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The development of superconducting electronics requires careful characterization of the components that make up electronic circuits. Superconducting weak links are the building blocks of most superconducting electronics components and are characterized by highly nonlinear current-to-phase relations (CPR), which are often not perfectly known. Recent research has found that the Josephson diode effect (JDE) can be related to the high harmonic content of the current-to-phase relation of the weak links embedded in superconducting interferometers. This makes the JDE a natural tool for exploring the harmonic content of weak links beyond single-harmonic CPR. In this study, we present the theoretical model and experimental characterization of a double-loop superconducting quantum interference device (DL-SQUID) that embeds all-metallic superconductor-normal metal-superconductor junctions. The proposed device exhibits the JDE due to the interference of the supercurrents of three weak links in parallel, and this feature can be adjusted through two magnetic fluxes, which act as experimental knobs. We carry out a theoretical study of the device in terms of the relative weight of the interferometer arms and the experimental characterization concerning flux tunability and temperature.

Efficient heat management at cryogenic temperatures is crucial for superconducting quantum technologies. This study demonstrates the controlled manipulation of the heat flow and heat rectification through an asymmetric superconducting tunnel junction. The system exhibits a non-reciprocal behavior, developing a thermoelectric regime exclusively when the electrode with the larger gap is heated. This feature significantly boosts thermal rectification effectively classifying the device as a heat diode. At the same time when operating as a thermoelectric engine, the same device also functions as a heat pipe, expelling heat from the cryogenic environment, minimizing losses at the cold terminal. This dual functionality is inherently passive, and the performance of the heat pipe and the heat diode can be finely adjusted by modifying the external electrical load., Comment: 6 pages, 4 color figures

Here we demonstrate superconducting Dayem-bridge weak-links made of different stoichiometric compositions of NbRe. Our devices possess a relatively high critical temperature, normal-state resistance, and kinetic inductance. In particular, the high kinetic inductance makes this material a good alternative to more conventional niobium-based superconductors (e.g., NbN or NbTiN) for the realization of superinductors and high-quality factor resonators, whereas the high normal-state resistance yields a large output voltage in superconducting switches and logic elements realized upon this compound. Moreover, out-of-plane critical magnetic fields exceeding 2 T ensure that possible applications requiring high magnetic fields can also be envisaged. Altogether, these features make this material appealing for a number of applications in the framework of quantum technologies., Comment: 10 pages, 4 figures

Ad-hoc interface PCBs are today the standard connection between cryogenic cabling and quantum chips. Besides low-loss and low-temperature-dependent-dielectric-permittivity materials, FR4 provides a low-cost solution for fabrication of cryogenic PCBs. Here, we report on an effective way to evaluate the dielectric performance of a FR4 laminate used as substrate for cryogenic microwave PCBs. We designed a coplanar waveguide {\lambda}/2 open-circuit series resonator and we fabricated the PCB using a low-cost manufacturing process. Such a geometry allows to exploit the resonance peak of the resonator to measure the variation of the complex dielectric permittivity as a function of the temperature. Resonance peak frequency and magnitude were used as sensing parameters for the real part of dielectric permittivity and dielectric loss tangent, respectively. We estimated a 9 % reduction of the real part of the dielectric permittivity and a 70 % reduction of the dielectric loss tangent in the temperature range from 300 to 4 K. The proposed approach can be immediately extended to the detection of cryogenic temperature-dependent dielectric performance of any kind on substrate., Comment: 5 pages, 6 figures, supporting information at the end of the paper

Recent studies have shown the potential for bipolar thermoelectricity in superconducting tunnel junctions with asymmetric energy gaps. The thermoelectric performance of these systems is significantly impacted by the inverse proximity effects present in the normal-superconducting bilayer, which is utilized to adjust the gap asymmetry in the junction. Here, we identify the most effective bilayer configurations, and we find that directly tunnel-coupling the normal metal side of the cold bilayer with the hot superconductor is more advantageous compared to the scheme used in experiments. By utilizing quasiclassical equations, we examined the nonlinear thermoelectric junction performance as a function of the normal metal film thickness and the quality of the normal-superconducting interface within the bilayer, thereby determining the optimal design to observe and maximize this nonequilibrium effect. Our results offer a roadmap to achieve improved thermoelectric performance in superconducting tunnel junctions, with promising implications for a number of applications., Comment: 6 pages, 3 figures

