Negative differential thermal conductance by photonic transport in electronic circuits

The negative differential thermal conductance (NDTC) provides the key mechanism for realizing thermal transistors. This exotic effect has been the object of an extensive theoretical investigation, but the implementation is still limited to a few specific physical systems. Here, we consider a simple circuit of two electrodes exchanging heat through electromagnetic radiation. We theoretically demonstrate that the existence of an optimal condition for power transmission, well known as impedance matching in electronics, provides a natural framework for engineering NDTC: the heat flux is reduced when the temperature increase is associated to an abrupt change of the electrode's impedance. As a case study, we numerically analyze a hybrid structure based on thin-film technology, in which the increased resistance is due to a superconductor-resistive phase transition. For typical metallic superconductors operating below $1\phantom{\rule{4pt}{0ex}}\mathrm{K}$, NDTC reflects in a temperature drop of the order of a few mK by increasing the power supplied to the system. Our numerical work draws new routes for implementing a thermal transistor in nanoscale circuits.