A thermally driven out-of-equilibrium two-impurity Kondo system

The archetypal two-impurity Kondo problem in a serially-coupled double quantum dot is investigated in the presence of a thermal bias $\theta$. The slave-boson formulation is employed to obtain the nonlinear thermal and thermoelectrical responses. When the Kondo correlations prevail over the antiferromagnetic coupling $J$ between dot spins we demonstrate that the setup shows negative differential thermal conductance regions behaving as a thermal diode. Besides, we report a sign reversal of the thermoelectric current $I(\theta )$ controlled by $t\mathrm{/}\mathrm{\Gamma }$ ($t$ and $\mathrm{\Gamma }$ denote the interdot tunnel and reservoir-dot tunnel couplings, respectively) and $\theta$. All these features are attributed to the fact that at large $\theta$, both $Q(\theta )$ (heat current) and $I(\theta )$ are suppressed regardless the value of $t\mathrm{/}\mathrm{\Gamma }$ because the double dot decouples at high thermal biases. Eventually, and for a finite $J$, we investigate how the Kondo-to-antiferromagnetic crossover is altered by $\theta$.