Superconducting spintronic heat engine.

Heat engines are key devices that convert thermal energy into usable energy. Strong thermoelectricity, at the basis of electrical heat engines, is present in superconducting spin tunnel barriers at cryogenic temperatures where conventional semiconducting or metallic technologies cease to work. Here we realize a superconducting spintronic heat engine consisting of a ferromagnetic insulator/superconductor/insulator/ferromagnet tunnel junction (EuS/Al/AlOx/Co). The efficiency of the engine is quantified for bath temperatures ranging from 25 mK up to 800 mK, and at different load resistances. Moreover, we show that the sign of the generated thermoelectric voltage can be inverted according to the parallel or anti-parallel orientation of the two ferromagnetic layers, EuS and Co. This realizes a thermoelectric spin valve controlling the sign and strength of the Seebeck coefficient, thereby implementing a thermoelectric memory cell. We propose a theoretical model that allows describing the experimental data and predicts the engine efficiency for different device parameters.

Josephson Diode Effect in High-Mobility InSb Nanoflags.

We report nonreciprocal dissipation-less transport in single ballistic InSb nanoflag Josephson junctions. Applying an in-plane magnetic field, we observe an inequality in supercurrent for the two opposite current propagation directions. Thus, 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 external field, and then it saturates as the Zeeman energy becomes relevant, before it finally decreases to zero at higher fields. 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 supercurrent asymmetry, 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.

Bipolar thermoelectric Josephson engine.

Thermoelectric effects in metals are typically small due to the nearly perfect particle-hole symmetry around their Fermi surface. Furthermore, thermo-phase effects and linear thermoelectricity in superconducting systems have been identified only when particle-hole symmetry is explicitly broken, since thermoelectric effects were considered impossible in pristine superconductors. Here, we experimentally demonstrate that superconducting tunnel junctions develop a very large bipolar thermoelectricity in the presence of a sizable thermal gradient thanks to spontaneous particle-hole symmetry breaking. Our junctions show Seebeck coefficients of up to ±300 µV K-1, which is comparable with quantum dots and roughly 105 times larger than the value expected for normal metals at subkelvin temperatures. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine generating phase-tunable electric powers of up to ~140 nW mm-2. Notably, our device implements also the prototype for a persistent thermoelectric memory cell, written or erased by current injection. We expect that our findings will lead to applications in superconducting quantum technologies.

Colossal Orbital Edelstein Effect in Noncentrosymmetric Superconductors.

In superconductors that lack inversion symmetry, the flow of supercurrent can induce a nonvanishing magnetization, a phenomenon which is at the heart of nondissipative magnetoelectric effects, also known as Edelstein effects. For electrons carrying spin and orbital moments, a question of fundamental relevance deals with the orbital nature of magnetoelectric effects in conventional spin-singlet superconductors with Rashba coupling. Remarkably, we find that the supercurrent-induced orbital magnetization is more than 1 order of magnitude greater than that due to the spin, giving rise to a colossal magnetoelectric 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. In the presence of superconducting phase inhomogeneities, a modulation of the Edelstein signal on the scale of the superconducting coherence length appears, leading to domains with opposite orbital moment orientations. These hallmarks are robust to real-space self-consistent treatment of the superconducting order parameter. The orbital-dominated magnetoelectric 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 multiorbital superconductors with inversion symmetry breaking.

Evidence of Josephson Coupling in a Few-Layer Black Phosphorus Planar Josephson Junction.

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 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 a Fraunhofer pattern with a transverse magnetic field is also reported, confirming the Josephson coupling. These findings represent evidence of proximity Josephson coupling in a planar junction based on a van der Waals material beyond graphene and will expedite further studies, exploiting the peculiar properties of exfoliated black phosphorus thin flakes.

Electrostatic Field-Driven Supercurrent Suppression in Ionic-Gated Metallic Superconducting Nanotransistors.

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 ∼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.

Preliminary demonstration of a persistent Josephson phase-slip memory cell with topological protection.

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.

Gate Control of Superconductivity in Mesoscopic All-Metallic Devices.

