Phase-dependent heat transport through superconductor-quantum dot hybrids

Phase-coherent charge transport in mesoscopic systems has received a lot of attention in past decades. Although phase-dependent heat currents through Josephson junctions have been predicted $[$1$]$ and observed recently $[$2$]$, phase-coherent heat transport has largely been neglected so far. Here, we consider a junction consisting of a quantum dot tunnel coupled to two superconducting leads. The system combines the interplay of superconducting correlations and strong Coulomb interaction on the dot in a nonequilibrium situation. We derive a generalized master equation using a real-time diagrammatic approach and calculate the phase-dependent heat and charge current in linear and nonlinear response.