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

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