Empirical band calculations of the optical properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-band metals. I. Cu, Ag, and Au

Abstract

The imaginary part of the dielectric constant ${\ensuremath{\epsilon}}_{2}$ has been calculated for Cu, Ag, and Au in the energy range $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\le}25$ eV with full inclusion of momentum matrix elements and spin-orbit effects. The calculations were performed by a second-principles method using a combined interpolation scheme. Overall agreement with experiment, both with regard to positions and intensitites of structures, is quite good, especially for Cu and Au. Band-by-band decompositions of ${\ensuremath{\epsilon}}_{2}$ are presented and are used to locate prominent structures in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space. In the case of Au, the prominent transitions seen in thermoreflectance data around 20 eV are shown to occur at the $L$ point (or possibly at the $X$ point) rather than at the zone center as previously proposed.