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 ${\Pi }_{rr}<0$ (${\Pi }_{rr}>0$).

18 pages, 7 figures

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