Dynamics of Quantal Heating in Electron Systems with Discrete Spectra

TL;DR

This study investigates the dynamics of quantal Joule heating in 2D electron systems within GaAs quantum wells under magnetic fields, revealing temperature-dependent inelastic scattering times and mechanisms through a novel microwave beat frequency method.

Contribution

Introduces a difference frequency method to directly measure the dynamical characteristics of quantal heating and inelastic scattering times in 2D electron systems.

Findings

Inelastic scattering time $ au_{in}$ varies from 0.13 ns to 1 ns with temperature.

Electron-electron interactions dominate at higher temperatures, with $1/\tau_{in} \propto T^2$.

Electron-phonon scattering contributes at lower temperatures, with $1/\tau_{in} \propto T^3$.

Abstract

The temporal evolution of quantal Joule heating of 2D electrons in GaAs quantum well placed in quantizing magnetic fields is studied using a difference frequency method. The method is based on measurements of the electron conductivity oscillating at the beat frequency $f=f_1-f_2$ between two microwaves applied to 2D system at frequencies $f_1$ and $f_2$. The method provides $direct$ access to the dynamical characteristics of the heating and yields the inelastic scattering time $\tau_{in}$ of 2D electrons. The obtained $\tau_{in}$ is strongly temperature dependent, varying from 0.13 ns at 5.5K to 1 ns at 2.4K in magnetic field $B$=0.333T. When temperature $T$ exceeds the Landau level separation the relaxation rate $1/\tau_{in}$ is proportional to $T^2$, indicating the electron-electron interaction as the dominant mechanism limiting the quantal heating. At lower temperatures the rate tends to be proportional to $T^3$, indicating considerable contribution from electron-phonon scattering.