Dielectric matrix for aluminum

Abstract

The dielectric screening matrix ${\epsilon }_{G{G}^{\prime }}\left(\overrightarrow{\mathrm{q}}\right)$ for aluminum is evaluated using realistic band energies and wave functions. The Bloch states are obtained from a self-consistent tight-binding calculation in which Gaussian orbitals are used as basis functions. Results are presented for three principal directions of $\overrightarrow{\mathrm{q}}$, [100], [110], and [111], with 15 values for the reciprocal-lattice vectors $\overrightarrow{\mathrm{G}}$ and ${\overrightarrow{\mathrm{G}}}^{\prime }$. It is found that the off-diagonal elements are, in general, small compared to the diagonal terms and that the diagonal terms show some directional effect in their monotonic decrease as $|\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{G}}|$ increases.