Collective excitations of a quasi-one-dimensional electron gas: nonlocal response theory

Abstract

Self-consistent calculations of the subband electronic structure of semiconductor quantum wires are reported. The sample parameters were chosen to match the GaAs/AlGaAs heterostructure recently fabricated by molecular-beam epitaxy and ion milling by Weiner et al. The Schrödinger and Poisson equations were solved simultaneously in a rectangular waveguide geometry, using Fermi statistics for electrons at finite temperature. Calculated energy levels, wave functions, charge density, and potential differ from the predictions of the simple square well and harmonic oscillator models because of the influence of accumulation and depletion regions. The subband energies depend on the free-carrier density and the temperature as well as the band bending. Based on the self-consistently determined subband structure, the dynamical structure factor was evaluated using a nonlocal description of dielectric response in the random-phase approximation at finite temperature. We obtain intersubband as well as intrasubband plasmons and discuss their dispersion relations, localization, and line shapes. The dynamical structure factor of our model quasi-one-dimensional electron gas displays unique line shapes and dispersion relations which are in sharp contrast with the results expected for higher-dimensional electron gases. Two well-defined spectral features, which are almost free of Landau damping, are found, The calculated shift of the intersubband resonance frequency, caused by the depolarization effect, agrees well with previous experiments.