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

TL;DR

This study investigates phonon emission in a 2D electron gas, revealing a transition to hydrodynamic behavior through temperature scaling and emission efficiency, supported by experimental data and hydrodynamic modeling.

Contribution

It provides experimental evidence of a transition to the hydrodynamic regime in a 2D electron gas via phonon emission analysis and introduces a hydrodynamic model to explain the observed phenomena.

Findings

Effective electron temperature scales with current as T_e ~ I^a with a ≈ 0.4-0.53.

Phonon energy emission rate shifts from T^5 to T^4 dependence.

Hydrodynamic model explains enhanced phonon emission efficiency.

Abstract

Using as a thermometer the temperature dependent magneto-transport of a two-dimensional electron gas, we find that effective temperature scales with current as $T_{\rm e} \sim I^a$, where $a=0.4 \pm 2\%$ in the {\it Shubnikov de-Haas} regime, and $0.53 \pm 2\%$ in both the {\it integer and fractional} quantum Hall effect. 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.