Coupled magnetoplasma and phonon systems

A long-wavelength Hamiltonian approach for coupled plasmons and polar phonons in a degenerate semiconductor with and without a uniform d.c. magnetic field is presented. Neglecting ionic motion, and with a uniform magnetic field present, a Hamiltonian is formulated for the magnetoplasma oscillations and a Hamiltonian is presented which includes the coupling between longitudinal optical phonons and collective hybrid-cyclotron plasma resonances. Canonical transformations, which put the latter Hamiltonian into second quantized diagonal form, are given. The normal modes, obtained by diagonalizing the appropriate Hamiltonian, correspond to the zeros and the infinities of the appropriate dielectric function. In analogy with the electron-phonon case, the resonances for a compensated system of coupled electrons and holes, in the presence of a uniform magnetic field, are treated by means of a Hamiltonian. The coupling in the above problems is represented by a product of two sets of plasma frequencies, the electron and ion or the electron and hole in the latter case. In all cases the coupling is independent of the magnetic field.