Cyclotron Resonance and the Cohen Nonellipsoidal Nonparabolic Model for Bismuth. II. Limiting - Point Masses

Abstract

An equation for the limiting-point (LP) cyclotron effective mass as a function of magnetic field direction is derived for the Cohen nonellipsoidal nonparabolic (NENP) model of the electron Fermi surface of Bi. The general NENP equation is used, in which the $L$-point valence and conduction bands are not assumed identical. For some orientations of the magnetic field, the NENP model, unlike the ellipsoidal nonparabolic (ENP) model, predicts a LP mass larger than the central-orbit extremal mass by as much as a factor of 2 for pure Bi. The previously published LP-mass data of Edel'man and Khaikin are found to be in good agreement qualitatively with the NENP model; the NENP fit is clearly superior to the ENP fit. Attempts to determine unambiguous values for the adjustable band parameters in the NENP model by fitting the experimental data were unsuccessful, but in general the experimental data indicate that the $L$-point valence and conduction bands have essentially identical parameters. For identical bands, the value $\frac{E_F}{E_g}=0.50\mathrm{}$ is required in order to fit the data.