Relativistic Band Calculation and the Optical Properties of Gold

Abstract

The energy band structure of gold is calculated by the relativistic augmented-plane-wave (RAPW) method. A nonrelativistic calculation is also presented, and a comparison between this and the RAPW results demonstrates that the shifts and splittings due to relativistic effects are of the same order of magnitude as the gaps (approximately 1 eV). Various integrated functions, density of states, joint density of states, and energy distributions of joint density of states are derived from the RAPW calculation. These functions are used in an interpretation of photoemission and static reflectance measurements. It is shown that the photoemission results are extremely well described in terms of a model assuming all transitions to be direct whereas a nondirect model fails. The ${\ensuremath{\epsilon}}_{2}$ profile calculated in a crude model assuming constant matrix elements matches well the corresponding experimental results. The calculated interband edge ($\ensuremath{\hbar}{\ensuremath{\omega}}_{i}=2.38$ eV) agrees with experimental values, and the absorption tail below the interband edge which is found in experimental traces is also contained in the theoretical curve. By means of a calculation of the Fermi surface and the constant-energy-difference surfaces it has been possible to trace out the regions in $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space where the edge and tail transitions occur. It is demonstrated that structure in the static reflection curves are not related to critical points in the band structure. The arguments are supported by calculations of temperature shifts of the critical-point energies and comparison to the observed temperature shifts of the elements of structure in the experimental ${\ensuremath{\epsilon}}_{2}$ function. Such structure may originate in extended rather than localized regions of $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}$ space. In contrast, critical-point transitions show up clearly in modulated reflectance spectra, and all elements of structure are fully accounted for by our band model. The temperature and strain responses in the band structure are determined by performing the RAPW calculation with two lattice constants and estimating the effects of the lattice vibrations by means of an OPW-LCAO (linear combination of atomic orbitals) scheme with pseudopotential Fourier constants reduced by the appropriate Debye-Waller factors. The phonon spectrum has been calculated for the latter purpose.