Thermal drag in electronic conductors

We study the electronic thermal drag in two different Coulomb-coupled systems, the first one composed of two Coulomb-blockaded metallic islands and the second one consisting of two parallel quantum wires. The two conductors of each system are electrically isolated and placed in the two circuits (the drive and the drag) of a four-electrode setup. The systems are biased, either by a temperature Delta T or a voltage V difference, on the drive circuit, while no biases are present on the drag circuit. In the case of a pair of metallic islands we use a master equation approach to determine the general properties of the dragged heat current I-drag((h)), accounting also for cotunneling contributions and the presence of large biases. Analytic results are obtained in the sequential tunneling regime for small biases, finding, in particular, that I-drag((h)) is quadratic in Delta T or V and nonmonotonic as a function of the interisland coupling. Finally, by replacing one of the electrodes in the drag circuit with a superconductor, we find that heat can be extracted from the other normal electrode. In the case of the two interacting quantum wires, using the Luttinger liquid theory and the bosonization technique, we derive an analytic expression for the thermal transresistivity rho((h))(12), in the weak-coupling limit and at low temperatures, rho((h))(12) turns out to be proportional to the electrical transresistivity, in such a way that their ratio (a kind of Wiedemann-Franz law) is proportional to T-3. We find that rho((h))(12) is proportional to T for low temperatures and decreases like 1/T for intermediate temperatures or like 1/T-3 for high temperatures. We complete our analyses by performing numerical simulations that confirm the above results and allow us to access the strong-coupling regime.