  As a fundamental requisite for thermotronics, controlling heat flow has been
a longstanding quest in solid state physics. Recently, there has been a lot of
interest in nanoscale hybrid systems as possible candidates for thermal
devices. In this context, we study the heat current in the simplest hybrid
device of a two level system weakly coupled to two heat baths. We use the
reduced density matrix approach together with a simple Born-Markov
approximation to calculate the heat current in the steady state. We consider
different kinds of reservoirs and show that the nature of the reservoir plays a
very important role in determining the thermal characteristics of the device.
In particular, we investigate the effectiveness of a conventional
superconductor as a reservoir with regard to manipulating the heat current. In
the emergent temperature characteristics, we find that superconductivity in the
reservoirs leads to enhanced thermal currents and that the superconducting
phase transition is clearly visible in the heat current. We observe negative
differential thermal conductance and a pronounced rectification of the heat
current, making this a good building block for a quantum thermal diode.
