Energy Bands of Alkali Metals. II. Fermi Surface

The Fermi energy, density of states, cyclotron effective mass, optical effective mass, and other parameters of the Fermi surfaces of the alkali metals are evaluated for the band structures calculated previously, using an interpolation formula suggested by the nearly free electron model. It is shown, however, that the nearly free electron model in its usual form based on a weak effective potential cannot provide a consistent description of the alkali band structures, and that generalization of the model to take account of the $l$ dependence of the effective potential is necessary. The calculated Fermi surface parameters are compared with the results of recent experiments and with analyses by Cohen, Heine, Dugdale, Collins, and Ziman of earlier experimental work. The trends in the calculated values agree qualitatively with those found in experiments and with trends in the band structure inferred by these authors. This comparison lends support to the interpretation that differences in the properties of the alkali metals arise to a considerable extent from differences in their electronic structure. The calculations predict appreciable anisotropy of the cyclotron mass, the de Haas-van Alphen effect, and the linear dimensions of the Fermi surface for all of the alkali metals except sodium. Values of the parameters are found to be changed considerably by distortion of the Fermi surface from values obtained in the spherical approximation. The calculated values for the thermal effective mass, however, are significantly smaller than the experimental values, except for cesium, so that at least for the lighter metals the effect of electron-electron correlation and electron-phonon interaction appears to be to enhance the effective mass.