Asymmetric superconducting tunnel junctions with gaps $\Delta_1>\Delta_2$ have been proven to show a peculiar nonlinear bipolar thermoelectric effect. This arises due to the spontaneous breaking of electron-hole symmetry in the system, and it is maximized at the matching-peak bias $|V|=V_p=(\Delta_1-\Delta_2)/e$. In this paper, we investigate the interplay of photon-assisted tunneling (PAT) and bipolar thermoelectric generation. In particular, we show how thermoelectricity, at the matching peak, is supported by photon absorption/emission processes at the frequency-shifted sidebands $V=\pm V_p+n\hbar\omega$, $n \in \mathbb{Z}$. This represents a sort of microwave-assisted thermoelectricity. We show the existence of multiple stable solutions, being associated with different photon sidebands, when a load is connected to the junction. Finally, we discuss how the nonlinear cooling effects are modified by the PAT. The proposed device can detect millimeter wavelength signals by converting a temperature gradient into a thermoelectric current or voltage., Comment: 8 pages, 3 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

Diodes are key elements for electronics, optics, and detection. The search for a material combination providing the best performances for the required application is continuously ongoing. Here, we present a superconducting spintronic tunnel diode based on the strong spin filtering and splitting generated by an EuS thin film between a superconducting Al and a normal metal Cu layer. The Cu/EuS/Al tunnel junction achieves a large rectification (up to $\sim40$\%) already for a small voltage bias ($\sim 200$ $\mu$V) thanks to the small energy scale of the system: the Al superconducting gap. With the help of an analytical theoretical model we can link the maximum rectification to the spin polarization of the barrier and describe the quasi-ideal Schottky-diode behavior of the junction. This cryogenic spintronic rectifier is promising for the application in highly-sensitive radiation detection for which two different configurations are evaluated. In addition, the superconducting diode may pave the way for future low-dissipation and fast superconducting electronics., Comment: 17 pages, 12 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

Ferromagnetic insulators can induce a strong exchange field in an adjacent superconductor 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 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 compare our theory with the tunneling spectroscopy measurements in several EuS/Al/AlO$_x$/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. 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., Comment: 14 pages, 6 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.

We investigate the noise current in a thermally biased tunnel junction between two superconductors with different zero-temperature gaps. When the Josephson effect is suppressed, this structure can support a nonlinear thermoelectric effect due to the spontaneous breaking of electron-hole symmetry, as we recently theoretically predicted. We discuss the possibly relevant role played by the noise in the junction. While a moderate noise contribution assists the generation of the thermoelectric signal, further unveiling the spontaneous nature of the electron-hole symmetry breaking, a large noise contribution can induce a switching between the two stationary thermoelectric values, thus hardening the detection of the effect and its application. We demonstrate that the thermoelectric effect is robust to the presence of noise for a wide range of parameters and that the spurious fluctuations of the thermoelectric signal can be lowered by increasing the capacitance of the junction, for instance by expanding the junction's size. Our results pave the way to the future experimental observation of the thermoelectric effect in superconducting junctions, and to improved performance in quantum circuits designed for thermal management.

Superconducting tunnel junctions constitute the units of superconducting quantum circuits and are massively used both for quantum sensing and quantum computation. In previous works, we predicted the existence of a nonlinear thermoelectric effect in a electron-hole symmetric system, namely, a thermally biased tunnel junction between two different superconductors, where the Josephson effect is suppressed. In this paper we investigate the impact of the phase-coherent contributions on the thermoelectric effect, by tuning the size of the Josephson coupling changing the flux of a direct-current Superconducting Quantum Interference Device (dc-SQUID). For a suppressed Josephson coupling, the system generates a finite average thermoelectric signal, combined to an oscillation due to the standard ac Josephson phenomenology. At large Josephson couplings, the thermoelectricity induces an oscillatory behaviour with zero average value of the current/voltage with an amplitude and a frequency associated to the Josephson coupling strength, and ultimately tuned by the dc-SQUID magnetic flux. In conclusion, we demonstrate to be able to control the dynamics of the spontaneous breaking of the electron-hole symmetry. Furthermore, we compute how the flux applied to the dc-SQUID and the lumped elements of the circuit determine the frequency of the thermoelectric signal across the structure, and we envision a frequency modulation application.

