Peltier cooling in Corbino-geometry quantum Hall systems

Abstract

Quantum Hall systems having Corbino geometry are expected to have a large Peltier coefficient $Π_{rr}$ in the quantum Hall plateau region. We present an analytic formula for $Π_{rr}$ calculated employing the spectral conductivity obtained based on the self-consistent Born approximation. The coefficient $Π_{rr}$ is shown to have a large negative (positive) value just above (below) an integer Landau-level filling, with the absolute value $|Π_{rr}|$ increasing with decreasing temperature or decreasing disorder, and approaching the saw-tooth shape $- (E_{N_\mathrm{F} σ_\mathrm{F}}-ζ)/e$ in the limit of vanishing disorder, where $E_{N_\mathrm{F} σ_\mathrm{F}}$ is the highest occupied Landau level and $ζ$ is the chemical potential. As an initial attempt to experimentally observe the effect of the large $|Π_{rr}|$, 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 $Π_{rr}$ 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 $Π_{rr} < 0$ ($Π_{rr} > 0$).

Figures (7)

• Figure 1: Magnetic-field dependence of the conductivity $\sigma_{rr}$ (a), the Seebeck coefficient $S_{rr}$ (b), and the Peltier coefficient $\Pi_{rr}$ (c) for various temperatures and the quantum mobility $\mu_\mathrm{q} = 6.0$ m$^2$/Vs. Green shaded areas highlight the quantum Hall plateau regions (for $T= 0.20$ K) and the vertical dashed lines with numbers mark the location of exact integer Landau-level fillings. The dotted line in (c) shows the upper limit of $|\Pi_{rr}|$ given by Eq. (\ref{['EqPirrCLT']}).
• Figure 2: Magnetic-field dependence of the conductivity $\sigma_{rr}$ (a), the Seebeck coefficient $S_{rr}$ (b), and the Peltier coefficient $\Pi_{rr}$ (c) for various quantum mobilities at $T = 0.20$ K. Green shaded areas highlight the quantum Hall plateau regions (for $\mu_\mathrm{q} = 6.0$ m$^2$/Vs) and the vertical dashed lines with numbers mark the location of exact integer Landau-level fillings. The dotted line in (c) shows the upper limit of $|\Pi_{rr}|$ given by Eq. (\ref{['EqPirrCLT']}).
• Figure 3: Experimentally measured magnetic-field dependence of the capacitance $C$ between the annular top gate and the 2DES measured at various bath temperatures $T_\mathrm{bath}$ (a) and at $T_\mathrm{bath} = 0.20$ K with inward ($I_\mathrm{dc} > 0$) or outward ($I_\mathrm{dc} < 0$) radial dc current, or without the dc current ($I_\mathrm{dc} = 0$) (b). The green shaded areas indicate the quantum Hall plateau areas, with vertical dashed lines marking the locations of exact integer fillings. Upward and downward triangles with vertical dotted lines indicate the positions of the magnetic field selected for further examination shown in Fig. \ref{['FigTCD']} and Table \ref{['table']}. Inset in (b) depicts the schematics of the measurement device. G: annular top gate. IC: inner electrode. OC: outer electrode.
• Figure 4: Temperature $T$ versus the difference $\Delta C$ of the capacitance $C$ from that at $T = 0.20$ K picked out from Fig. \ref{['expFigs']}(a) at four magnetic fields in the quantum Hall plateau regions. The symbols for the plot here are the same as those employed to indicate the magnetic-field locations in Fig. \ref{['expFigs']}.
• Figure 5: The functions $u_1(\nu)$ (a) and $u_2(\nu)$ (b).