Heat current across a capacitively coupled double quantum dot for high magnetic field.

We study the heat current through two capacitively coupled quantum dots coupled in series with two conducting leads in the spinless case (valid for a high applied magnetic field). Our results are also valid for the heat current through a single quantum dot with strongly ferromagnetic leads pointing in opposite directions (so that the electrons with given spin at the dot can jump only to one lead) or through a quantum dot with two degenerate levels with destructive quantum interference and high magnetic field. Although the charge current is always zero, the heat current is finite when the interdot Coulomb repulsion is taken into account due to many-body effects. We generalize previous results for high temperatures and particular parameters obtained by Yadalam and Harbola [Phys. Rev. B 99, 195449 (2019)]. In particular we consider temperatures for which an orbital Kondo regime takes place. In contrast to previous results, we find that the heat current is finite even for $U \rightarrow \infty$. In the Kondo regime, for temperatures much less than the Kondo energy scale, we obtain that the dependence of the thermal current with the temperature difference $\Delta T$ is $\sim (\Delta T)^4$ when the cold lead is at $ T_C \ll \Delta T$, and linear in $\Delta T$ if $ T_C \gg \Delta T$. For large $T_C$ the current saturates. As a function of Coulomb strength $U$, for high $\Delta T$ and $ T_C=0$, the charge current has a maximum for $U \sim 3 \Delta T$ and decreases with increasing $U$ reaching a finite value for $U \rightarrow \infty$. We also consider the case of different energy levels of the dots for which the device has rectifying properties.