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 Tₑ~Iᵃ, where a0ex0ex=0ex0ex0.4±2% in the Shubnikov--de Haas regime, and 0.53±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~T⁵ to P~T⁴. We explain this as well as the dramatic enhancement in phonon emission efficiency using a hydrodynamic model.