Modulation of electrostatic Langmuir waves in quantum electron-hole semiconductor plasmas

Abstract

Amplitude modulation of electrostatic Langmuir waves in a quantum electron–hole semiconductor plasma is considered in the quantum magnetohydrodynamic regime. The important ingredients of this study are the inclusion of the particle degeneracy pressure, exchange-correlation potential, and the quantum diffraction effects via the Bohm potential. A nonlinear Schrödinger equation (NLSE) is developed for the evolution of the amplitude of the electrostatic wave by employing the standard reductive perturbation technique. The dynamics of the wave in the slow space-time scales is governed by the NLSE. Typical values of the parameters for GaAs, GaSb, and GaN semiconductors are considered in analyzing the nonlinear dispersion of the electrostatic wave. Detail analysis of the nature of the modulation, here modulation instability, in the long-wavelength regime is presented. For some parameter ranges of the semiconductor plasmas, and at the long-wavelength regime, it is found that the electrostatic wave is modulationally unstable. Effects of the exchange-correlation potential and the Bohm potential are also studied. It is found that the exchange-correlation potential has profound effects compared to the Bohm potential in the amplitude modulation of the electrostatic wave.