Elementary Excitations in Two Dimensional Electron Gas Arrays

Abstract

Two examples of elementary excitations in layered electron gas systems are considered, magneto-excitons of a system with integral Landau level filling and plasmons of a quasiperiodic system. For the former case, the simplest elementary excitations are obtained by promoting an electron from the highest occupied Landau level to the lowest unoccupied one. The single particle picture doesn’t adequately describe these excitations because the resulting electron and hole interact to form a magneto-exciton. The energies of the singlet and triplet magneto-excitons can be calculated in perturbation theory if the Coulomb energy is small compared to the cyclotron energy. For a periodic array of two dimensional electron gas layers, the magneto-exciton dispersion broadens into a band with Bloch wavenumber k_z describing the relative phase of the excitation amplitude on neighboring layers. A qualitative comparison of the elementary excitations of these simple systems with the magneto-roton excitations and Laughlin quasiparticles in the quantum Hall effect is made. The second example, plasmons of a quasiperiodic layered electron gas system, can be studied using a transfer matrix method. The band structure found is quite similar to the electron energy bands of a quasiperiodic potential. As the size of the quasiperiodic array tends to infinity, an infinite number of very narrow bands is found, which display typical self-similar Cantor set structure. The behavior of the total band width as function of size, which is a measure of localized vs. extended behavior of the plasmons, is discussed. The global scaling properties of the spectrum and the infrared resonant absorption are studied.