Memory function and dynamic conductivity of a type-I superlattice in a magnetic field: Hydrodynamic theory of magnetoplasma resonance.

Abstract

The effect of a magnetic field on the rather pronounced plasma resonance in the dynamic conductivity of a closely packed type-I superlattice is examined here. In this, we treat scatterings by remote impurity sheets and background impurities (randomly smeared). Our analysis is focused on the explicit determination of the influence of the magnetic field on the frequency-dependent memory function of the type-I superlattice in the neighborhood of plasma resonance. A closed-form evaluation is developed here for the finite jump in the imaginary part of the memory function characterizing a plasma resonance shifted by the ambient magnetic field to the magnetoplasmon frequency (${\ensuremath{\omega}}_{p}^{2}$+${\ensuremath{\omega}}_{c}^{2}$${)}^{1/2}$, where ${\ensuremath{\omega}}_{c}$ is the cyclotron frequency and ${\ensuremath{\omega}}_{p}$=(4\ensuremath{\pi}${e}^{2}$${n}_{2\mathrm{D}/\mathrm{md}{)}^{1/2}}$ is the bulk plasmon frequency for a closely packed type-I superlattice. (${n}_{2\mathrm{D}}$ is the two-dimensional sheet density of carriers in a quantum well, d the superlattice period associated with the separation of adjacent quantum wells, m the effective mass, and e the electron charge.) This shifted plasma resonance is shown to be a salient feature of dynamic conductivity for close packing of the superlattice planes, but it diminishes in importance as d gets larger and as temperature increases.