathrm{c}}$. For this calculation, a numerical-integration procedure has been developed to carry out the full-zone integrations. The results for the dielectric constant are primarily dependent on the values of the McClure parameters ${\gamma }_0$, ${\gamma }_1$, ${\gamma }_3$, and ${\gamma }_4$, which enter the Slonczewski-Weiss Hamiltonian for graphite.