Calculation of the anisotropy of the electron-phonon mass-enhancement parameter and the cyclotron mass in indium

Abstract

A detailed calculation of the cyclotron masses in indium is presented for various extremal cyclotron orbits on both the electron and hole surfaces. The anisotropic mass enhancement lambda k is also calculated at a number of places on the Fermi surface using realistic pseudopotential models for the phonon frequencies and polarisation vectors and for the Fermi surface, many-OPW electronic wavefunctions, Fermi velocities, and the electron-phonon interaction. The authors have carried out the line integrals on the Fermi surface both without and including lambda k for the central and non-central orbits in all directions in the (110), (010), (111) and (001) planes for the second-zone hole surface and in the (011), (110) and (111) planes for the third-zone electron surface. In general, the calculated cyclotron effective masses are in reasonable agreement with the experimental results for most of the orbits observed by Mina and Khaikin (1960) and by Hughes and Shepherd (1969). The authors find a 43% difference between the maximum and minimum values of lambda k over the second-zone surface. Their calculations also show that the lambda k on the third-zone electron surface are generally larger than those on the hole surface. The variation of the orbit-averaged mass enhancement over the second-zone surface or over the third-zone surface does not correlate well with experiment. They attribute this to inaccuracies in the electron-band velocity.