The Coupling of Collective Cyclotron Excitations and Longitudinal Optic Phonons in Polar Semiconductors

Abstract

Much work has been reported recently on the coupling of longitudinal optic phonons and free-carrier collective excitations in degenerate polar semiconductors in the absence (^1–6,12) as well as in the presence (^7–11) of a magnetic field. The coupling takes place via “macroscopic” longitudinal electric fields, producing the combined normal modes of the system which are strong admixtures of the two excitations. We shall briefly review the simpler case of no magnetic field, for which theories and experiments are more extensive, in order to illustrate the general feature of the problem. The theory of the coupling is based upon the assumption that the polariza-bility of the free carriers in the random phase approximation and that of the polar ions contribute additively to make up the total dielectric constant. The q-dependent complex dielectric function derived by Lindhard (¹³), or its approximation (²), is invoked to describe the former, and the polar lattice dielectric constant derived by Born and Huang (¹⁴) the latter. Free longitudinal oscillations will then occur in the system whenever the conditions are such that the total dielectric constant equals zero. The above procedure is particularly simple in the long-wavelength limit q ≈ 0.

Work supported in part by the U. S. Office of Naval Research.