Nonequilibrium transport properties of an asymmetric tunnel Josephson junction.

We delve into the electric transport properties of a Josephson junction (JJ) formed by diverse superconductors residing at different temperatures. We demonstrate the peculiar behavior of Josephson and quasiparticles currents as a function of both temperatures and superconducting gaps, shedding light on the role played by the alignment of singularities in the DOS and anomalous components, which can be triggered in different ways, $e.g.$, temperature, biasing, or exchange fields. We first discuss the unusual behavior of the critical current, which shows abrupt variations and may even counterintuitively increase by enhancing the temperature of one electrode, instead of monotonically reducing as naively expected. Then, we present the bipolar thermoelectric effect on the quasiparticle current generated by the spontaneous breaking of the particle-hole symmetry, due to the thermal gradient across the JJ as the supercurrent is suppressed. Finally, we present the feasibility of controlling the response of a thermally biased JJ by a more convenient "magnetic knob", $i.e.$, via an alternative setup taking advantage of magnetic fluxes through superconducting loops enclosing the JJ electrodes.