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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., 11 pages, 6 colour figures

We propose the concept of a quantized single-electron source based on the interplay between Coulomb blockade and magnetic flux-controllable superconducting proximity effect. We show that flux dependence of the induced energy gap in the density of states of a nanosized metallic wire can be exploited as an efficient tunable energy barrier which enables charge pumping configurations with enhanced functionalities. This control parameter strongly affects the charging landscape of a normal metal island with non-negligible Coulombic energy. Under a suitable evolution of a time-dependent magnetic flux the structure behaves likewise a turnstile for single electrons in a fully electrostatic regime., Comment: 6 pages, 4 colour figures

We present a microwave quantum refrigeration principle based on the Josephson effect. When a superconducting quantum interference device (SQUID) is pierced by a time-dependent magnetic flux, it induces changes in the macroscopic quantum phase and an effective finite bias voltage appears across the SQUID. This voltage can be used to actively cool, well below the lattice temperature, one of the superconducting electrodes forming the interferometer. The achievable cooling performance combined with the simplicity and scalability intrinsic to the structure pave the way to a number of applications in quantum technology.

We demonstrate a novel nanoheating scheme that yields very large and uniform temperature gradients up to about 1K every 100nm, in an architecture which is compatible with the field-effect control of the nanostructure under test. The temperature gradients demonstrated largely exceed those typically obtainable with standard resistive heaters fabricated on top of the oxide layer. The nanoheating platform is demonstrated in the specific case of a short-nanowire device., 6 pages, 6 figures

Phase-tunable hybrid devices, built upon nanostructures combining normal metal and superconductors, have been the subject of intense studies due to their numerous combinations of different charge and heat transport configurations. They exhibit solid applications in quantum metrology and coherent caloritronics. Here we propose and realize a new kind of hybrid device with potential application in single charge manipulation and quantized current generation. We show that by tuning superconductivity on two proximized nanowires, coupled via a Coulombic normal metal island, we are able to control its charge state configuration. This device supports a one-control-parameter-cycle being actuated by the sole magnetic flux. In a voltage biased regime, the phase-tunable superconducting gaps can act as energy barriers for charge quanta leading to an additional degree of freedom in single electronics. The resulting configuration is fully electrostatic and the current across the device is governed by the quasiparticle populations in the source and drain leads. Notably, the proposed device can be realized using standard nanotechniques opening the possibility to a straightforward coupling with the nowadays well developed superconducting electronics., Comment: 7 pages, 4 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., 9 pages, 7 colour figures

Macroscopic quantum phase coherence has one of its pivotal expressions in the Josephson effect [1], which manifests itself both in charge [2] and energy transport [3-5]. The ability to master the amount of heat transferred through two tunnel-coupled superconductors by tuning their phase difference is the core of coherent caloritronics [4-6], and is expected to be a key tool in a number of nanoscience fields, including solid state cooling [7], thermal isolation [8, 9], radiation detection [7], quantum information [10, 11] and thermal logic [12]. Here we show the realization of the first balanced Josephson heat modulator [13] designed to offer full control at the nanoscale over the phase-coherent component of thermal currents. Our device provides magnetic-flux-dependent temperature modulations up to 40 mK in amplitude with a maximum of the flux-to-temperature transfer coefficient reaching 200 mK per flux quantum at a bath temperature of 25 mK. Foremost, it demonstrates the exact correspondence in the phase-engineering of charge and heat currents, breaking ground for advanced caloritronic nanodevices such as thermal splitters [14], heat pumps [15] and time-dependent electronic engines [16-19]., Comment: 6+ pages, 4 color figures

We propose a variation, based on very low energy and extremely intense photon sources, on the well established technique of Light-Shining-through-Wall (LSW) experiments for axion-like particle searches. With radiation sources at 30 GHz, we compute that present laboratory exclusion limits on axion-like particles might be improved by at least four orders of magnitude, for masses m_a, Comment: 10 pages, 5 figures, comments added, 1 figure added, to appear in Phys. Dark. Univ

We discuss heat transport in thermally-biased long Josephson tunnel junctions in the presence of an in-plane magnetic field. In full analogy with the Josephson critical current, the phase-dependent component of the heat current through the junction displays coherent diffraction. Thermal transport is analyzed as a function of both the length and the damping of the junction, highlighting deviations from the standard Fraunhofer pattern characteristic of short junctions. The heat current diffraction patterns show features strongly related to the formation and penetration of Josephson vortices, i.e. solitons. We show that a dynamical treatment of the system is crucial for the realistic description of the Josephson junction and it leads to peculiar results. In fact, hysteretic behaviors in the diffraction patterns when the field is swept up and down are observed, corresponding to the trapping of vortices in the junction., 9 pages, 7 figures

