Helicons, Doppler-Shifted Cyclotron Resonance, and Gantmakher-Kaner Oscillations. II. p-Fold Azimuthal Symmetry
The conductivity of a metal, for the case of the wave vector in the direction of a magnetic field which in turn lies along an axis of p-fold symmetry, is examined. General properties are adduced which explicitly exhibit all the singularities of the conductivity (it is shown that there are no others) and reduce the problem to the conductivity of a collection of cylindrically symmetric Fermi surfaces with progressively smaller weightings. A model, which allows analytic computation, is used for the purpose of examining the possible modes of the electromagnetic field and the Gantmakher-Kaner oscillations. Additional modes, arising from the lack of cylindrical symmetry, are all heavily damped. The Gantmakher-Kaner oscillations are discussed as to damping, amplitude, and position. A general relation between Fermi-surface properties and the optical mass is derived in the absence of phonon effects.