The possibility to tune, through the application of a control gate voltage, the superconducting properties of mesoscopic devices based on Bardeen-Cooper-Schrieffer metals was recently demonstrated. Despite the extensive experimental evidence obtained on different materials and geometries, a description of the microscopic mechanism at the basis of such an 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: first, 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 a half-wave rectifier. Second, we discuss the origin of the gating effect by showing 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 employing finite element simulations and compare the results with experimental data. In our view, the presented data provide a strong indication regarding the unlikelihood of the thermal origin of the gating effect.

Gate Control of the Current-Flux Relation of a Josephson Quantum Interferometer Based on Proximitized Metallic Nanojuntions.

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.

Proximitized Josephson junctions in highly-doped InAs nanowires robust to optical illumination.

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.

Gate-Controlled Suspended Titanium Nanobridge Supercurrent Transistor.

Under standard conditions, the electrostatic field-effect is negligible in conventional metals and was expected to be completely ineffective also in superconducting metals. This common belief was recently put under question by a family of experiments that displayed full gate-voltage-induced suppression of critical current in superconducting all-metallic gated nanotransistors. To date, the microscopic origin of this phenomenon is under debate, and trivial explanations based on heating effects given by the negligible electron leakage from the gates should be excluded. Here, we demonstrate the control of the supercurrent in fully suspended superconducting nanobridges. Our advanced nanofabrication methods allow us to build suspended superconducting Ti-based supercurrent transistors which show ambipolar and monotonic full suppression of the critical current for gate voltages of VGC ≃ 18 V and for temperatures up to ∼80% of the critical temperature. The suspended device architecture minimizes the electron-phonon interaction between the superconducting nanobridge and the substrate, and therefore, it rules out any possible contribution stemming from charge injection into the insulating substrate. Besides, our finite element method simulations of vacuum electron tunneling from the gate to the bridge and thermal considerations rule out the cold-electron field emission as a possible driving mechanism for the observed phenomenology. Our findings promise a better understanding of the field effect in superconducting metals.

A Josephson phase battery.

A classical battery converts chemical energy into a persistent voltage bias that can power electronic circuits. Similarly, a phase battery is a quantum device that provides a persistent phase bias to the wave function of a quantum circuit. It represents a key element for quantum technologies based on phase coherence. Here we demonstrate a phase battery in a hybrid superconducting circuit. It consists of an n-doped InAs nanowire with unpaired-spin surface states, that is proximitized by Al superconducting leads. We find that the ferromagnetic polarization of the unpaired-spin states is efficiently converted into a persistent phase bias φ0 across the wire, leading to the anomalous Josephson effect1,2. We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ0. Hence, we can charge and discharge the quantum phase battery. The observed symmetries of the anomalous Josephson effect in the vectorial magnetic field are in agreement with our theoretical model. Our results demonstrate how the combined action of spin-orbit coupling and exchange interaction induces a strong coupling between charge, spin and superconducting phase, able to break the phase rigidity of the system.

Field-Effect Controllable Metallic Josephson Interferometer.

Gate-tunable Josephson junctions (JJs) are the backbone of superconducting classical and quantum computation. Typically, these systems exploit low-charge-concentration materials and present technological difficulties limiting their scalability. Surprisingly, electric field modulation of a supercurrent in metallic wires and JJs has been recently demonstrated. Here, we report the realization of titanium-based monolithic interferometers which allow tuning both JJs independently via voltage bias applied to capacitively coupled electrodes. Our experiments demonstrate full control of the amplitude of the switching current (Is) and of the superconducting phase across the single JJ in a wide range of temperatures. Astoundingly, by gate-biasing a single junction, the maximum achievable total Is is suppressed down to values much lower than the critical current of a single JJ. A theoretical model including gate-induced phase fluctuations on a single junction accounts for our experimental findings. This class of quantum interferometers could represent a breakthrough for several applications such as digital electronics, quantum computing, sensitive magnetometry, and single-photon detection.

Josephson Field-Effect Transistors Based on All-Metallic Al/Cu/Al Proximity Nanojunctions.

