Inelastic coulomb scattering rate of a multisubband Q1D electron gas

Abstract

We study, the Coulomb scattering lifetimes of electrons in two coupled quantum wires by calculating the quasiparticle self-energy within a multisubband model of quasi-one-dimensional Q1D electron system. We consider two strongly coupled quantum wires with two occupied subbands. The intrasubband and intersubband inelastic scattering rates are caculated for electrons in di erent subbands. Contributions of the intrasubband, intersubband plasmon excitations, as well as the quasiparticle excitations are investigated. Our results show that the plasmon exictations of the rst subband are the most important scattering mechanism for electrons in both subbands. I IntroductionSingle-particle properties of electrons in quasi-onedimensional Q1D systems have attracted considerable interest. By calculating the quasiparticle renormalization factor Z k 1 and the momentum distribution function n k around the Fermi surface, Hu and Das Sarma 2 h a ve clari ed that a clean Q1D electron system in a semiconductor quantum wire shows the Luttinger liquid behavior, whereas even slightest amount of impurities restores the Fermi surface and the Fermi-liquid behavior remains. Within a one-band model, they calculated the self-energy due to electron-electron Coulomb i n teractions for an unclean Q1D system by using the leadingorder GW dynamical screening approximation. 2, 3 This self-energy gives rise to the inelastic Coulomb scattering rate that plays a fundamental role in measurements of the quasiparticle lifetime in Q1D doped systems. In the inelastic-scattering processes, the quasiparticle loses energy each time it scatters and its lifetime provides informationabout the di erent excitation channels associated with energy relaxation. 4, 5This paper is devoted to study the collective excitation and the Coulomb inelastic-scattering rate in a multisubband Q1D doped semiconductor. The numerical calculations are applied to two strongly coupled GaAs AlGaAs quantum wires in which the occupation of higher subbands provides more scattering channels. We show that the intersubband coupling and intersubband excitations can be important in the energy relaxation process. II Theoretical formulationBy assuming zero thickness in the z direction, the subband energies E n and the wave functions k;n y are obtained from the numerical solution of the coupled one-dimensional Schr odinger equation in the y direction. The Coulomb inelastic-scattering rate of an electron in a subband n with momentum k is obtained 1 b y the imaginary part of the screened exchange self-energy n k; n k , where n k = E n +~2k 2 =2m , is the single-particle energy with being the chemical potential and m the electron e ective mass in GaAs. At zero temperature 6 , the screened exchange self-energy is given bywhere G 0 n1 k;! is the bare Green's function of noninteracting electrons and V s nn1n1n q;! 0 is the dynamically screened electron-electron interaction potential. The self-energy n k; n k was written by taking the leading pertubative term in an expansion in the dynamically screened RP...