Phonon Emission from a 2D Electron Gas: Evidence of Transition to the Hydrodynamic Regime

Abstract

Using as a thermometer the temperature dependent magnetotransport of a two-dimensional electron gas, we find that the effective temperature scales with current as ${T}_{e}\ensuremath{\sim}{I}^{a}$, where $a\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.4\ifmmode\pm\else\textpm\fi{}2%$ in the Shubnikov--de Haas regime, and $0.53\ifmmode\pm\else\textpm\fi{}2%$ at the critical points between adjacent quantum Hall plateaus, both integer and fractional. This implies the phonon energy emission rate changes from the expected $P\ensuremath{\sim}{T}^{5}$ to $P\ensuremath{\sim}{T}^{4}$. We explain this as well as the dramatic enhancement in phonon emission efficiency using a hydrodynamic model.