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Superconductors are known to be excellent thermal insulators at low temperature owing to the presence of the energy gap in their density of states (DOS). In this context, the superconducting \textit{proximity effect} allows to tune the local DOS of a metallic wire by controlling the phase bias ($\varphi$) imposed across it. As a result, the wire thermal conductance can be tuned over several orders of magnitude by phase manipulation. Despite strong implications in nanoscale heat management, experimental proofs of phase-driven control of thermal transport in superconducting proximitized nanostructures are still very limited. Here, we report the experimental demonstration of efficient heat current control by phase tuning the superconducting proximity effect. This is achieved by exploiting the magnetic flux-driven manipulation of the DOS of a quasi one-dimensional aluminum nanowire forming a weal-link embedded in a superconducting ring. Our thermal superconducting quantum interference transistor (T-SQUIPT) shows temperature modulations up to $\sim 16$ mK yielding a temperature-to-flux transfer function as large as $\sim 60$ mK/$\Phi_0$. Yet, phase-slip transitions occurring in the nanowire Josephson junction induce a hysteretic dependence of its local DOS on the direction of the applied magnetic field. Thus, we also prove the operation of the T-SQUIPT as a phase-tunable \textit{thermal memory}, where the information is encoded in the temperature of the metallic mesoscopic island. Besides their relevance in quantum physics, our results are pivotal for the design of innovative coherent caloritronics devices such as heat valves and temperature amplifiers suitable for thermal logic architectures., Comment: 15 pages, 10 figures

We propose a passive single-photon detector based on the bipolar thermoelectric effect occurring in tunnel junctions between two different superconductors thanks to spontaneous electron-hole symmetry breaking. Our thermoelectric detector (TED) converts a finite temperature difference caused by the absorption of a single photon into an open circuit thermovoltage. Designed with feasible parameters, our TED is able to reveal single-photons of frequency ranging from about 15 GHz to about 150 PHz depending on the chosen design and materials. In particular, this detector is expected to show values of signal-to-noise ratio SNR about 15 at {\nu} = 50 GHz when operated at a temperature of 10 mK. Interestingly, this device can be viewed as a digital single-photon detector, since it generates an almost constant voltage VS for the full operation energies. Our TED can reveal single photons in a frequency range wider than 4 decades with the possibility to discern the energy of the incident photon by measuring the time persistence of the generated thermovoltage. Its broadband operation suggests that our TED could find practical applications in several fields of quantum science and technology, such as quantum computing, telecommunications, optoelectronics, THz spectroscopy and astro-particle physics., Comment: 5 pages, 4 figures

Not so long ago, thermoelectricity in superconductors was believed to be possible only by breaking explicitly the particle-hole symmetry. Recently, it has been theoretically predicted that a superconducting tunnel junction can develop bipolar thermoelectric phenomena in the presence of a large thermal gradient owing to non-equilibrium spontaneous PH symmetry breaking. The experimental realization of the first thermoelectric Josephson engine then followed. Here, we give a more extended discussion and focus on the impact of the Josephson contribution on thermoelectricity modulating the Cooper pairs transport in a double-loop SQUID. When the Cooper pairs current prevails on the quasiparticle one, the Josephson contribution short-circuits the junction thereby screening the thermoelectric effect. We demonstrate that the thermoelectric generation due to the pure quasiparticle transport is phase-independent, once Josephson contribution is appropriately removed from the net current measured. At the same time, we investigate an additional metastable state at V\simeq0 determined by the presence of the Josephson coupling, which peculiarly modifies the hysteretic behavior of our thermoelectric engine realized. At the end, we also discuss how the current-voltage characteristics are affected by the presence of multiple thermoelectric elements, which improve the generated output power., Comment: 16 pages, 11 figures

The design for an inductive superconducting quantum interference proximity transistor with enhanced performance, the L-SQUIPT, is presented and analyzed. The interferometer is based on a double-loop structure, where each ring comprises a superconductor-normal metal-superconductor mesoscopic Josephson weak-link and the read-out electrode is implemented in the form of a superconducting tunnel probe. Our design allows both to improve the coupling of the transistor to the external magnetic field and to increase the characteristic magnetic flux transfer functions, thereby leading to an improved ultrasensitive quantum limited magnetometer. The L-SQUIPT behavior is analyzed in both the dissipative and the dissipationless Josephson-like operation modes, in the dissipative or in the dissipationless Josephson-like operation mode in the latter case by exploiting both an inductive and a dispersive readout scheme. The improved performance makes the L-SQUIPT promising for magnetic field detection as well as for specific applications in quantum technology, where a responsive dispersive magnetometry at milliKelvin temperatures is required., Comment: 11 pages, 8 figures