A macroscopic fluid pump works according to the law of Newtonian mechanics and transfers a large number of molecules per cycle (of the order of 10^23). By contrast, a nano-scale charge pump can be thought as the ultimate miniaturization of a pump, with its operation being subject to quantum mechanics and with only few electrons or even fractions of electrons transfered per cycle. It generates a direct current in the absence of an applied voltage exploiting the time-dependence of some properties of a nano-scale conductor. The idea of pumping in nanostructures was discussed theoretically a few decades ago [1-4]. So far, nano-scale pumps have been realised only in system exhibiting strong Coulombic effects [5-12], whereas evidence for pumping in the absence of Coulomb-blockade has been elusive. A pioneering experiment by Switkes et al. [13] evidenced the difficulty of modulating in time the properties of an open mesoscopic conductor at cryogenic temperatures without generating undesired bias voltages due to stray capacitances [14,15]. One possible solution to this problem is to use the ac Josephson effect to induce periodically time-dependent Andreev-reflection amplitudes in a hybrid normal-superconducting system [16]. Here we report the experimental detection of charge flow in an unbiased InAs nanowire (NW) embedded in a superconducting quantum interference device (SQUID). In this system, pumping may occur via the cyclic modulation of the phase of the order parameter of different superconducting electrodes. The symmetry of the current with respect to the enclosed magnetic flux [17,18] and bias SQUID current is a discriminating signature of pumping. Currents exceeding 20 pA are measured at 250 mK, and exhibit symmetries compatible with a pumping mechanism in this setup which realizes a Josephson quantum electron pump (JQEP)., Comment: 7+ pages, 6 color figures

We present the realization and characterization of a novel-concept interferometer, the superconducting quantum interference proximity transistor (SQUIPT). Its operation relies on the modulation with the magnetic field of the density of states of a proximized metallic wire embedded in a superconducting ring. Flux sensitivities down to $\sim 10^{-5} \Phi_0$Hz$^{-1/2}$ can be achieved even for a non-optimized design, with an intrinsic dissipation ($\sim 100$ fW) which is several orders of magnitude smaller than in conventional superconducting interferometers. Our results are in agreement with the theoretical prediction of the SQUIPT behavior, and suggest that optimization of the device parameters would lead to a large enhancement of sensitivity for the detection of tiny magnetic fields. The features of this setup and their potential relevance for applications are further discussed.

In spite of extended efforts, detecting thermoelectric effects in superconductors have proven to be a challenging task, due to the inherent superconducting particle-hole symmetry. Here we present a theoretical study of an experimentally attainable Superconductor -- Quantum Dot -- Superconductor (SC-QD-SC) Josephson Junction with highly tunable thermoelectric properties and a thermal response that is far larger than previous suggestions. The QD energy level between the SCs breaks particle-hole symmetry in a gradual manner, allowing, in the presence of a temperature gradient, for gate controlled appearance of a superconducting thermo-phase. This thermo-phase increases up to a maximal value of $\pi/2$ after which thermovoltage is expected to develop. Using time-independent Keldysh countour Green's functions we derive the exact thermo-phase and thermal response on the junction. These are shown to be orders of magnitude larger than usual SC tunnel junctions with a sharp dependence on gate voltage., Comment: Journal version - added interaction and discussion of HF validity

We report the fabrication and characterization of an alternative design for a superconducting quantum interference proximity transistor (SQUIPT) based on a normal metal (N) probe. The absence of direct Josephson coupling between the proximized metal nanowire and the N probe allows us to observe the full modulation of the wire density of states around zero voltage and current via the application of an external magnetic field. This results into a drastic suppression of power dissipation which can be as low as a few ∼10-17 W. In this context, the interferometer allows an improvement of up to four orders of magnitude with respect to earlier SQUIPT designs and makes it ideal for extra-low power cryogenic applications. In addition, the N-SQUIPT has been recently predicted to be the enabling candidate for the implementation of coherent caloritronic devices based on proximity effect.

