A Thermometer for the 2D Electron Gas using 1D Thermopower

TL;DR

This paper introduces a novel method to measure the temperature of a 2D electron gas using thermopower in a 1D ballistic constriction, revealing a $T^5$ power loss dependence under hot electron conditions.

Contribution

It demonstrates a new thermometry technique for 2D electron gases via 1D thermopower, confirming the $T^5$ phonon emission dependence in the Gruneisen-Bloch regime.

Findings

Thermopower-based temperature measurement is effective for 2D electron gases.

Power loss follows a $T^5$ dependence in hot electron conditions.

Discrepancy observed between thermopower and Shubnikov-de Haas thermometry results.

Abstract

We measure the temperature of a 2D electron gas in GaAs from the thermopower of a one-dimensional ballistic constriction, using the Mott relation to confirm the calibration from the electrical conductance. Under hot electron conditions, this technique shows that the power loss by the electrons follows a $T^5$ dependence in the Gruneisen-Bloch regime, as predicted for acoustic phonon emission with a screened piezoelectric interaction. An independent measurement using conventional thermometry based on Shubnikov-de Haas oscillations gives a $T^3$ loss rate; we discuss reasons for this discrepancy.