We report evidence of non-reciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions, owing to a strong spin-orbit coupling. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. This demonstrates that these devices can work as Josephson diodes, with dissipation-less current flowing in only one direction. For small fields, the supercurrent asymmetry increases linearly with the external field, then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. We show that the effect is maximum when the in-plane field is perpendicular to the current vector, which identifies Rashba spin-orbit coupling as the main symmetry-breaking mechanism. While a variation in carrier concentration in these high-quality InSb nanoflags does not significantly influence the diode effect, it is instead strongly suppressed by an increase in temperature. Our experimental findings are consistent with a model for ballistic short junctions and show that the diode effect is intrinsic to this material. Our results establish InSb Josephson diodes as a useful element in superconducting electronics.

We demonstrate an Al superconducting quantum interference device in which the Josephson junctions are implemented through gate-controlled proximity Cu mesoscopic weak links. This specific kind of metallic weak links behaves analogously to genuine superconducting metals in terms of the response to electrostatic gating and provides a good performance in terms of current-modulation visibility. We show that through the application of a static gate voltage we can modify the interferometer current-flux relation in a fashion that seems compatible with the introduction of π-channels within the gated weak link. Our results suggest that the microscopic mechanism at the origin of the suppression of the switching current in the interferometer is apparently phase coherent, resulting in an overall damping of the superconducting phase rigidity. We finally tackle the performance of the interferometer in terms of responsivity to magnetic flux variations in the dissipative regime and discuss the practical relevance of gated proximity-based all-metallic SQUIDs for magnetometry at the nanoscale.

Superconducting interferometers are quantum devices able to transduce a magnetic flux into an electrical output with excellent sensitivity, integrability and power consumption. Yet, their voltage response is intrinsically non-linear, a limitation which is conventionally circumvented through the introduction of compensation inductances or by the construction of complex device arrays. Here we propose an intrinsically-linear flux-to-voltage mesoscopic transducer, called bi-SQUIPT, based on the superconducting quantum interference proximity transistor as fundamental building block. The bi-SQUIPT provides a voltage-noise spectral density as low as $\sim10^{-16}$ V/Hz$^{1/2}$ and, more interestingly, under a proper operation parameter selection, exhibits a spur-free dynamic range as large as $\sim60$ dB, a value on par with that obtained with state-of-the-art SQUID-based linear flux-to-voltage superconducting transducers. Furthermore, thanks to its peculiar measurement configuration, the bi-SQUIPT is tolerant to imperfections and non-idealities in general. For the above reasons, we believe that the bi-SQUIPT could provide a relevant step-beyond in the field of low-dissipation and low-noise current amplification with a special emphasis on applications in cryogenic quantum electronics., 9 pages, 6 figures

The Italian institute for nuclear physics (INFN) has financed the SIMP project (2019-2021) in order to strengthen its skills and technologies in the field of meV detectors with the ultimate aim of developing a single microwave photon detector. This goal will be pursued by improving the sensitivity and the dark count rate of two types of photodetectors: current biased Josephson Junction (JJ) for the frequency range 10-50 GHz and Transition Edge Sensor (TES) for the frequency range 30-100 GHz. Preliminary results on materials and devices characterization are presented., Comment: 7 pages, 4 figures

