Nonequilibrium transport through a Josephson quantum dot

We study the electronic current through a quantum dot coupled to two superconducting leads which is driven by either a voltage V or temperature Delta T bias. Finite biases beyond the linear response regime are considered. The local two-particle interaction U on the dot is treated using an approximation scheme within the functional renormalization group approach set up inKeldysh-Nambu space with U being the small parameter. For V > 0, we compare our renormalization group enhanced results for the dc component of the current to earlier weak coupling approaches such as the Hartree-Fock approximation and second-order perturbation theory in U. We show that in parameter regimes in which finite-bias-driven multiple Andreev reflections prevail, small-|U| approaches become unreliable for interactions of appreciable strength. In the complementary regime, the convergence of the current with respect to numerical parameters becomes an issue, but can eventually be achieved, and interaction effects turn out to be smaller than expected based on earlier results. For Delta T > 0, we find a surprising increase of the current as a function of the superconducting phase difference in the regime which at T = 0 becomes the pi (doublet) phase.