Phase-coherent heat circulators with normal or superconducting contacts

We investigate heat circulators where a phase coherent region is contacted by three leads that are either normal- or superconducting. A magnetic field, and potentially the superconducting phases, allow to control preferential direction of flow between three-different temperature-biased contacts. The main goal this study analyze requirements for circulation in non-ideal devices, particular focusing on sample-to-sample variations. Quite generally, we find performance devices good as long only few transport channels involved. compare with normalconducting contacts those coefficient essentially unchanged.