Thermoelectric effects in metals are typically small due to the nearly-perfect particle-hole (PH) symmetry around their Fermi surface [1, 2]. Despite being initially considered paradoxical [3], thermophase effects [4-8] and linear thermoelectricity [9] in superconducting systems were identified only when PH symmetry is explicitly broken [10-14]. Here, we experimentally demonstrate that a superconducting tunnel junction can develop a very large bipolar thermoelectric effect in the presence of a nonlinear thermal gradient thanks to spontaneous PH symmetry breaking [15]. Our junctions show a maximum thermovoltage of $\pm150\; \mu$ V at $\pm650$ mK, directly proportional to the superconducting gap. Notably, the corresponding Seebeck coefficient of $\pm300\; \mu$V/K is roughly $10^5$ times larger than the one expected for a normal metal at the same temperature [16, 17]. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine (BTJE) [18] with phase-coherent thermopower control [19]. When connected to a generic load, the BTJE generates a phase-tunable electric power up to about 140 mW/m$^2$ at subKelvin temperatures. In addition, our device implements the prototype for a persistent thermoelectric memory cell, written or erased by current injection [20]. We expect that our findings will trigger thermoelectricity in PH symmetric systems, and will lead to a number of groundbreaking applications in superconducting electronics [21], cutting-edge quantum technologies [22-24] and sensing [25]., Comment: 18 pages, 10 figures

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a non-vanishing magnetization, a phenomenon which is at the heart of non-dissipative magneto-electric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments a question of fundamental relevance deals with the orbital nature of magneto-electric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than one order of magnitude greater than that due to the spin, giving rise to a colossal magneto-electric effect. The induced orbital magnetization is shown to be sign tunable, with the sign change occurring for the Fermi level lying in proximity of avoiding crossing points in the Brillouin zone and in the presence of superconducting phase inhomogeneities, yielding domains with opposite orbital moment orientation. The orbital-dominated magneto-electric phenomena, hence, have clear-cut marks for detection both in the bulk and at the edge of the system and are expected to be a general feature of multi-orbital superconductors without inversion symmetry breaking., Comment: 7 pages, 5 figures

Recent experiments have shown the possibility of tuning the transport properties of metallic nanosized superconductors through a gate voltage. These results renewed the longstanding debate on the interaction between electrostatic fields and superconductivity. Indeed, different works suggested competing mechanisms as the cause of the effect: an unconventional electric field-effect or quasiparticle injection. Here, we provide conclusive evidence for the electrostatic-field-driven control of the supercurrent in metallic nanosized superconductors, by realizing ionic-gated superconducting field-effect nanotransistors (ISFETs) where electron injection is impossible. Our Nb ISFETs show giant suppression of the superconducting critical current of up to similar to 45%. Moreover, the bipolar supercurrent suppression observed in different ISFETs, together with invariant critical temperature and normal-state resistance, also excludes conventional charge accumulation/depletion. Therefore, the microscopic explanation of this effect calls upon a novel theory able to describe the nontrivial interaction of static electric fields with conventional superconductivity.

Setting up strong Josephson coupling in van der Waals materials in close proximity to superconductors offers several opportunities both to inspect fundamental physics and to develop novel cryogenic quantum technologies. Here we show evidence of Josephson coupling in a planar few-layer black Phosphorus junction. The planar geometry allows us to probe the junction behavior by means of external gates, at different carrier concentrations. Clear signatures of Josephson coupling are demonstrated by measuring supercurrent flow through the junction at milli Kelvin temperatures. Manifestation of Fraunhofer pattern with a transverse magnetic field is also reported, confirming the Josephson coupling. These findings represent the first evidence of proximity Josephson coupling in a planar junction based on a van der Waals material beyond graphene and open the way to new studies, exploiting the peculiar properties of exfoliated black phosphorus thin flakes.

We propose and theoretically investigate the behavior of a ballistic Aharonov-Bohm (AB) ring when embedded in a N-S two-terminal setup, consisting of a normal metal (N) and superconducting (S) leads. This device is based on available current technologies and we show in this work that it constitutes a promising hybrid quantum thermal device, as a quantum heat engine and quantum thermal rectifier. Remarkably, we evidence the interplay of single-particle quantum interferences in the AB ring and of the superconducting properties of the structure to achieve the hybrid operating mode for this quantum device. Its efficiency as a quantum heat engine reaches 55 % of the Carnot efficiency, and we predict a thermal rectification factor attaining 350%. These results make this device highly promising for future phase-coherent caloritronic nanodevices.

