Collective Effects in Interband Optical Absorption

Determination of the Fermi-surface anisotropy of alkali metals by the de Haas-van Alphen effect has provided reliable numerical values for electronic energy gaps at Brillouin-zone boundaries. These determinations allow a quantitative comparison of interband optical absorption power with theory. Serious discrepancies with standard theory are found. For Na, the theoretical absorption is too small by a factor of 4, whereas for Rb and Cs it is too large by a factor greater than 3. We observe that interband matrix elements must include not only the direct interaction with the photon field, but also the Hartree-Fock potential arising from collective motions of all electrons responding to that field. The interband matrix elements are calculated using time-dependent, self-consistent perturbation theory. If only the Hartree term arising from collective motion is added, matrix elements are reduced by a few percent. However, inclusion of the exchange potential profoundly alters the magnitude of the matrix element. For Na the theoretical absorption power is enhanced by a factor of 4, and for Rb and Cs it is suppressed by a factor of 6 or more. This apparent success of the time-dependent, Hartree-Fock method indicates that exchange interactions can contribute unexpectedly to electronic processes in solids.