Cyclotron resonance and cyclotron waves at far-infrared frequencies in a semimetal with nonparabolic bands

Abstract

We develop a theory of quantum cyclotron resonance in semimetals at far-infrared frequencies, assuming the ordinary polarization ($E\ensuremath{\parallel}{H}_{0}$) and the ellipsoidal nonparabolic two-band model, and compare it with the second harmonic, measured for the same polarization in bismuth at 890.7 and 964.3 GHz. For this purpose we derive the corresponding nonlocal conductivity tensor in a way which takes the nonparabolicity fully into account and which enables us to relate lifetimes to quantities calculable microscopically. Although the theory derived is not exact, it accounts in a quantitative way for the important features of the observed spectra. We show that absorption on the high-field side of the resonances is related to high-frequency cyclotron waves propagating in the sample, which are damped and have reduced amplitudes due to the finite lifetimes and due to the electrons which collide with the surface and are thus non-resonant. It was therefore necessary to find an adequate treatment of the surface effects. The only adjustable parameters in the theory are the band parameters and lifetimes. To get a good agreement with the experiment it was necessary to assume that the lifetimes were energy dependent. We made only a very approximate estimate of this dependence. A more careful study of the lifetimes is left for a subsequent paper.