We discuss the charge and the spin tunneling currents between two Bardeen-Cooper-Schrieffer (BCS) superconductors, where one density of states is spin-split by the proximity of a ferromagnetic insulator. In the presence of a large temperature bias across the junction, we predict the generation of a spin-polarized thermoelectric current. This thermospin effect is the result of a spontaneous particle-hole symmetry breaking in the absence of any polarizing tunnel barrier. The two spin components, which move in opposite directions, generate a spin current larger than the purely polarized case when the thermoactive component dominates over the dissipative one.

Thermal transport and quantum thermodynamics at the nanoscale is nowadays garnering an increasing attention, in particular in the context of quantum technologies. Experiments relevant for quantum technology are expected to be performed in the non-linear regime. In this work, we build on previous results derived in the linear response regime for the performance of an Aharonov-Bohm (AB) interferometer operated as heat engine. In the non-linear regime, we demonstrate the tunability, large efficiency and thermopower that this mesoscopic quantum machine can achieve, confirming the exciting perspectives that this AB ring offers for developing efficient thermal machines in the fully quantum regime., 6 pages, 5 figures, invited contribution to AVS Quantum Science, Special Topic Collection on Quantum Thermodynamics, published version. Featured paper by the Editor

The composition of dark matter is one of the puzzling topics in astrophysics. To address this issue, several experiments searching for the existence of axions have been designed, built and realized in the last twenty years. Among all the others, light shining through walls experiments promise to push the exclusion limits to lower energies. For this reason, effort is put for the development of single-photon detectors operating at frequencies $, 15 pages, 7 figures. arXiv admin note: text overlap with arXiv:2011.08745

Superconducting computing promises enhanced computational power in both classical and quantum approaches. Yet, efficient schemes for scalable and fast superconducting memories are still missing. On the one hand, the large inductance required in magnetic flux-controlled Josephson memories impedes device miniaturization and scalability. On the other hand, schemes based on the ferromagnetic order to store information often degrades superconductivity, and limits the operation speed to the magnetization switching rate of a few GHz. Here, we overcome these limitations with a fully superconducting memory cell based on the hysteretic phase-slip transition existing in long aluminum nanowire Josephson junctions. The memory logic state is codified in the topological index of the junction providing a robust protection against stocastic phase slips and magnetic flux noise. Our direct and non-destructive read-out schemes, based on local DC or AC tunneling spectroscopy, ensure reduced dissipation (≤ 40 fW) thereby yielding a very low energy per bit read-out power consumption as low as ~ 10-24 J as estimated from the typical time response of the structure (≤ 30 ps). The memory, measured over several days, showed no evidence of information degradation up to ~1.1 K, i.e., ~85% of the critical temperature of aluminum. The ease of operation combined with remarkable performance elects the Josephson phase-slip memory as an attractive storage cell to be exploited in advanced superconducting classical logic architectures or flux qubits.

The effect of electrostatic gating on metallic elemental superconductors was recently demonstrated in terms of modulation of the switching current and control of the current phase relation in superconducting quantum interferometers. The latter suggests the existence of a direct connection between the macroscopic quantum phase in a superconductor and the applied gate voltage. The measurement of the switching current cumulative probability distributions (SCCPD) is a convenient and powerful tool to analyze such relation. In particular, the comparison between the conventional Kurkijarvi-Fulton-Dunkleberger model and the gate-driven distributions give useful insights into the microscopic origin of the gating effect. In this review, we summarize the main results obtained in the analysis of the phase slip events in elemental gated superconducting weak-links in a wide range of temperatures between 20 mK and 3.5 K. Such a large temperature range demonstrates both that the gating effect is robust as the temperature increases, and that fluctuations induced by the electric field are not negligible in a wide temperature range.

It was recently demonstrated the possibility to tune, through the application of a control gate voltage, the superconducting properties of mesoscopic devices based on Bardeen-Cooper-Schrieffer metals. In spite of the several experimental evidence obtained on different materials and geometries, a description of the microscopic mechanism at the basis of such unconventional effect has not been provided yet. This work discusses the technological potential of gate control of superconductivity in metallic superconductors and revises the experimental results which provide information regarding a possible thermal origin of the effect: in the first place, we review experiments performed on high critical temperature elemental superconductors (niobium and vanadium) and show how devices based on these materials can be exploited to realize basic electronic tools such as, e. g., a half-wave rectifier. In a second part, we discuss the origin of the gating effect by showing the gate-driven suppression of the supercurrent in a suspended titanium wire and by providing a comparison between thermal and electric switching current probability distributions. Furthermore, we discuss the cold field-emission of electrons from the gate by means of finite element simulations and compare the results with experimental data. Finally, the presented data provide a strong indication regarding the unlikelihood of thermal origin of the gating effect.

