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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 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 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 $1$K, NDTC reflects in a temperature drop of the order of a few mK by increasing the power supplied to the system. Our work draws new routes for implementing a thermal transistor in nanoscale circuits.

Since the the first studies of thermodynamics, heat transport has been a crucial element for the understanding of any thermal system. Quantum mechanics has introduced new appealing ingredients for the manipulation of heat currents, such as the long-range coherence of the superconducting condensate. The latter has been exploited by phase-coherent caloritronics, a young field of nanoscience, to realize Josephson heat interferometers, which can control electronic thermal currents as a function of the external magnetic flux. So far, only one output temperature has been modulated, while multi-terminal devices that allow to distribute the heat flux among different reservoirs are still missing. Here, we report the experimental realization of a phase-tunable thermal router able to control the heat transferred between two terminals residing at different temperatures. Thanks to the Josephson effect, our structure allows to regulate the thermal gradient between the output electrodes until reaching its inversion. Together with interferometers, heat diodes and thermal memories, the thermal router represents a fundamental step towards the thermal conversion of non-linear electronic devices, and the realization of caloritronic logic components., Comment: 9 pages, 5 figures

We propose a system where coherent thermal transport between two reservoirs in non-galvanic contact is modulated by independently tuning the electron-photon and the electron-phonon coupling. The scheme is based on two gate-controlled electrodes capacitively coupled through a dc-SQUID as intermediate phase-tunable resonator. Thereby the electron-photon interaction is modulated by controlling the flux threading the dc-SQUID and the impedance of the two reservoirs, while the electron-phonon coupling is tuned by controlling the charge carrier concentration in the electrodes. To quantitatively evaluate the behavior of the system we propose to exploit graphene reservoirs. In this case, the scheme can work at temperatures reaching 1 K, with unprecedented temperature modulations as large as 245 mK, transmittance up to 99% and energy conversion efficiency up to 50%. Finally, the accuracy of heat transport control allows to use this system as an experimental tool to determine the electron-phonon coupling in two dimensional electronic systems (2DES)., Comment: 5 pages, 4 figures

Two superconductors coupled by a weak link support an equilibrium Josephson electrical current which depends on the phase difference $\varphi$ between the superconducting condensates [1]. Yet, when a temperature gradient is imposed across the junction, the Josephson effect manifests itself through a coherent component of the heat current that flows oppositely to the thermal gradient for $ \varphi <\pi/2$ [2-4]. The direction of both the Josephson charge and heat currents can be inverted by adding a $\pi$ shift to $\varphi$. In the static electrical case, this effect was obtained in a few systems, e.g. via a ferromagnetic coupling [5,6] or a non-equilibrium distribution in the weak link [7]. These structures opened new possibilities for superconducting quantum logic [6,8] and ultralow power superconducting computers [9]. Here, we report the first experimental realization of a thermal Josephson junction whose phase bias can be controlled from $0$ to $\pi$. This is obtained thanks to a superconducting quantum interferometer that allows to fully control the direction of the coherent energy transfer through the junction [10]. This possibility, joined to the completely superconducting nature of our system, provides temperature modulations with unprecedented amplitude of $\sim$ 100 mK and transfer coefficients exceeding 1 K per flux quantum at 25 mK. Then, this quantum structure represents a fundamental step towards the realization of caloritronic logic components, such as thermal transistors, switches and memory devices [10,11]. These elements, combined with heat interferometers [3,4,12] and diodes [13,14], would complete the thermal conversion of the most important phase-coherent electronic devices and benefit cryogenic microcircuits requiring energy management, such as quantum computing architectures and radiation sensors., Comment: 10 pages, 9 color figures

We investigate the thermal transport properties of a temperature-biased Josephson tunnel junction composed of two different superconductors. We show that this simple system can provide a large negative differential thermal conductance (NDTC) with a peak-to-valley ratio of $\sim 3$ in the transmitted electronic heat current. The NDTC is then exploited to outline the caloritronic analogue of the tunnel diode, which can exhibit a modulation of the output temperature as large as 80 mK at a bath temperature of 50 mK. Moreover, this device may work in a regime of thermal hysteresis that can be used to store information as a thermal memory. On the other hand, the NDTC effect offers the opportunity to conceive two different designs of a thermal transistor, which might operate as a thermal switch or as an amplifier/modulator. The latter shows a heat amplification factor $>1$ in a 500-mK-wide working region of the gate temperature. After the successful realization of heat interferometers and thermal diodes, this kind of structures would complete the conversion of the most important electronic devices in their thermal counterparts, breaking ground for coherent caloritronics nanocircuits where heat currents can be manipulated at will., Comment: 9 pages, 7 colour figures