Theory of Cyclotron Resonance of Piezoelectric Polarons

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Abstract
The cyclotron resonance of piezoelectric materials with special reference to cadmium sulfide is discussed on the basis of the recently developed general quantum-mechanical expression for conductivity. The previous analysis by Mahan and Hopfield is shown to be valid only for very weak magnetic fields, viz., under the semiclassical conditions. In the actual experimental conditions, however, where the Landau level separation is larger than k B T (quantum conditions), the cyclotron mass m c differs from the result of semiclassical analysis: (a) in most regions of temperature, m c is an increasing function of temperature, and (b) m c depends on the magnetic field and thus on the incident microwave frequency. The line width is finite and differs appreciably from the inverse of the lifetime of the electronic state, which is shown by simple treatments to be infinite. Numerical calculation of the line shape shows that m c is, though smaller, very close to m , in contrast to Mahan and Hopfield. It is proved on the basis of the general expression that m c reduces to the tube mass and the line width tends to the inverse of the static transport relaxation time in the weak magnetic field limit.