Superconducting computing promises enhanced computational power in both classical and quantum approaches. Yet, scalable and fast superconducting memories are not implemented. Here, we propose a fully superconducting memory cell based on the hysteretic phase-slip transition existing in long aluminum nanowire Josephson junctions. Embraced by a superconducting ring, the memory cell codifies the logic state in the direction of the circulating persistent current, as commonly defined in flux-based superconducting memories. But, unlike the latter, the hysteresis here is a consequence of the phase-slip occurring in the long weak link and associated to the topological transition of its superconducting gap. This disentangles our memory scheme from the large-inductance constraint, thus enabling its miniaturization. Moreover, the strong activation energy for phase-slip nucleation provides a robust topological protection against stochastic phase-slips and magnetic-flux noise. These properties make the Josephson phase-slip memory a promising solution for advanced superconducting classical logic architectures or flux qubits., Superconducting computing promises enhanced computational power, but scalable and fast superconducting memories are still not implemented. Here, the authors demonstrate a superconducting memory cell based on hysteretic phase-slip transition, without degradation up to ~1 K over several days.

We theoretically investigate a quantum heat diode based on two interacting flux qubits coupled to two heat baths. Rectification of heat currents is achieved by asymmetrically coupling the qubits to the reservoirs, which are modeled as dissipative $RLC$ resonators. We find that the coherent interaction between the qubits can be exploited to enhance the rectification factor, which otherwise would be constrained by the temperatures and couplings of the baths. Remarkably high values of the rectification ratio, up to $\mathcal{R}\ensuremath{\sim}3.5$, can be obtained for realistic system parameters, with an enhancement up to approximately $230\mathrm{%}$ compared to the noninteracting case. The system features the possibility of manipulating both the rectification amplitude and direction, allowing for an enhancement or suppression of the heat flow to a chosen bath. For the parameter regime in which rectification is maximized, we find a significant increase of the rectification above a critical interaction value, which corresponds to the onset of a nonvanishing entanglement in the system. Finally, we discuss the dependence of the rectification factor on the bath temperatures and couplings.

We have studied the effects of optical-frequency light on proximitized InAs/Al Josephson junctions based on highly n-doped InAs nanowires at varying incident photon flux and at three different photon wavelengths. The experimentally obtained IV curves were modeled using a resistively shunted junction model which takes scattering at the contact interfaces into account. Despite the fact that the InAs weak link is photosensitive, the Josephson junctions were found to be surprisingly robust, interacting with the incident radiation only through heating, whereas above the critical current our devices showed non-thermal effects resulting from photon exposure. Our work indicates that Josephson junctions based on highly-doped InAs nanowires can be integrated in close proximity to photonic circuits. The results also suggest that such junctions can be used for optical-frequency photon detection through thermal processes by measuring a shift in critical current.

The origin and the evolution of the universe are concealed in the evanescent diffuse extragalactic background radiation (DEBRA). To reveal these signals, the development of innovative ultra-sensitive bolometers operating in the gigahertz band is required. Here, we review the design and experimental realization of two bias-current-tunable sensors based on one dimensional fully superconducting Josephson junctions: the nanoscale transition edge sensor (nano-TES) and the Josephson escape sensor (JES). In particular, we cover the theoretical basis of the sensors operation, the device fabrication, their experimental electronic and thermal characterization, and the deduced detection performance. Indeed, the nano-TES promises a state-of-the-art noise equivalent power (NEP) of about $5 \times 10^{-20}$ W$/\sqrt{\text{Hz}}$, while the JES is expected to show an unprecedented NEP of the order of $10^{-25}$ W$/\sqrt{\text{Hz}}$. Therefore, the nano-TES and JES are strong candidates to push radio astronomy to the next level., Comment: 14 pages, 5 figures