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., Comment: 7 pages, 4 color figures

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 disentangle 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., Comment: 14 pages, 10 color figures

Recently, the possibility to tune the critical current of conventional metallic superconductors via electrostatic gating was shown in wires, Josephson weak-links and superconductor-normal metal-superconductor junctions. Here we exploit such a technique to demonstrate a gate-controlled vanadium-based Dayem nano-bridge operated as a \emph{half-wave} rectifier at $3$ K. Our devices exploit the gate-driven modulation of the critical current of the Josephson junction, and the resulting steep variation of its normal-state resistance, to convert an AC signal applied to the gate electrode into a DC one across the junction. All-metallic superconducting gated rectifiers could provide the enabling technology to realize tunable photon detectors and diodes useful for superconducting electronics circuitry., Comment: 5 pages, 4 figures

We investigate electronic thermal rectification in ferromagnetic insulator-based superconducting tunnel junctions. Ferromagnetic insulators coupled to superconductors are known to induce sizable spin splitting in the superconducting density of states, and also lead to efficient spin filtering if operated as tunnel barriers. The combination of spin splitting and spin filtering is shown to yield a substantial self-amplification of the electronic heat diode effect due to breaking of the electron-hole symmetry in the system which is added to the thermal asymmetry of the junction. Large spin splitting and large spin polarization can potentially lead to thermal rectification efficiency exceeding 5 .10^4 for realistic parameters in a suitable temperature range, thereby outperforming up to a factor of 250 the heat diode effect achievable with conventional superconducting tunnel junctions. These results could be relevant for improved mastering of the heat currents in innovative phase-coherent caloritronic nanodevices, and for enhanced thermal management of quantum circuits at the nanoscale., Comment: 5 pages; 4 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, that can be associated to a spontaneous breaking of electron-hole symmetry, 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 non-linear 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 non-idealities 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., Comment: 12 pages, 5 figures

A battery is a classical apparatus which converts a chemical reaction into a persistent voltage bias able to power electronic circuits. Similarly, a phase battery is a quantum equipment which provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on quantum coherence. Unlike the voltage batteries, a phase battery has not been implemented so far, mainly because of the natural rigidity of the quantum phase that, in typical quantum circuits, is imposed by the parity and time-reversal symmetry constrains. Here we report on the first experimental realization of a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states and proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias $\varphi_0$ across the wire, leading to the anomalous Josephson effect. By applying an external in-plane magnetic field a continuous tuning of $\varphi_0$ is achieved. This allows the charging and discharging of the quantum phase battery and reveals the symmetries of the anomalous Josephson effect predicted by our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction breaks the phase rigidity of the system inducing a strong coupling between charge, spin and superconducting phase. This interplay opens avenues for topological quantum technologies, superconducting circuitry and advanced schemes of circuit quantum electrodynamics.}, Comment: 6 pages, 3 figures and Supplementary Material

The investigation of the switching current probability distribution of a Josephson junction is a conventional tool to gain information on the phase slips dynamics as a function of the temperature. Here we adopt this well-established technique to probe the impact of an external static electric field on the occurrence of phase slips in gated all-metallic titanium (Ti) Josephson weak links. We show, in a temperature range between 20 mK and 420 mK, that the evolution of the phase slips dynamics as a function of the electrostatic field starkly differs from that observed as a function of the temperature. This fact demonstrates, on the one hand, that the electric field suppression of the critical current is not simply related to a conventional thermal-like quasiparticle overheating in the weak-link region. On the other hand, our results may open the way to operate an electrostatic-driven manipulation of phase slips in metallic Josephson nanojunctions, which can be pivotal for the control of decoherence in superconducting nanostructures., Comment: 9 pages, 7 color figures, 1 table

