Normal and hot-electron magnetophonon resonance in a GaAs heterostructure

Abstract

Linear and nonlinear magnetophonon resonances are investigated in a two-dimensional electron gas in a single-interface GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructure, within the momentum-balance equation approach. The linear transverse resistivity obtained from the present approach reduces to the high-magnetic-field result based on the Kubo formula. The Landau-level broadening is taken to be Gaussian with a constant background. We find that a Lorentzian broadening of the density of states gives slightly different results from our Gaussian broadening even when a constant background term is included. The effect of the broadening parameters on the shape of the magnetophonon oscillations in the transverse resistivity ${\rho }_{\mathrm{xx}}$, the energy relaxation rate, and the warm-electron coefficient, is found to be appreciable and stronger than in the corresponding three-dimensional case. The nonlinear momentum-balance equation is solved for arbitrary average electron velocity. We find that the maxima at the linear magnetophonon resonance evolve to minima (and the minima become maxima), when the average electron velocity is sufficiently large.