Towards phase-coherent caloritronics in superconducting circuits

The emerging field of phase-coherent caloritronics (from the Latin word "calor", i.e., heat) is based on the possibility to control heat currents using the phase difference of the superconducting order parameter. The goal is to design and implement thermal devices able to master energy transfer with a degree of accuracy approaching the one reached for charge transport by contemporary electronic components. This can be obtained by exploiting the macroscopic quantum coherence intrinsic to superconducting condensates, which manifests itself through the Josephson and the proximity effect. Here, we review recent experimental results obtained in the realization of heat interferometers and thermal rectifiers, and discuss a few proposals for exotic non-linear phase-coherent caloritronic devices, such as thermal transistors, solid-state memories, phase-coherent heat splitters, microwave refrigerators, thermal engines and heat valves. Besides being very attractive from the fundamental physics point of view, these systems are expected to have a vast impact on many cryogenic microcircuits requiring energy management, and possibly lay the first stone for the foundation of electronic thermal logic.Comment: 11 pages, 6 colour figure

Efficient and tunable Aharonov-Bohm quantum heat engine

We propose a quantum heat engine based on an Aharonov-Bohm interferometer in a two-terminal geometry, and investigate its thermoelectric performances in the linear response regime. Sizeable thermopower (up to $\sim 0.3\,\text{mV}$/K) as well as $ZT$ values largely exceeding unity can be achieved by simply adjusting parameters of the setup and temperature bias across the interferometer leading to thermal efficiency at maximum power approaching $30\%$ of the Carnot limit. This is close to the optimal efficiency at maximum power achievable for a two-terminal heat engine. Changing the magnetic flux, the asymmetry of the structure, a side-gate bias voltage through a capacitively-coupled electrode and the transmission of the T-junctions connecting the AB ring to the contacts allows to finely tune the operation of the quantum heat engine. The exploration of the parameters' space demonstrates that the high performances of the Aharonov-Bohm two-terminal device as a quantum heat engine are stable over a wide range of temperatures and length imbalances, promising towards experimental realization.Comment: 5 pages, 4 figures, published versio

Phase-dependent heat transport through magnetic Josephson tunnel junctions

We present an exhaustive study of the coherent heat transport through superconductor-ferromagnet(S-F) Josephson junctions including a spin-filter (I$_{sf}$) tunneling barrier. By using the quasiclassical Keldysh Green's function technique we derive a general expression for the heat current flowing through a S/F/I$_{sf}$/F/S junction and analyze the dependence of the thermal conductance on the spin-filter efficiency, the phase difference between the superconductors and the magnetization direction of the ferromagnetic layers. In the case of non-collinear magnetizations we show explicitly the contributions to the heat current stemming from the singlet and triplet components of the superconducting condensate. We also demonstrate that the magnetothermal resistance ratio of a S/F/I$_{sf}$/F/S heat valve can be increased by the spin-filter effect under suitable conditions.Comment: 8 pages; 6 figure

Manifestation of a spin-splitting field in a thermally-biased Josephson junction

We investigate the behavior of a Josephson junction consisting of a ferromagnetic insulator-superconductor (FI-S) bilayer tunnel-coupled to a superconducting electrode. We show that the Josephson coupling in the structure is strenghtened by the presence of the spin-splitting field induced in the FI-S bilayer. Such strenghtening manifests itself as an increase of the critical current $I_c$ with the amplitude of the exchange field. Furthermore, the effect can be strongly enhanced if the junction is taken out of equilibrium by a temperature bias. We propose a realistic setup to assess experimentally the magnitude of the induced exchange field, and predict a drastic deviation of the $I_c(T)$ curve ($T$ is the temperature) with respect to equilibrium.Comment: 4.5 pages, 3 color figure

On-Chip Cooling by Heating with Superconducting Tunnel Junctions

Heat management and refrigeration are key concepts for nanoscale devices operating at cryogenic temperatures. The design of an on-chip mesoscopic refrigerator that works thanks to the input heat is presented, thus realizing a solid state implementation of the concept of cooling by heating. The system consists of a circuit featuring a thermoelectric element based on a ferromagnetic insulator-superconductor tunnel junction (N-FI-S) and a series of two normal metal-superconductor tunnel junctions (SINIS). The N-FI-S element converts the incoming heat in a thermovoltage, which is applied to the SINIS, thereby yielding cooling. The cooler's performance is investigated as a function of the input heat current for different bath temperatures. We show that this system can efficiently employ the performance of SINIS refrigeration, with a substantial cooling of the normal metal island. Its scalability and simplicity in the design makes it a promising building block for low-temperature on-chip energy management applications.Comment: 7 pages, 6 figure

Quantum interference hybrid spin-current injector

We propose a quantum interference spin-injector nanodevice consisting of a superconductor-normal metal hybrid loop connected to a superconductor-ferromagnet bilayer via a tunneling junction. We show that for certain values of the applied voltage bias across the tunnel barrier and the magnetic flux through the loop the spin-current can be fully polarized. Moreover, by tuning the magnetic flux one can switch the sign of the spin polarization. This operation can be performed at frequencies within the tens of GHz range. We explore the nanodevice in a wide range of parameters, establish the optimum conditions for its experimental realization and discuss its possible applications.Comment: 4.5 pages, 4 color figure