In the linear regime, thermo-electric effects between two conductors are possible only in the presence of an explicit breaking of the electron-hole symmetry. We consider a tunnel junction between two electrodes and show that this condition is no longer required outside the linear regime. In particular, we demonstrate that a thermally-biased junction can display an absolute negative conductance (ANC), and hence thermo-electric power, at a small but finite voltage bias, provided that the density of states of one of the electrodes is gapped and the other is monotonically decreasing. We consider a prototype system that fulfills these requirements, namely a tunnel junction between two different superconductors where the Josephson contribution is suppressed. We discuss this nonlinear thermo-electric effect based on the spontaneous breaking of electron-hole symmetry in the system, characterize its main figures of merit and discuss some possible applications., Comment: biblio information updated

We consider effects of an externally applied electrostatic field on superconductivity, self-consistently within a BCS mean field model, for a clean 3D metal thin film. The electrostatic change in superconducting condensation energy scales as $\mu^{-1}$ close to subband edges as a function of the Fermi energy $\mu$, and follows 3D scaling $\mu^{-2}$ away from them. We discuss nonlinearities beyond gate effect, and contrast results to recent experiments., Comment: 8 pages, 5 figures

A superconductor with a spin-split excitation spectrum behaves as an ideal ferromagnetic spin-injector in a tunneling junction. It was theoretical predicted that the combination of two such spin-split superconductors with independently tunable magnetizations, may be used as an ideal $absolute$ spin-valve. Here we report on the first switchable superconducting spin-valve based on two EuS/Al bilayers coupled through an aluminum oxide tunnel barrier. The spin-valve shows a relative resistance change between the parallel and antiparallel configuration of the EuS layers up to 900% that demonstrates a highly spin-polarized currents through the junction. Our device may be pivotal for realization of thermoelectric radiation detectors, logical element for a memory cell in cryogenics superconductor-based computers and superconducting spintronics in general., Comment: 6 pages, 4 color figures, 1 table

We consider a Josephson junction consisting of superconductor/ferromagnetic insulator (S/FI) bilayers as electrodes which proximizes a nearby 2D electron gas. By starting from a generic Josephson hybrid planar setup we present an exhaustive analysis of the the interplay between the superconducting and magnetic proximity effects and the conditions under which the structure undergoes transitions to a non-trivial topological phase. We address the 2D bound state problem using a general transfer matrix approach that reduces the problem to an effective 1D Hamiltonian. This allows for straightforward study of topological properties in different symmetry classes. As an example we consider a narrow channel coupled with multiple ferromagnetic superconducting fingers, and discuss how the Majorana bound states can be spatially controlled by tuning the superconducting phases. Following our approach we also show the energy spectrum, the free energy and finally the multiterminal Josephson current of the setup., Comment: 8 pages; 5 figures

We propose a single photon detector based on a superconducting quantum interference device (SQUID) with superconductor-normal metal-superconductor Josephson weak links. One of the two Josephson junctions is connected to an antenna, and is heated when a photon is absorbed. The increase of the weak link temperature exponentially suppresses the Josephson critical current thereby inducing an asymmetry in the SQUID. This generates a voltage pulse across the SQUID that can be measured with a threshold detector. Realized with realistic parameters the device can be used as a single photon detector, and as a calorimeter since it is able to discriminate photons frequency above $5~$THz with a signal-to-noise ratio larger than $20$. The detector performance are robust with respect to working temperatures between $0.1~$ K and $0.5~$K, and thermal noise perturbation., Comment: 8 pages, 6 figures. Updated version

In their original formulation of superconductivity, the London brothers predicted the exponential suppression of an $electrostatic$ field inside a superconductor over the so-called London penetration depth, $\lambda_L$. Despite a few experiments indicating hints of perturbation induced by electrostatic fields, no clue has been provided so far on the possibility to manipulate metallic superconductors via field-effect. Here we report field-effect control of the supercurrent in $all$-metallic transistors made of different Bardeen-Cooper-Schrieffer (BCS) superconducting thin films. At low temperature, our field-effect transistors (FETs) show a monotonic decay of the critical current under increasing electrostatic field up to total quenching for gate voltage values as large as $\pm 40$V in titanium-based devices. This $bipolar$ field effect persists up to $\sim 85\%$ of the critical temperature ($\sim 0.41$K), and in the presence of sizable magnetic fields. A similar behavior was observed in aluminum thin film FETs. A phenomenological theory accounts for our observations, and points towards the interpretation in terms of an electric-field-induced perturbation propagating inside the superconducting film. In our understanding, this affects the pairing potential and quenches the supercurrent. These results could represent a groundbreaking asset for the realization of an $all$-metallic superconducting field-effect electronics and leading-edge quantum information architectures., Comment: 9 pages, 7 color figures, revised text version

