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 [Formula presented] in the Shubnikov-de Haas regime, and [Formula presented] at the critical points between adjacent quantum Hall plateaus, both integer and fractional. This implies the phonon energy emission rate changes from the expected [Formula presented]. We explain this, as well as the dramatic enhancement in phonon emission efficiency using a hydrodynamic model.