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

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.

💡 Research Summary

In this work the authors present a comprehensive theoretical study of heat transport in a mesoscopic device consisting of two metallic islands (floating Ohmic contacts) embedded in a two‑dimensional electron gas (2DEG) that is tuned to the integer quantum Hall regime. Each island is capacitively isolated with a charging energy (E_C = e^2/2C) and is coupled to the external reservoirs by (2M) ballistic edge channels (the factor 2 accounts for the two directions of propagation). In addition, the islands are connected to each other by (N) ballistic channels. This geometry extends the single‑island “heat Coulomb blockade” (HCB) previously observed, where at low temperature ((k_B T \ll E_C)) the charge mode is frozen and the heat conductance is reduced by exactly one quantum (\kappa_0 T) ((\kappa_0 = \pi^2 k_B^2/3h)).

The authors formulate the low‑energy Hamiltonian as a sum of a kinetic term for the chiral bosonic edge fields and a charging term that couples the total charge on each island. By solving the Langevin equations for charge conservation and incorporating stochastic current sources that obey equilibrium Johnson‑Nyquist noise, they obtain the spectral density of the outgoing current fluctuations. The heat current carried by each outgoing channel is expressed in terms of this spectral density, and the total heat flow follows from a sum over all channels.

Two experimental configurations are analyzed.

1. Standard HCB configuration – All external reservoirs are kept at a common base temperature (T_{\text{in}}) while a symmetric dc bias heats both islands to a higher temperature (T_C). In the low‑temperature limit the authors evaluate the integral function (F(x)) that appears in the exact expression for the heat current and derive the compact result

\