We suggest a new type of an ultrasensitive detector of electromagnetic fields exploiting the giant thermoelectric effect recently found in superconductor/ferromagnet hybrid structures. Compared to other types of superconducting detectors where the detected signal is based on variations of the detector impedance, the thermoelectric detector has the advantage of requiring no external driving fields. This becomes especially relevant in multi-pixel detectors where the number of bias lines and the heating induced by them becomes an issue. We propose different material combinations to implement the detector and provide a detailed analysis of its sensitivity and speed. In particular, we perform to our knowledge the first proper noise analysis that includes the cross correlation between heat and charge current noise and thereby describes also thermoelectric detectors with a large thermoelectric figure of merit., Comment: 7 pages + appendix; 7 figures

A ferromagnetic insulator attached to a superconductor is known to induce an exchange splitting of the Bardeen-Cooper-Schrieffer (BCS) singularity by a magnitude proportional to the magnetization, and penetrating into the superconductor to a depth comparable with the superconducting coherence length. We study this long-range magnetic proximity effect in EuS/Al bilayers and find that the exchange splitting of the BCS peaks is present already in the unpolarized state of the ferromagnetic insulator (EuS), and is being further enhanced when magnetizing the sample by a magnetic field. The measurement data taken at the lowest temperatures feature a high contrast which has allowed us to relate the line shape of the split BCS conductance peaks to the characteristic magnetic domain structure of the EuS layer in the unpolarized state. These results pave the way to engineering triplet superconducting correlations at domain walls in EuS/Al bilayers. Furthermore, the hard gap and clear splitting observed in our tunneling spectroscopy measurements indicate that EuS/Al bilayers are excellent candidates for substituting strong magnetic fields in experiments studying Majorana bound states., Comment: 9 pages, 4 color figures

We theoretically investigate the temperature-to-phase conversion (TPC) process occurring in dc superconducting quantum interferometers based on superconductor--normal metal--superconductor (SNS) mesoscopic Josephson junctions. In particular, we predict the temperature-driven rearrangement of the phase gradients in the interferometer under the fixed constraints of fluxoid quantization and supercurrent conservation. This allows sizeable phase variations across the junctions for suitable structure parameters and temperatures. We show that the TPC can be a basis for sensitive single-photon sensors or bolometers. We propose a radiation detector realizable with conventional materials and state-of-the-art nanofabrication techniques. Integrated with a superconducting quantum interference proximity transistor (SQUIPT) as a readout set-up, an aluminum (Al)-based TPC calorimeter can provide a large signal to noise (S/N) ratio $>100$ in the 10~GHz$\cdots$10~THz frequency range, and a resolving power larger than $10^2$ below 50~mK for THz photons. In the bolometric operation, electrical NEP of $\sim10^{-22}$~W$/\sqrt{\text{Hz}}$ is predicted at 50 mK. This device can be attractive as a cryogenic single-photon sensor operating in the giga- and terahertz regime, with applications in dark matter searches., Comment: 13 pages, 10 figures

We discuss thermal transport through a Josephson junction in a time-dependent situation. We write the spectral representation of the heat current pumped by a generic drive. This enables separation of the dissipative and reactive contributions, of which the latter do not contribute to long-time averages. We discuss the physical interpretation, and note that the condensate heat current identified in [K. Maki and A. Griffin, Phys. Rev. Lett. 15, 921 (1965)] is purely reactive. The results enable a convenient description of heat exchanges in a Josephson system in the presence of an external drive, with possible applications for the implementation of new cooling devices., Comment: 6 pages, 4 figures

