Peltier cooling in Corbino-geometry quantum Hall systems

TL;DR

This paper derives an analytic formula for the Peltier coefficient in Corbino-geometry quantum Hall systems, predicts its behavior near Landau levels, and experimentally observes related temperature changes due to the Peltier effect.

Contribution

It provides the first analytic expression for the Peltier coefficient in quantum Hall systems and demonstrates experimental temperature modulation consistent with theoretical predictions.

Findings

The Peltier coefficient $\Pi_{rr}$ exhibits large positive or negative values near Landau levels.

Experimental measurements show temperature changes consistent with the sign of $\Pi_{rr}$ and the Peltier effect.

$\\Pi_{rr}$ approaches a saw-tooth shape as disorder decreases, matching theoretical expectations.

Abstract

Quantum Hall systems having Corbino geometry are expected to have a large Peltier coefficient $\Pi_{rr}$ in the quantum Hall plateau region. We present an analytic formula for $\Pi_{rr}$ calculated employing the spectral conductivity obtained based on the self-consistent Born approximation. The coefficient $\Pi_{rr}$ is shown to have a large negative (positive) value just above (below) an integer Landau-level filling, with the absolute value $|\Pi_{rr}|$ increasing with decreasing temperature or decreasing disorder, and approaching the saw-tooth shape $- (E_{N_\mathrm{F} \sigma_\mathrm{F}}-\zeta)/e$ in the limit of vanishing disorder, where $E_{N_\mathrm{F} \sigma_\mathrm{F}}$ is the highest occupied Landau level and $\zeta$ is the chemical potential. As an initial attempt to experimentally observe the effect of the large $|\Pi_{rr}|$, we measure the electron temperature $T_\mathrm{out}$ near the outer perimeter of a Corbino disk, applying a radial dc current $I_\mathrm{dc}$. The temperature $T_\mathrm{out}$ is observed to increase or decrease depending on the direction of $I_\mathrm{dc}$ and the sign of $\Pi_{rr}$ as expected from the Peltier effect. Notably, $T_\mathrm{out}$ becomes lower than the bath temperature for outward (inward) $I_\mathrm{dc}$ in the region where $\Pi_{rr} < 0$ ($\Pi_{rr} > 0$).