The quest for solid-state thermoelectric (TE) conversion has been one of the prime driving forces behind semiconductor research before the discovery of the transistor effect. The achievement of efficient TE devices indeed requires a non-trivial trade-off between interdependent material characteristics and can be expressed in terms of the maximization of the figure of merit ZT = S2T/, where S is the Seebeck coefficient,  and  are the electrical and thermal conductivity, T the average operation temperature. Large ZT values, though, have proven elusive over the past decades despite the great design flexibility offered by semiconductor materials1. Here, we present results on thermovoltages in single InAs nanowire (NW) field effect transistors. Thanks to a buried heating scheme (see Fig. 1), we achieved both a large thermal bias, T > 10K and a strong field-effect modulation of electric conduction through nanostructures randomly positioned on oxidized silicon. This experimental arrangement allows a detailed mapping of S(; T) and the comparison with classic models for thermoelectric transport in degenerate semiconductors. The adopted approximations lead to a novel estimate of the electron mobility e~ 11000 cm2/Vs in the NW. Such value is significantly larger than the one obtain by field-effect, e, FE, on the same wire. The discrepancy can be understood in terms of history effects in the NW free charge filling by electric field, as a consequence of the slow surface and trap charge dynamics. On the other hand, the S vs  dependence is largely independent of spurious charge screening and hysteresis. Our results also indicate that special care should be taken in the interpretation of transport results based on field-effects in these nanostructures.

We report the realization of an ultra-efficient low-temperature hybrid heat current rectifier, thermal counterpart of the well-known electric diode. Our design is based on a tunnel junction between two different elements: a normal metal and a superconducting island. Electronic heat current asymmetry in the structure arises from large mismatch between the thermal properties of these two. We demonstrate experimentally temperature differences exceeding $60$ mK between the forward and reverse thermal bias configurations. Our device offers a remarkably large heat rectification ratio up to $\sim 140$ and allows its prompt implementation in true solid-state thermal nanocircuits and general-purpose electronic applications requiring energy harvesting or thermal management and isolation at the nanoscale., Comment: 8 pages, 6 color figures

arXiv:1411.0990v3.-- et al., We have studied mesoscopic Josephson junctions formed by highly n-doped InAs nanowires and superconducting Ti/Pb source and drain leads. The current-voltage properties of the system are investigated by varying temperature and external out-of-plane magnetic field. Superconductivity in the Pb electrodes persists up to ∼7 K and with magnetic field values up to 0.4 T. Josephson coupling at zero backgate voltage is observed up to 4.5 K and the critical current is measured to be as high as 615 nA. The supercurrent suppression as a function of the magnetic field reveals a diffraction pattern that is explained by a strong magnetic flux focusing provided by the superconducting electrodes forming the junction., Partial financial support from the Marie Curie Initial Training Action (ITN) Q-NET 264034 and the Tuscany region through the project :TERASQUID” is acknowledged. The work of F.G. has been partially funded by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant 615187-COMANCHE. The work of F.S.B. was supported by the Spanish Ministry of Economy and Competitiveness under Projects No. FIS2011-28851-C02-02.

We study several parasitic effects on the implementation of a Josephson radiation comb generator based on a dc superconducting quantum interference device (SQUID) driven by an external magnetic field. This system can be used as a radiation generator similarly to what is done in optics and metrology, and allows one to generate up to several hundreds of harmonics of the driving frequency. First we take into account how the assumption of a finite loop geometrical inductance and junction capacitance in each SQUID may alter the operation of the devices. Then, we estimate the effect of imperfections in the fabrication of an array of SQUIDs, which is an unavoidable source of errors in practical situations. We show that the role of the junction capacitance is, in general, negligible, whereas the geometrical inductance has a beneficial effect on the performance of the device. The errors on the areas and junction resistance asymmetries may deteriorate the performance, but their effect can be limited to a large extent by a suitable choice of fabrication parameters.

We discuss the statistics of heat current between two superconductors at different temperatures connected by a generic weak link. As the electronic heat in superconductors is carried by Bogoliubov quasiparticles, the heat transport fluctuations follow the Levitov--Lesovik relation. We identify the energy-dependent quasiparticle transmission probabilities and discuss the resulting probability density and fluctuation relations of the heat current. We consider multichannel junctions, and find that heat transport in diffusive junctions is unique in that its statistics is independent of the phase difference between the superconductors. Curiously, phase dependence reappears if phase coherence is partially broken., 7 pages, 7 figures

