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 the preferential direction of the heat flow between the three-different temperature-biased contacts. The main goal of this study is to analyze the requirements for heat circulation in nonideal devices, in particular focusing on sample-to-sample variations. Quite generally, we find that the circulation performance of the devices is good as long as only a few transport channels are involved. We compare the performance of circulators with normal conducting contacts to those with superconducting contacts and find that the circulation coefficients are essentially unchanged.