  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 non-ideal 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 normalconducting contacts to those
with superconducting contacts and find that the circulation coefficient are
essentially unchanged.

Mesoscale and Nanoscale Physics;Superconductivity