Under the terms of the Creative Commons Attribution License 3.0 (CC-BY)., The concept of thermophase refers to the appearance of a phase gradient inside a superconductor originating from the presence of an applied temperature bias across it. The resulting supercurrent flow may, in suitable conditions, fully counterbalance the temperature-bias-induced quasiparticle current therefore preventing the formation of any voltage drop, i.e., a thermovoltage, across the superconductor. Yet, the appearance of a thermophase is expected to occur in Josephson-coupled superconductors as well. Here, we theoretically investigate the thermoelectric response of a thermally biased Josephson junction based on a ferromagnetic insulator. In particular, we predict the occurrence of a very large thermophase that can reach π/2 across the contact for suitable temperatures and structure parameters; i.e., the quasiparticle thermal current can reach the critical current. Such a thermophase can be several orders of magnitude larger than that predicted to occur in conventional Josephson tunnel junctions. In order to assess experimentally the predicted very large thermophase, we propose a realistic setup realizable with state-of-the-art nanofabrication techniques and well-established materials, based on a superconducting quantum interference device. This effect could be of strong relevance in several low-temperature applications, for example, for revealing tiny temperature differences generated by coupling the electromagnetic radiation to one of the superconductors forming the junction., F. G. acknowledges the Marie Curie Initial Training Action (ITN) Q-NET 264034 and the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement No. 615187-COMANCHE for partial financial support. The work of F.S.B has been supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2011-28851-C02-02, and the work of T. T. H. has been supported by the ERC (Grant No. 240362-Heattronics) and the Academy of Finland through its Center of Excellence program.

We investigate the photon-mediated heat flow between two Josephson-coupled Bardeen-Cooper-Schrieffer (BCS) superconductors. We demonstrate that in standard low temperature experiments involving temperature-biased superconducting quantum interference devices (SQUIDs), this radiative contribution is negligible if compared to the direct galvanic one, but it largely exceeds the heat exchanged between electrons and the lattice phonons. The corresponding thermal conductance is found to be several orders of magnitude smaller, for real experiments setup parameters, than the universal quantum of thermal conductance, kappa_0(T)=pi k_B^2T/6hbar., Comment: 8 pages, 6 figures

This review presents an overview of the thermal properties of mesoscopic structures. The discussion is based on the concept of electron energy distribution, and, in particular, on controlling and probing it. The temperature of an electron gas is determined by this distribution: refrigeration is equivalent to narrowing it, and thermometry is probing its convolution with a function characterizing the measuring device. Temperature exists, strictly speaking, only in quasiequilibrium in which the distribution follows the Fermi-Dirac form. Interesting nonequilibrium deviations can occur due to slow relaxation rates of the electrons, e.g., among themselves or with lattice phonons. Observation and applications of nonequilibrium phenomena are also discussed. The focus in this paper is at low temperatures, primarily below 4 K, where physical phenomena on mesoscopic scales and hybrid combinations of various types of materials, e.g., superconductors, normal metals, insulators, and doped semiconductors, open up a rich variety of device concepts. This review starts with an introduction to theoretical concepts and experimental results on thermal properties of mesoscopic structures. Then thermometry and refrigeration are examined with an emphasis on experiments. An immediate application of solid-state refrigeration and thermometry is in ultrasensitive radiation detection, which is discussed in depth. This review concludes with a summary of pertinent fabrication methods of presented devices., Comment: Close to the version published in RMP; 59 pages, 35 figures

Macroscopic phase coherence between weakly coupled superconductors leads to peculiar interference phenomena. Among these, magnetic flux-driven diffraction might be produced, in full analogy to light diffraction through a rectangular slit. This can be experimentally revealed by the electric current and, notably, also by the heat current transmitted through the circuit. The former was observed more than 50 years ago and represented the first experimental evidence of the phase-coherent nature of the Josephson effect, whereas the second one was still lacking. Here we demonstrate the existence of heat diffraction by measuring the modulation of the electronic temperature of a small metallic electrode nearby-contacted to a thermally biased short Josephson junction subjected to an in-plane magnetic field. The observed temperature dependence exhibits symmetry under magnetic flux reversal, and clear resemblance with a Fraunhofer-like modulation pattern. Our approach, joined to widespread methods for phase-biasing superconducting circuits, might represent an effective tool for controlling the thermal flux in nanoscale devices. © 2014 Macmillan Publishers Limited.

