Heat Coulomb blockade in a double-island metal-semiconductor device

Abstract

We study the thermal transport properties of a mesoscopic device comprising two metallic islands embedded in a two-dimensional electron gas in the integer quantum Hall regime. It is shown that the $2M$ ballistic edge channels connecting the islands to the external reservoirs and the $N$ inter-island channels play a central role in the phenomenon of heat Coulomb blockade. Unlike the single-island case, where the heat flux is reduced by exactly one quantum of thermal conductance, we predict an additional suppression proportional to the factor $M^2/(2N+M)^2$. We further examine a configuration in which the islands are placed between electrodes at different temperatures and identify the conditions under which the Wiedemann-Franz law is violated.

Figures (3)

• Figure 1: Schematic representation of the double-island hybrid metal-semiconductor device: two large metallic islands (i.e., two floating Ohmic contacts) are embedded in a two-dimensional electron gas that is set in the integer quantum Hall regime with filling factor $\nu$. Two islands are electrically connected to (i) each other via $N$ ballistic channels, and to (ii) all reservoirs via $2M$ channels. As for example, we show the case of $\nu=3$, $M=2$, and $N=1$. For the heat Coulomb blockade experiment configuration, we assume all reservoirs are at the same base temperatures $T_{\rm in,1}$$=$$T_{\rm in,2}$$=$$T_{\rm in}$. At the same time, two islands are heated up (e.g., by applying dc voltages that dissipate Joule heat into both islands) to the temperature $T_{1}$$=$$T_2$$=$$T_{\rm C}$$>$$T_{\rm in}$. For the heat transport experiment configuration where both islands are placed between heat source and drain, we assume $T_{\rm in,1}$$=$$T_S$, $T_{\rm in,2}$$=$$T_D$, while the temperatures of both islands $T_{1,2}$ are not fixed.
• Figure 2: Normalized heat conductance $\kappa/\kappa_0T_{\rm C}$ from Eq. (\ref{['hconductance']}) as a function of dimensionless temperature $\tau_{\rm C} k_BT_{\rm C}=\pi k_BT_{\rm C}/E_{\rm C}$. Blue, red, and green solid lines indicate the heat conductance for $N=1$ and $M=4,5,6$, respectively. The black line indicates the case of $M=6$ and large $N\gg M$. Black and purple dashed lines depict asymptotic limits of $2M$ and $2M$$-$$1$$-$$M^2/(M+2N)^2$, respectively.
• Figure 3: Normalized Lorenz ratio $\mathcal{R}=\mathcal{L}/\mathcal{L}_0$ from Eq. (\ref{['lorenz_ratio']}) as a function of the number of ballistic channels $M$. The maximal possible value of Lorenz number $\mathcal{R}_{\rm max}=11/10$ occurs for $N=1$, $M=2$.