Cyclotron resonance of polarons in ellipsoidal bands. I. Simple limiting cases

The cyclotron resonance energy at zero temperature and vanishing concentration of carriers in a band with ellipsoidal constant-energy surfaces is studied under the assumption that the carriers interact with long-wavelength LO phonons. The problem is treated variationally, and the electron-LO phonon interaction is not assumed very small. Two special cases are considered: (i) the applied magnetic field is pointing in an arbitrary direction but is weak; (ii) the applied field has arbitrary strength but points along an axis of cylindrical symmetry of the energy ellipsoid. Numerical results are given for conduction band and on-axis valence band cyclotron resonance in AgBr.