We discuss how phase coherence manifests in the heat transport through superconducting single and multichannel Josephson junctions in time dependent situations. We consider the heat current driven through the junction by a temperature difference in dc voltage and ac phase biased situations. At low bias, the electromagnetic driving mainly modifies the form of the coherent resonance that transports a large part of the heat current, rather than simply dissipating energy in the junction. We find a description for the heat current in terms of quasiparticle n-photon absorption and emission rates, and discuss analytical and numerical results concerning them. In addition to the ensemble average heat transport, we describe also its fluctuations., Comment: 13 pages, 13 figures

We propose the implementation of a Josephson Radiation Comb Generator (JRCG) based on a dc superconducting quantum interference device (SQUID) driven by an external magnetic field. When the magnetic flux crosses a diffraction node of the critical current interference pattern, the superconducting phase undergoes a jump of $\pi$ and a voltage pulse is generated at the extremes of the SQUID. Under periodic drive this allows one to generate a sequence of sharp, evenly spaced voltage pulses. In the frequency domain, this corresponds to a comb-like structure similar to the one exploited in optics and metrology. With this device it is possible to generate up to several hundreds of harmonics of the driving frequency. For example, a chain of $50$ identical high-critical-temperature SQUIDs driven at 1 GHz can deliver up to a $0.5$ nW at 200 GHz. The availability of a fully solid-state radiation comb generator such as the JRCG, easily integrable on chip, may pave the way to a number of technological applications, from metrology to sub-millimeter wave generation., Comment: 9 pages, 6 color figures

Identifying materials and devices which offer efficient thermoelectric effects at low temperature is a major obstacle for the development of thermal management strategies for low-temperature electronic systems. Superconductors cannot offer a solution since their near perfect electron-hole symmetry leads to a negligible thermoelectric response; however, here we demonstrate theoretically a superconducting thermoelectric transistor which offers unparalleled figures of merit of up to ∼45 and Seebeck coefficients as large as a few mV/K at sub-Kelvin temperatures. The device is also phase-tunable meaning its thermoelectric response for power generation can be precisely controlled with a small magnetic field. Our concept is based on a superconductor-normal metal-superconductor interferometer in which the normal metal weak-link is tunnel coupled to a ferromagnetic insulator and a Zeeman split superconductor. Upon application of an external magnetic flux, the interferometer enables phase-coherent manipulation of thermoelectric properties whilst offering efficiencies which approach the Carnot limit., The work of F.G. has been partially funded by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC grant Agreement No. 615187-COMANCHE, and by the Marie Curie Initial Training Action (ITN) Q-NET 264034. J.W.A.R. acknowledges funding from the Royal Society (“Superconducting Spintronics”). J.W.A.R. and F.S.B. jointly acknowledge funding from the Leverhulme Trust through an International Network Grant (Grant No. IN-2013-033). J.S.M acknowledges funding from the National Science Foundation (Grant No. DMR 1207469) and the Office of Naval Research (Grant No. N00014-13-1-0301). The work of F.S.B. has been supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2011-28851-C02-02.

We report the design and implementation of a high-performance superconducting quantum interference proximity transistor (SQUIPT) based on aluminum-copper (Al-Cu) technology. With the adoption of a thin and short copper nanowire we demostrate full phase-driven modulation of the proximity-induced minigap in the normal metal density of states. Under optimal bias we record unprecedently high flux-to-voltage (up to 3 mV/$\Phi_0$) and flux-to-current (exceeding 100 nA/$\Phi_0$) transfer function values at sub-Kelvin temperatures, where $\Phi_0$ is the flux quantum. The best magnetic flux resolution (as low as 500 n$\Phi_0/\sqrt{Hz}$ at 240 mK, being limited by the room temperature pre-amplification stage) is reached under fixed current bias. These figures of merit combined with ultra-low power dissipation and micrometer-size dimensions make this mesoscopic interferometer attractive for low-temperature applications such as the investigation of the magnetization of small spin populations., Comment: 7 pages, 5 color figures

A niobium titanite nitride-based superconducting nanodevice — a Cooper-pair transistor — has a remarkably long parity lifetime, exceeding one minute close to absolute zero.

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 strengthened by the presence of the spin-splitting field induced in the FI-S bilayer. Such strengthening manifests itself as an increase of the critical current Ic 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 Ic(T) curve (T is the temperature) with respect to equilibrium. © 2014 American Physical Society., The work of F.S.B was supported by the Spanish Ministry of Economy and Competitiveness under Project No. FIS2011-28851-C02-02. F.G. acknowledges the Italian Ministry of Defense through the PNRMproject “Terasuper”, and theMarie Curie Initial Training Action (ITN) Q-NET 264034 for partial financial support.

