Dielectric matrix for aluminum

Abstract

The dielectric screening matrix ${\ensuremath{\epsilon}}_{G{G}^{\ensuremath{'}}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}})$ 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 $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$, [100], [110], and [111], with 15 values for the reciprocal-lattice vectors $\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}}^{\ensuremath{'}}$. 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 $|\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}+\stackrel{\ensuremath{\rightarrow}}{\mathrm{G}}|$ increases.