Current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field

TL;DR

This study demonstrates a current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field, caused by thermomagnetic effects like the Ettingshausen effect, leading to localized temperature reduction.

Contribution

The paper introduces a numerical analysis of thermoelectric and thermomagnetic effects in a 2DEG, revealing a novel cooling effect near the boundary due to the Ettingshausen effect.

Findings

Localized cooling near the boundary due to Ettingshausen effect

Temperature reduction occurs despite Joule heating

Thermal diffusion balances heat flow from thermomagnetic effects

Abstract

We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential phi and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with phi_{left} < phi_{right} and T_{left} =T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.