We report the experimental realization of a nongalvanic, primary thermometer capable of measuring the electron temperature of a two-dimensional electron gas with negligible thermal load. Such a thermometer consists of a quantum dot whose temperature-dependent, single-electron transitions are detected by means of a quantum-point-contact electrometer. Its operating principle is demonstrated for a wide range of electron temperatures from 40 to 800 mK. This noninvasive thermometry can find application in experiments addressing the thermal properties of micrometer-scale mesoscopic electron systems, where heating or cooling electrons require relatively low thermal budgets. © 2013 American Physical Society.

We report the realization of a ballistic Josephson interferometer. The interferometer is made by a quantum ring etched in a nanofabricated two-dimensional electron gas confined in an InAs-based heterostructure laterally contacted to superconducting niobium leads. The Josephson current flowing through the structure shows oscillations with h/e flux periodicity when threading the loop with a perpendicular magnetic field. This periodicity, in sharp contrast with the h/2e one observed in conventional dc superconducting quantum interference devices, confirms the ballistic nature of the device in agreement with theoretical predictions. This system paves the way for the implementation of interferometric Josephson pi-junctions, and for the investigation of Majorana fermions., 4+ pages, 4 colored figures

We describe here the first experimental realization of a heat interferometer, thermal counterpart of the well-known superconducting quantum interference device (SQUID). These findings demonstrate, on the first place, the existence of phase-dependent heat transport in Josephson-based superconducting circuits and, on the second place, open the way to novel ways of mastering heat at the nanoscale. Combining the use of external magnetic fields for phase biasing and different Josephson junction architectures we show here that a number of heat interference patterns can be obtained. The experimental realization of these architectures, besides being relevant from a fundamental physics point of view, might find important technological application as building blocks of phase-coherent quantum thermal circuits. In particular, the performance of two different heat rectifying devices is analyzed., Comment: 34 pages, 15 figures, review article for Ultra-low temperatures and nanophysics ULTN2013. Microkelvin Proceedings

We theoretically investigate heat transport in hybrid normal metal-superconductor (NS) nanojunctions focusing on the effect of thermal rectification. We show that the heat diode effect in the junction strongly depends on the transmissivity and the nature of the NS contact. Thermal rectification efficiency can reach up to ∼123% for a fully transmissive ballistic junction and up to 84% in diffusive NS contacts. Both values exceed the rectification efficiency of a NIS tunnel junction (I stands for an insulator) by a factor close to ∼5 and ∼3, respectively. Furthermore, we show that for NS point-contacts with low transmissivity, inversion of the heat diode effect can take place. Our results could prove useful for tailoring heat management at the nanoscale, and for mastering thermal flux propagation in low-temperature caloritronic nanocircuitry. © 2013 AIP Publishing LLC., F.G. acknowledges the Italian Ministry of Defense through the PNRM project “TERASUPER,” and the Marie Curie Initial Training Action (ITN) Q-NET 264034 for partial financial support. The work of F.S.B was supported by the Spanish Ministry of Economy and Competitiveness under Project FIS2011-28851-C02-02.

New journal of physics 18(8), 083019 (2016). doi:10.1088/1367-2630/18/8/083019, Published by Dt. Physikalische Ges., [Bad Honnef]

We report on the fabrication and characterization of a two-terminal mesoscopic interferometer based on three V/Cu/V Josephson junctions having nanoscale cross-section. The junctions have been arranged in a double-ring geometry realized by metallic thin film deposition through a suspended mask defined by electron beam lithography. Although a significant amount of asymmetry between the critical current of each junction is observed we show that the interferometer is able to suppress the supercurrent to a level lower than 6 parts per thousand, being here limited by measurement resolution. The present nano-device is suitable for low-temperature magnetometric and gradiometric measurements over the micrometric scale., 5 pages, 4 figures

