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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 at different temperatures $T_L$ and $T_R$ 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 $U$ is taken into account due to many-body effects. We study the thermal conductance as a function of temperature and the dependence of the thermal current with the couplings to the leads, $T_L-T_R$, energy levels of the dots and $U$, including conditions for which an orbital Kondo regime takes place. When the energy levels of the dots are different, the device has rectifying properties for the thermal current. We find that the ratio between the thermal current resulting from a thermal bias $T_L>T_R$ and the one from $T_L<T_R$ is maximized for particular values of the energy levels, one above and the other below the Fermi level.