Hot-electron temperatures of two-dimensional electron gases using both de Haas–Shubnikov oscillations and the electron-electron interaction effect

The experiments described in this paper were undertaken to investigate the possibility that cyclotron phonon emission plays a significant role in the energy-loss rate of hot electrons in the liquid${\mathrm{-}}^4$He temperature range. Electron temperatures have been measured by the usual de Haas–Shubnikov method, and also by a technique based on the temperature dependence of the nonoscillatory magnetoresistivity, which is believed to arise from the electron-electron interaction effect (EEI). Combining results from both methods should give a more or less continuous measurement of electron temperature as a function of magnetic field; however, the method based on EEI is found to fail when ${\mathrm{\omega }}_{\mathit{c}}$ ${\mathrm{\tau }}_{\mathit{q}}$>1/2, where ${\mathrm{\omega }}_{\mathit{c}}$ is the cyclotron frequency and ${\mathrm{\tau }}_{\mathit{q}}$ the quantum lifetime. For those samples where ${\mathrm{\tau }}_{\mathit{q}}$ is low, we deduce that cyclotron phonon emission plays no major role in energy loss, but the experiments give no information in this regard when ${\mathrm{\tau }}_{\mathit{q}}$ is high. When the EEI method fails (i.e., ${\mathrm{\omega }}_{\mathit{c}}$ ${\mathrm{\tau }}_{\mathit{q}}$>1/2), then the nonoscillatory resistivity is found to be influenced by both ${\mathrm{\tau }}_{\mathit{q}}$ and the lattice temperature, and the electron temperature plays a lesser role, particularly when ${\mathrm{\tau }}_{\mathit{q}}$ is very high.