Calculation of the cyclotron mass and superconducting energy gap as a function of Fermi surface position in zinc

Abstract

The anisotropic mass enhancement and anisotropic superconducting energy gap are calculated for zinc using pseudopotential theory. The phonon frequencies and polarization vectors are obtained from a model developed here which uses Shaw's optimized model potential with three force-constant terms adjusted to obtain agreement with neutron scattering data. A realistic Fermi-surface geometry is used and the electron wave functions are made up of several orthogonalized plane waves being those obtained by using the Stark and Falicov nonlocal pseudopotential. The band mass and velocities are calculated again using the Stark and Falicov pseudopotential, but with an empirically determined energy dependence of the nonlocal part off of the Fermi surface. With these models, the phonon mass enhancement of the electrons which shows up in the electronic specific heat is calculated, as is the superconducting transition temperature, anisotropic mass enhancement, and the anisotropic superconducting energy gap. The model produces a quasiparticle velocity in good agreement with the magnetic-surface-state measurements of Rahn and Sabo, gives cyclotron resonance masses that agree well with the measurements of Brookbanks, and produces an anisotropy of the energy gap that is in good agreement with the ultrasonic-attenuation measurements of Cleavelin and Marshall. There are other experiments that are not inmore » agreement with the results of this model, but they are not in agreement with the three experiments above, either.« less