Phase dependent heat transport in superconducting junctions with scattering theory

Abstract: The operation of nanoscale devices at low temperatures is highly sensitive to heating effects. This motivates current research on controlling heat currents in these devices. A particularly important class of setups are hybrid superconducting devices, since (1) there exist a variety of sensitive applications such as qubits, in which heating is an issue, and (2) because the superconducting energy gap as well as the controllable phase-difference across junctions allow for cooling and heat control. This thesis deals with phase-controllable heat currents through superconducting-normal conducting-superconducting (SNS) Josephson junctions. Elaborate devices containing junctions of this type have in recent years been proposed and partly even experimentally been implemented in heat interferometers, heat switch-es and heat diodes. These complex structures motivate our study on how the properties of an extended, diffusive junction affect the phase-dependent heat conductance of SNS Josephson junctions. In order to analyse the heat conductance of such junctions, in which heat is carried by quasiparticle excitations of the superconducting condensate, we use a scattering matrix formalism for hybrid superconducting systems. The transmission of quasiparticles through the diffusive region takes place via a large number of transmission channels with transmission probabilities characterized by a statistical distribution. We implement these statistical properties using previously obtained results from random-matrix theory. Our main findings are that the channel average of the diffusive conductor leads to a full suppression of the phase-dependence of the heat conductance. In contrast, the weak-localization correction to the heat conductance, as well as the heat conductance fluctuations are still sensitive to the phase. We also find that these heat conductance fluctuations have a similarly universal behavior as the well-known conductance fluctuations of charge currents in normal conductors. However, we identify an additional non-trivial temperature dependence, which is due to the superconducting phase difference.