Calculation of the Interband Optical Conductivity of Sodium and Potassium

Abstract

The orthogonalized-plane-wave-pseudopotential formalism for an independent-particle model is used in a first-order-perturbation-theory calculation of the interband contribution to the optical conductivity in Na and K. Particular attention is given to the modifications to the transition matrix element that arise owing to the presence of the core. The core manifests itself in two ways: as a direct "core contribution" and as a condition on the pseudopotential to ensure orthogonality of the wave functions between which the interband transitions occur. These effects were found to be important. It is shown that the theory can be summarized by a modified Wilson-Butcher formula utilizing an "effective optical pseudopotential" which incorporates the core effects and depends on the pseudopotential coefficient (110). The theoretical results are sensitive to the magnitude and sign of this coefficient and if one uses a magnitude consistent with Fermi-surface data, the optical data enable one to determine the sign. For Na, Lee's value of +0.25 eV for the coefficient resulted in a good fit to the optical data. In the case of K where the pseudopotential coefficient has not been well established from Fermi-surface measurements the present theory used in conjunction with the optical data indicates a value of approximately -0.16 eV. The results show that the interband optical conductivity can be understood in terms of an independent-particle model which incorporates the Fermi-surface data without introducing large many-body corrections.