We present an exhaustive theoretical analysis of a double-loop Josephson proximity interferometer, as the one recently realized by Strambini et al. for the control of the Andreev spectrum via an external magnetic field. This system, called $\omega$-SQUIPT, consists of a T-shaped diffusive normal metal (N) attached to three superconductors (S) forming a double loop configuration. By using the quasiclassical Green function formalism, we calculate the local normalized density of states, the Josephson currents through the device and the dependence of the former on the length of the junction arms, the applied magnetic field and the S/N interface transparencies. We show that by tuning the fluxes through the double loop, the system undergoes transitions from a gapped to a gapless state. We also evaluate the Josephson currents flowing in the different arms as a function of magnetic fluxes and explore the quasi-particle transport, by considering a metallic probe tunnel-coupled to the Josephson junction and calculating its I-V characteristics. Finally, we study the performances of the $\omega$-SQUIPT and its potential applications, by investigating its electrical and magnetometric properties., Comment: 11 pages, 12 figures

We consider properties of a fully superconducting variant of the superconducting quantum interference proximity transistor magnetic flux sensor. We study the density of states in a finite-size superconducting metal wire in the diffusive limit, and how it depends on the phase gradient of the order parameter. We describe the dependence on the junction length and interface transparency, and discuss properties relevant for using the structure in magnetic flux detection applications., Comment: 9 pages

The design of a mesoscopic self-oscillating heat engine that works thanks to purely quantum effects is presented. The proposed scheme is amenable to experimental implementation with current state-of-the-art nanotechnology and materials. One of the main features of the structure is its versatility: The engine can deliver work to a generic load without galvanic contact. This makes it a promising building block for low-temperature on-chip energy management applications. The heat engine consists of a circuit featuring a thermoelectric element based on a ferromagnetic insulator-superconductor tunnel junction and a Josephson weak link that realizes a purely quantum DC/AC converter. This enables contactless transfer of work to the load (a generic RL circuit). The performance of the heat engine is investigated as a function of the thermal gradient applied to the thermoelectric junction. Power up to $1$ pW can be delivered to a load $R_L=10\ \Omega$., Comment: 6 pages, 4 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

Multi-terminal superconducting Josephson junctions based on the proximity effect offer the bright opportunity to tailor non trivial quantum states in nanoscale weak-links. These structures can realize exotic topologies in multidimensions as, for example, artificial topological superconductors able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here, we report the first realization of a three-terminal Josephson interferometer based on a proximized nanosized weak-link. Our tunneling spectroscopy measurements reveal transitions between gapped (i.e., insulating) and gapless (i.e., conducting) states, those being controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the $topological$ nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological index, very much like the interface between two insulators of different topology is necessarily conducting. The topological numbers characterizing such gapped states are given by superconducting phase windings over the two loops forming the Josephson interferometer. Since these gapped states cannot be transformed to one another continuously withouth passing through a gapless condition, these are topologically $protected$. Our observation of the gapless state is pivotal for enabling phase engineering of more sophisticated artificial topological materials realizing Weyl points or the anomalous Josephson effect., Comment: 10 pages, 8 color figures

The Josephson effect is a fundamental quantum phenomenon consisting in the appearance of a dissipationless supercurrent in a weak link between two superconducting (S) electrodes. While the mechanism leading to the Josephson effect is quite general, i.e., Andreev reflections at the interface between the S electrodes and the weak link, the precise physical details and topology of the junction drastically modify the properties of the supercurrent. Specifically, a strong enhancement of the critical supercurrent $I_C$ is expected to occur when the topology of the junction allows the emergence of Majorana bound states. Here we report charge transport measurements in mesoscopic Josephson junctions formed by InAs nanowires and Ti/Al superconducting leads. Our main observation is a colossal enhancement of the critical supercurrent induced by an external magnetic field applied perpendicular to the substrate. This striking and anomalous supercurrent enhancement cannot be ascribed to any known conventional phenomenon existing in Josephson junctions including, for instance, Fraunhofer-like diffraction or a $\pi$-state behavior. We also investigate an unconventional model related to inhomogenous Zeeman field caused by magnetic focusing, and note that it can not account for the observed behaviour. Finally, we consider these results in the context of topological superconductivity, and show that the observed $I_C$ enhancement is compatible with a magnetic field-induced topological transition of the junction., Comment: 9 pages, 4 color figures