The Josephson effect represents perhaps the prototype of macroscopic phase coherence and is at the basis of the most widespread interferometer, i.e., the superconducting quantum interference device (SQUID). Yet, in analogy to electric interference, Maki and Griffin predicted in 1965 that thermal current flowing through a temperature-biased Josephson tunnel junction is a stationary periodic function of the quantum phase difference between the superconductors. The interplay between quasiparticles and Cooper pairs condensate is at the origin of such phase-dependent heat current, and is unique to Josephson junctions. In this scenario, a temperature-biased SQUID would allow heat currents to interfere thus implementing the thermal version of the electric Josephson interferometer. The dissipative character of heat flux makes this coherent phenomenon not less extraordinary than its electric (non-dissipative) counterpart. Albeit weird, this striking effect has never been demonstrated so far. Here we report the first experimental realization of a heat interferometer. We investigate heat exchange between two normal metal electrodes kept at different temperatures and tunnel-coupled to each other through a thermal `modulator' in the form of a DC-SQUID. Heat transport in the system is found to be phase dependent, in agreement with the original prediction. With our design the Josephson heat interferometer yields magnetic-flux-dependent temperature oscillations of amplitude up to ~21 mK, and provides a flux-to-temperature transfer coefficient exceeding ~ 60mK/Phi_0 at 235 mK [Phi_0 2* 10^(-15) Wb is the flux quantum]. Besides offering remarkable insight into thermal transport in Josephson junctions, our results represent a significant step toward phase-coherent mastering of heat in solid-state nanocircuits, and pave the way to the design of novel-concept coherent caloritronic devices., Comment: 4+ pages, 3 color figures

The analysis of the performance and the very understanding of the physical mechanisms governing the behavior of nanostructured devices requires the detailed knowledge of all parameters of electronic systems confined in ever shrinking microdomains. The role of temperature and the investigation of heat transport in solidstate nanoscale systems are currently under the spotlight [1]. Electronic thermometers [2‐4], refrigerators [5‐8] and heat transistors [9] based on metallic and superconductor nanostructures were already demonstrated. Such devices are typically operated at subkelvin temperatures, where electron-phonon interaction is weak and, as a result, the relevant electronic temperature may significantly dier from that of the lattice (if at all defined). In this context, the ability to perform local measurements of the electronic temperature becomes highly desirable. While in metallic systems superconducting tunnel junctions are routinely employed for this purpose, for the case of two-dimensional electron gases (2DEGs) or semiconductor nanowires at thermal equilibrium, quantum dots (QDs) were shown to be suitable for absolute thermometry [10, 11], due to the fact that in these conditions the linewidth of zero-bias Coulomb blockade (CB) peaks in the weak-coupling regime is directly related to the electronic temperature of the leads. Here, we propose a method for the detection of the local electronic temperature in a 2DEG, based on the analysis of the CB-peak lineshape. We shall first discuss zero-bias transport through a weakly-coupled QD in the presence of a temperature bias and show that zerobias conductance measurements can be used to experimentally determine both temperature values. We shall then employ this technique to investigate energy relaxation mechanisms in an electronic microdomain defined electrostatically in a GaAs/AlGaAs heterostructure and heated by an externally-driven current. The domain is connected to the surrounding 2DEG regions through the QD and three quantum point contacts (QPCs). As a known heating power is delivered to the domain, conductance across the QD is probed and the steady-state temperature detected. The dependence of the measured electron temperature on heating power will also be studied for dierent values of the QPC resistances: as the coupling to the surrounding 2DEG regions is reduced, we observe the crossover from a regime where excess heat is carried away by hot quasiparticles tunneling through the QPCs to one where power exchange with lattice phonons dominates. We shall show that the latter mechanism follows the T 5 power law expected [12] for the screened electron-acoustic phonon piezoelectric interaction, and obtain a measurement of the relative coupling constant consistent with theoretical estimates [1, 13].

We report low-temperature transport measurements performed on a planar Nb-InGaAs-Nb proximity Josephson junction hosting a gate-defined lateral quantum dot in the weak-link. We first study quasiparticle and Josephson transport through the open junction, when all gates are grounded. When the quantum dot is defined in the normal region by electrostatic depletion, cotunneling spectroscopy allows us to directly probe the energy gap induced in the two dimensional electron gas. Our data show good qualitative agreement with a model describing resonant tunneling through an Anderson impurity connected to superconducting electrodes. These results demonstrate the feasibility of top-gated nanodevices based on a two-dimensional electron gas coupled to a superconductor., Comment: 5 pages, 5 figures

The fabrication and operation of V-based superconducting nanorefrigerators is reported. Specifically, electrons in an Al island are cooled, thanks to hot-quasiparticle extraction provided by tunnel-coupled V electrodes. Electronic temperature reduction down to 400 mK starting from 1 K is demonstrated with an estimated cooling power of similar to 20 pW at 1 K for a junction area of 0.3 mu m(2).

