Electron relaxation in the quantum-Hall-effect geometry: One- and two-phonon processes.

Abstract

The longitudinal-optical (LO) phonon-assisted electron relaxation has been investigated in a two-dimensional electron system in the quantum-Hall-effect geometry. The phonon emission rates versus inter-Landau-level separations are calculated. One LO- and two LO+LA-phonon emission processes via polar optical and deformation acoustical itneractions are considered. To obtain a finite relaxation rate associated with one-phonon emission, the allowance for the Landau-level broadening or for the LO-phonon dispesion is made. Below the LO-phonon energy ${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$ within an energy range of the order of \ensuremath{\Elzxh} \ensuremath{\surd}${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$/\ensuremath{\tau} the one-phonon relaxation rate exceeds 1 ${\mathrm{ps}}^{\mathrm{\ensuremath{-}}1}$. (Here \ensuremath{\tau} is the relaxation time deduced from the mobility, and ${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$ is the cyclotron fjrequency. In GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure with the mobility \ensuremath{\mu}=25 ${\mathrm{V}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ ${\mathrm{m}}^{2}$ this range makes up 0.7 MeV.) The two-phonon emission has a significant contribution to the relaxation above ${\mathrm{\ensuremath{\omega}}}_{\mathrm{LO}}$. At energy separations of the order of ${\mathit{ca}}_{\mathit{B}}^{\mathrm{\ensuremath{-}}1}$ (c is the sound velocity, ${\mathit{a}}_{\mathit{B}}$ is the magnetic length) the LO+LA-phonon emission provides a mechanism of subpicosecond relaxation while in a wide energy range of the order of \ensuremath{\Elzxh}${\mathrm{\ensuremath{\omega}}}_{\mathit{B}}$ the subnanosecond relaxation can be achieved.