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

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 <~ 0.01~meV. This could motivate research and development programs on dedicated single-photon sub-THz detectors., Comment: 10 pages, 5 figures, comments added, 1 figure added, to appear in Phys. Dark. Univ

A niobium titanite nitride-based superconducting nanodevice in which the Josephson critical current can be modulated by a gate voltage - a Cooper-pair transistor - has proven a remarkably long parity lifetime exceeding one minute at temperatures close to absolute zero., Comment: 2 pages, 1 color figure

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 \textit{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 $\sim 10^{-17}$ 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., Comment: 5 pages, 4 color figures

We present an exhaustive theoretical analysis of charge and thermoelectric transport in a normal metal-ferromagnetic insulator-superconductor (NFIS) junction, and explore the possibility of its use as a sensitive thermometer. We investigated the transfer functions and the intrinsic noise performance for different measurement configurations. A common feature of all configurations is that the best temperature noise performance is obtained in the non-linear temperature regime for a structure based on an europium chalcogenide ferromagnetic insulator in contact with a superconducting Al film structure. For an open-circuit configuration, although the maximal intrinsic temperature sensitivity can achieve $10$nKHz$^{-1/2}$, a realistic amplifying chain will reduce the sensitivity up to $10$$\mu$KHz$^{-1/2}$. To overcome this limitation we propose a measurement scheme in a closed-circuit configuration based on state-of-art SQUID detection technology in an inductive setup. In such a case we show that temperature noise can be as low as $35$nKHz$^{-1/2}$. We also discuss a temperature-to-frequency converter where the obtained thermo-voltage developed over a Josephson junction operated in the dissipative regime is converted into a high-frequency signal. We predict that the structure can generate frequencies up to $\sim 120$GHz, and transfer functions up to $200$GHz/K at around $\sim 1$K. If operated as electron thermometer, the device may provide temperature noise lower than $35$nKHz$^{-1/2}$ thereby being potentially attractive for radiation sensing applications., Comment: 11 pages, 10 color figures

We propose the implementation of a Josephson radiation comb generator (JRCG) based on an extended Josephson junction subject to a time dependent magnetic field. The junction critical current shows known diffraction patterns and determines the position of the critical nodes when it vanishes. When the magnetic flux passes through one of such critical nodes, the superconducting phase must undergo a $\pi$-jump to minimize the Josephson energy. Correspondingly a voltage pulse is generated at the extremes of the junction. Under periodic driving this allows us to produce a comb-like voltage pulses sequence. In the frequency domain it is possible to generate up to hundreds of harmonics of the fundamental driving frequency, thus mimicking the frequency comb used in optics and metrology. We discuss several implementations through a rectangular, cylindrical and annular junction geometries, allowing us to generate different radiation spectra and to produce an output power up to $10$~pW at $50$~GHz for a driving frequency of $100$~MHz., Comment: 4+ pages, 4 color figures

We propose and analyze a mesoscopic Josephson junction consisting of two ferromagnetic insulator-superconductors (FI-Ss) coupled through a normal metal (N) layer. The Josephson current of the junction is non-trivially affected by the spin-splitting field induced by the FIs in the two superconductors. In particular, it shows sizeable enhancement by increasing the amplitude of the exchange field ($h_{ex}$) and displays a switchable current-phase relation which depends on the relative orientation of $h_{ex}$ in the FIs. In a realistic EuS/Al-based setup this junction can be exploited as a high-resolution threshold sensor for the magnetic field as well as an on-demand tunable kinetic inductor., Comment: 4.5 pages, 5 color figures

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 $ \sim 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., Comment: 6 pages, 5 color 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

We propose a phase-controlled heat-flux quantum valve based on the proximity effect driven by a superconducting quantum interference proximity transistor (SQUIPT). Its operation relies on the phase-dependent quasiparticle density of states in the Josephson weak-link of the SQUIPT which controls thermal transport across the device. In a realistic Al/Cu-based setup the structure can provide efficient control of thermal current inducing temperature swings exceeding $\sim100$~mK, and flux-to-temperature transfer coefficients up to $\sim 500$~mK/$\Phi_0$ below 100~mK. The nanovalve performances improve by lowering the bath temperature, making the proposed structure a promising building-block for the implementation of coherent caloritronic devices operating below 1~K.