Motivated by recent experiments reporting the suppression of the critical current in superconducting Dayem bridges by the application of strong electrostatic fields, in this work we study the impact on the superconducting gap of charge redistribution in response to an applied electric field in thin crystalline metals. By numerically solving the BCS gap equation and the Poisson equation in a fully self-consistent way, we find that by reducing the pairing strength we observe an increased sensitivity of the gap on the applied field, showing sudden rises and falls that are compatible with surface modifications of the local density of states. The effect is washed out by increasing the pairing strength towards the weak-to-moderate coupling limit or by introduction of a weak smearing in the density of states, showing the evolution from a clean crystal to a weakly disordered metal., Comment: 7 pages, 8 figures

In a previous work, we predicted that a thermally biased tunnel junction between two different superconductors can display a thermoelectric effect of nonlinear nature in the temperature gradient under proper conditions. In this work we give a more extended discussion, and we focus on the two main features of the nonlinear contributions: (i) the linear-in-bias thermoelectricity, which can be associated to a spontaneous breaking of electron-hole symmetry, and (ii) the strong contribution at the matching peak singularity, which is typically associated to the maximum output power and efficiency. We discuss the nonlinear origin of the thermoelectricity and its relationship with the nonlinear cooling mechanism in superconducting junctions previously discussed in the literature. Finally, we design and characterize the performance of the system as a heat engine for a realistic design and experimental parameter values. We discuss possible nonidealities demonstrating that the system is amenable to current experimental realization.

We study the magnetic and superconducting proximity effects in a semiconducting nanowire (NW) attached to superconducting leads and a ferromagnetic insulator (FI). We show that a sizable equilibrium spin polarization arises in the NW due to the interplay between the superconducting correlations and the exchange field in the FI. The resulting magnetization has a nonlocal contribution that spreads in the NW over the superconducting coherence length and is opposite in sign to the local spin polarization induced by the magnetic proximity effect in the normal state. For a Josephson-junction setup, we show that the nonlocal magnetization can be controlled by the superconducting phase bias across the junction. Our findings are relevant for the implementation of Majorana bound states in state-of-the-art hybrid structures., This work was supported by Spanish Ministerio de Ciencia e Innovacion (MICINN) through the Project FIS2017-82804-P, and EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

In a family of experiments carried on all-metallic supercurrent nano-transistors a surprising gating effect has been recently shown. These include the full suppression of the critical supercurrent, the increase of quasiparticle population, the manipulation of the superconducting phase, and the broadening of the switching current distributions. Aside from the high potential for future applications, these findings raised fundamental questions on the origin of these phenomena. To date, two complementary hypotheses are under debate: an electrostatically-triggered orbital polarization at the superconductor surface, or the injection of highly-energetic quasiparticles extracted from the gate. Here, we tackle this crucial issue via a fully suspended gate-controlled Ti nano-transistor. Our geometry allows to eliminate any direct injection of quasiparticles through the substrate thereby making cold electron field emission through the vacuum the only possible charge transport mechanism. With the aid of a fully numerical 3D model in combination with the observed phenomenology and thermal considerations we can rule out, with any realistic likelihood, the occurrence of cold electron field emission. Excluding these two trivial phenomena is pivotal in light of understanding the microscopic nature of gating effect in superconducting nanostructures, which represents an unsolved puzzle in contemporary superconductivity. Yet, from the technological point of view, our suspended fabrication technique provides the enabling technology to implement a variety of applications and fundamental studies combining, for instance, superconductivity with nano-mechanics., 7 pages, 4 color figures

We investigate the photon-mediated thermal transport between a superconducting electrode and a normal metal. When the quasiparticle contribution can be neglected, the photon-mediated channel becomes an efficient heat transport relaxation process for the superconductor at low temperatures, being larger than the intrinsic contribution due to the electron-phonon interaction. Furthermore, the superconductor-normal metal system acts as a nearly-perfect thermal diode, with a rectification factor up to $10^8$ for a realistic aluminum superconducting island. The rectification factor can be also tuned in a phase-controlled fashion through a non-galvanic coupling, realized by changing the magnetic flux piercing a superconducting quantum interference device (SQUID), which modifies the coupling impedance between the superconductor and the normal metal. The scheme can be exploited for passive cooling in superconducting quantum circuits by transferring heat toward normal metallic pads where it dissipates more efficiently or for more general thermal management purposes.