We report the fabrication and characterization of superconducting quantum interference devices (SQUIDs) based on InAs nanowires and vanadium superconducting electrodes. These mesoscopic devices are found to be extremely robust against thermal cycling and to operate up to temperatures of $\sim2.5$~K with reduced power dissipation. We show that our geometry allows to obtain nearly-symmetric devices with very large magnetic-field modulation of the critical current. All these properties make these devices attractive for on-chip quantum-circuit implementation., 3 pages, 3 figures

A superconducting quantum magnetometer based on magnetic flux-driven modulation of the density of states of a proximized metallic nanowire is theoretically analyzed. With optimized geometrical and material parameters transfer functions up to a few mV/Phi_0 and intrinsic flux noise ~10^{-9}Phi_0 Hz^{-1/2} below 1 K are achievable. The opportunity to access single-spin detection joined with limited dissipation (of the order of ~ 10^{-14} W) make this magnetometer interesting for the investigation of the switching dynamics of molecules or individual magnetic nanoparticles., 6 pages, 6 color figures, added calculation of the Josephson current, published version

Spin-polarized transport is investigated in normal metal--superconductor (NS) junctions as a function of interface transmissivity as well as temperature when the density of states of a superconductor is Zeeman-split in response to an exchange field $({h}_{\text{exc}})$. Similarly to the ``absolute spin-valve effect'' predicted by Huertas-Hernando et al. [Phys. Rev. Lett. 88, 047003 (2002)] in superconducting proximity structures, we show that NS junctions can be used to generate highly spin-polarized currents, in alternative to half-metallic ferromagnets. In particular, the spin-polarized current obtained is largely tunable in magnitude and sign by acting on bias voltage and ${h}_{\text{exc}}$. While for tunnel contacts the current polarization can be as high as 100%, for transparent junctions it is dominated by the minority spin species. The effect can be enhanced by electron ``cooling'' provided by the superconducting gap.

We have investigated theoretically the influence of an AC drive on heat transport in a hybrid normal metal - superconductor tunnel junction in the photon-assisted tunneling regime. We find that the useful heat flux out from the normal metal is always reduced as compared to its magnitude under the static and quasi-static drive conditions. Our results are useful to predict the operative conditions of AC driven superconducting electron refrigerators., Comment: 10 pages, 8 colour figures, published version

We propose a mesoscopic kinetic-inductance radiation detector based on a long superconductor--normal metal--superconductor Josephson junction. The operation of this proximity Josephson sensor (PJS) relies on large kinetic inductance variations under irradiation due to the exponential temperature dependence of the critical current. Coupled with a dc SQUID readout, the PJS is able to provide a signal to noise (S/N) ratio up to ~10^3 in the THz regime if operated as calorimeter, while electrical noise equivalent power (NEP) as low as ~7x10^{-20} W(Hz)^(-1/2) at 200 mK can be achieved in the bolometer operation. The high performance together with the ease of fabrication make this structure attractive as an ultrasensitive cryogenic detector of THz electromagnetic radiation., 4 pages, 3 figures

We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat as compared to that in the normal state, and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A measurement setup to confirm these predictions is also suggested., Comment: 4+ pages, 4 figures

The electro-magnetostatic Aharonov-Bohm effect is shown to allow a full control of a Josephson junction. Both the sign and the magnitude of the supercurrent can be tuned if the junction between two superconductors is realized with a ring-shaped ballistic normal region. The implementation in a realistic set-up is discussed. (C) 2007 Elsevier B.V. All rights reserved.

We demonstrate experimentally manipulation of supercurrent in Al-AlO_x-Ti Josephson tunnel junctions by injecting quasiparticles in a Ti island from two additional tunnel-coupled Al superconducting reservoirs. Both supercurrent enhancement and quenching with respect to equilibrium are achieved. We demonstrate cooling of the Ti line by quasiparticle injection from the normal state deep into the superconducting phase. A model based on heat transport and non-monotonic current-voltage characteristic of a Josephson junction satisfactorily accounts for our findings., Comment: 4 pages, 4 colour figures, published version

An electron-cooling principle based on Landau quantization is proposed for nanoscale conductor systems. Operation relies on energy-selective electron tunneling into a two-dimensional electron gas in quantizing magnetic fields. This quantum refrigerator provides significant cooling power (~1 nW at a few K for realistic parameters) and offers a unique flexibility thanks to its tunability via the magnetic-field intensity. The available performance is only marginally affected by nonidealities such as disorder or imperfections in the semiconductor. Methods for the implementation of this system and its characterization are discussed., Comment: 4 pages, 4 color figures