Phase-dependent heat transport in topologically nontrivial Josephson junctions

In this thesis, we theoretically investigate phase-coherent heat transport in Josephson junctions. At first, we study phase-dependent heat currents in junctions with a nontrivial topology, which are of tremendous interest since they can host Majorana modes. These exotic quasiparticles are their own particle-hole conjugate with no charge. As a result, this makes experimental detection via electrical measurements notoriously difficult. In this thesis, we predict that phase-dependent heat transport offers a novel and compelling tool for probing Majorana modes by clear and distinctive transport signatures. In particular, we study two different geometries. We begin with the analysis of a two-terminal superconductor-normal metal-superconductor (S-N-S) junction made from intrinsic p-wave superconductors. We reveal the formation of 0D Majorana bound states with the help of a potential barrier. In particular, we find that the positions of maxima and minima occur for phase bias of 0 and π, respectively, independent of the barrier strength. This is in stark contrast to a trivial S-N-S junction made from s-wave superconductors, which illustrates out that phase-coherent heat transport can be used as a tool to probe Majoranas. Additionally, the phase dependence of the thermal conductance allows for an effective pairing analysis of the p-wave order parameters. As a second topological geometry, we study a four-terminal superconductor-topological insulator-superconductor (S-TI-S) junction. In particular, we study phase-dependent heat transport in the nonsuperconducting region perpendicular to the direction of phase bias. We find a perfectly quantized thermal conductance of one-half flux quantum for a phase difference of π. Furthermore, we find that the quantization persists in the presence of a potential barrier as well as an applied Zeeman field. This results directly from the 1D Majorana modes which counterpropagate along the superconducting interfaces. A conventional S-N-S junction, in contrast, does not exhibit the same behaviour due to the gapped energy spectrum of the trivial ABS. Here, one finds an exponential supression of the heat transport. Hence, we predict that this geometry allows for a direct measurement of Majorana modes. Subsequently, we study heat-driven transport in strongly interacting Josephson junctions. In particular, we investigate superconducting single-electron transistors (SETs). In the presence of a finite thermal as well as phase bias, the Coulomb interactions are revealed by thermoelectrical effects which arise even in the vicinity of the particle-hole symmetrical point as a result of interaction-driven level renormalization. Additionally, we find a finite thermoelectric effect even for the case of an inversion symmetric temperature bias due to a symmetry breaking by the applied phase bias. Hence, phase-dependent transport marks also a compelling tool to reveal the impact of Coulomb interactions onto transport in Josephson geometries.