Ferromagnetic insulators (FI) can induce a strong exchange field in an adjacent superconductor (S) via the magnetic proximity effect. This manifests as spin splitting of the BCS density of states of the superconductor, an important ingredient for numerous superconducting spintronics applications and the realization of Majorana fermions. A crucial parameter that determines the magnitude of the induced spin splitting in FI/S bilayers is the thickness of the S layer d: In very thin samples, the superconductivity is suppressed by the strong magnetism. By contrast, in very thick samples, the spin splitting is absent at distances away from the interface. In this work, we calculate the density of states and critical exchange field of FI/S bilayers of arbitrary thickness. From here, we determine the range of parameters of interest for applications, where the exchange field and superconductivity coexist. We show that for d>3.0ξs, the paramagnetic phase transition is always of the second order, in contrast to the first-order transition in thinner samples at low temperatures. Here ξs is the superconducting coherence length. Finally, we compare our theory with the tunneling spectroscopy measurements in several EuS/Al/AlOx/Al samples. If the Al film in contact with the EuS is thinner than a certain critical value, we do not observe superconductivity, whereas, in thicker samples, we find evidence of a first-order phase transition induced by an external field. The complete transition is preceded by a regime in which normal and superconducting regions coexist. We attribute this mixed phase to inhomogeneities of the Al film thickness and the presence of superparamagnetic grains at the EuS/Al interface with different switching fields. The steplike evolution of the tunnel-barrier magnetoresistance supports this assumption. Our results demonstrate on the one hand, the important role of the S layer thickness, which is particularly relevant for the fabrication of high-quality samples suitable for applications. On the other hand, the agreement between theory and experiment demonstrates the accuracy of our theory, which, originally developed for homogeneous situations, is generalized to highly inhomogeneous systems., F.S.B. acknowledges funding by the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) (Project FIS2017-82804-P). T.T.H. acknowledges funding from the Academy of Finland (Project number 317118). A.H. acknowledges funding by the Department of Education of the Basque Government (Ikasiker grant). C.G.-O. acknowledges funding of the Ph.D. fellowship from MPC foundation. S.K. acknowledges for the fellowship of the ICTP Program for Training and Research in Italian laboratories, Trieste, Italy. C.R. acknowledges support from Gobierno Vasco (Grant No. IT 1255-19). F.G. acknowledges the European Research Council under the EU’s Horizon 2020 Grant Agreement No. 899315-TERASEC for partial financial support. We acknowledge funding from EU’s Horizon 2020 research and innovation program under Grant Agreement No. 800923 (SUPERTED).

From the sixties a deep and surprising connection has followed the development of superconductivity and quantum field theory. The Anderson-Higgs mechanism and the similarities between the Dirac and Bogoliubov-de Gennes equations are the most intriguing examples. In this last analogy, the massive Dirac particle is identified with a quasiparticle excitation and the fermion mass energy with the superconducting gap energy. Here we follow further this parallelism and show that it predicts an outstanding phenomenon: the superconducting Schwinger effect (SSE). As in the quantum electrodynamics Schwinger effect, where an electron-positron couple is created from the vacuum by an intense electric field, we show that an electrostatic field can generate two coherent excitations from the superconducting ground-state condensate. Differently from the dissipative thermal excitation, these form a new macroscopically coherent and dissipationless state. We discuss how the superconducting state is weakened by the creation of this kind of excitations. In addition to shed a different light and suggest a method for the experimental verification of the Schwinger effect, our results pave the way to the understanding and exploitation of the interaction between superconductors and electric fields., Comment: 12 pages, 3 figures

Josephson junctions, in appropriate configurations, can be excellent candidates for detection of single photons in the microwave frequency band. Such possibility has been recently addressed in the framework of galactic axion detection. Here are reported recent developments in the modelling and simulation of dynamic behaviour of a Josephson junction single microwave photon detector. For a Josephson junction to be enough sensitive, small critical currents and operating temperatures of the order of ten of mK are necessary. Thermal and quantum tunnelling out of the zero-voltage state can also mask the detection process. Axion detection would require dark count rates in the order of 0.001 Hz. It is, therefore, is of paramount importance to identify proper device fabrication parameters and junction operation point., Comment: 7 pages, 9 figures