Transport Phenomena and Optical Properties of a Layered Electron Gas.

The high-frequency conductivity of superlattices was investigated. Here, the systems are under the influence of electromagnetic waves whose frequencies are high compared to the collision frequencies, and whose wavelengths are long compared to the Bohr (Debye) radius. The treatment rests on the kinetic description for electron-ion system and on the Kubo's formula for the conductivity and the temperature dependent Green's function technique. An exact expression for conductivity, to the lowest order in plasma parameter, is obtained, which depends on frequency, electron -hole mass ratio, electron-LO phonon coupling, spacing between adjacent layers and density per unit area. We calculate the resistivity numerically for some typical value of the above four parameters. To examine the effect of finite width of the electron distribution, we consider a model function in our calculation for type-I superlattice and find an increase in the absorption constant. The Raman scattering cross-section from a two -component layered electron gas (such as InAs-GaSb, GaAs -AlGaAs superlattices, etc.) has been calculated within the random-phase-approximation. It is found that for a separation between two components larger than a critical value, the scattered spectra have two resonant peaks in the high-frequency regime. For small separation and small mass ratio, there is a resonant peak due to an ion acoustic mode at the low frequency regime and to a plasma mode at the high frequency regime. The finite width of the wave function of the charged particles will reduce the resonant frequencies and enhance the Raman intensities.