Velocity operator and far-infrared electrodynamics for non-parabolic bands of the type E(1 + E/ EG). The case of bismuth

Abstract

Calculations are reported of far-infrared absorption as a function of magnetic field for the ranges of frequencies and fields: 1000–7000 GHz and 0.2–5 T, binary direction. The use of velocity matrix elements for non-parabolic, two- and one-band models of the type E(1 + E/ E G) is discussed. The absorption spectra are analyzed in terms of the resonant structures in the conductivity. The fields at which the resonant structures terminate are found to originate from resonant transitions of non-extremal orbits. They coincide with a characteristic feature in the measured absorption spectra provided a field dependence, −0.9 meV/T, of the energy gap is accounted for. This field dependence also resolves a previously found discrepancy between calculated and measured positions of dielectric anomalies.