Peltier cooling in Corbino-geometry quantum Hall systems

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 $\Pi_{rr} < 0$ ($\Pi_{rr} > 0$).