Peltier Cooling in Corbino-Geometry Quantum Hall Systems

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 $$- (E_{N_\textrm{F} \sigma _\textrm{F}}-\zeta )/e$$ in the limit of vanishing disorder, where $$E_{N_\textrm{F} \sigma _\textrm{F}}$$ 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 $$T_\textrm{out}$$ near the outer perimeter of a Corbino disk, applying a radial dc current $$I_\textrm{dc}$$ . The temperature $$T_\textrm{out}$$ is observed to increase or decrease depending on the direction of $$I_\textrm{dc}$$ and the sign of $$\Pi _{rr}$$ as expected from the Peltier effect. Notably, $$T_\textrm{out}$$ becomes lower than the bath temperature for outward (inward) $$I_\textrm{dc}$$ in the region where $$\Pi _{rr} < 0$$ ( $$\Pi _{rr} > 0$$ ).