We demonstrate proximity-based all-metallic mesoscopic superconductor-normal metal-superconductor (SNS) field-effect controlled Josephson transistors (SNS-FETs) and show their full characterization from the critical temperature Tc down to 50 mK in the presence of both electric and magnetic fields. The ability of a static electric field-applied by means of a lateral gate electrode-to suppress the critical current Is in a proximity-induced superconductor is proven for both positive and negative gate voltage values. Is reached typically about one-third of its initial value, saturating at high gate voltages. The transconductance of our SNS-FETs obtains values as high as 100 nA/V at 100 mK. On the fundamental physics side, our results suggest that the mechanism at the basis of the observed phenomenon is quite general and does not rely on the existence of a true pairing potential, but rather the presence of superconducting correlations is enough for the effect to occur. On the technological side, our findings widen the family of materials available for the implementation of all-metallic field-effect transistors to synthetic proximity-induced superconductors.

Thermodynamic cycles in Josephson junctions.

A superconductor/normal metal/superconductor Josephson junction is a coherent electron system where the thermodynamic entropy depends on temperature and difference of phase across the weak-link. Here, exploiting the phase-temperature thermodynamic diagram of a thermally isolated system, we argue that a cooling effect can be achieved when the phase drop across the junction is brought from 0 to π in a iso-entropic process. We show that iso-entropic cooling can be enhanced with proper choice of geometrical and electrical parameters of the junction, i.e. by increasing the ratio between supercurrent and total junction volume. We present extensive numerical calculations using quasi-classical Green function methods for a short junction and we compare them with analytical results. Interestingly, we demonstrate that phase-coherent thermodynamic cycles can be implemented by combining iso-entropic and iso-phasic processes acting on the weak-link, thereby engineering the coherent version of thermal machines such as engines and cooling systems. We therefore evaluate their performances and the minimum temperature achievable in a cooling cycle.

Toward the Absolute Spin-Valve Effect in Superconducting Tunnel Junctions.

A superconductor with a spin-split excitation spectrum behaves as an ideal ferromagnetic spin-injector in a tunneling junction. It was theoretically 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 current through the junction. Our device may be pivotal for realization of thermoelectric radiation detectors, a logical element for a memory cell in cryogenics, superconductor-based computers, and superconducting spintronics in general.

Phase-coherent solitonic Josephson heat oscillator.

Since its recent foundation, phase-coherent caloritronics has sparkled continuous interest giving rise to numerous concrete applications. This research field deals with the coherent manipulation of heat currents in mesoscopic superconducting devices by mastering the Josephson phase difference. Here, we introduce a new generation of devices for fast caloritronics able to control local heat power and temperature through manipulation of Josephson vortices, i.e., solitons. Although most salient features concerning Josephson vortices in long Josephson junctions were comprehensively hitherto explored, little is known about soliton-sustained coherent thermal transport. We demonstrate that the soliton configuration determines the temperature profile in the junction, so that, in correspondence of each magnetically induced soliton, both the flowing thermal power and the temperature significantly enhance. Finally, we thoroughly discuss a fast solitonic Josephson heat oscillator, whose frequency is in tune with the oscillation frequency of the magnetic drive. Notably, the proposed heat oscillator can effectively find application as a tunable thermal source for nanoscale heat engines and coherent thermal machines.

Metallic supercurrent field-effect transistor.

In their original formulation of superconductivity, the London brothers predicted1 the exponential suppression of an electrostatic field inside a superconductor over the so-called London penetration depth2-4, λL. Despite a few experiments indicating hints of perturbation induced by electrostatic fields5-7, no clue has been provided so far on the possibility to manipulate metallic superconductors via the field effect. Here, we report field-effect control of the supercurrent in all-metallic transistors made of different Bardeen-Cooper-Schrieffer superconducting thin films. At low temperature, our field-effect transistors show a monotonic decay of the critical current under increasing electrostatic field up to total quenching for gate voltage values as large as ±40 V in titanium-based devices. This bipolar field effect persists up to ~85% of the critical temperature (~0.41 K), and in the presence of sizable magnetic fields. A similar behaviour is observed in aluminium thin-film field-effect transistors. 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 all-metallic superconducting field-effect electronics and leading-edge quantum information architectures8,9.

Ultra-Efficient Superconducting Dayem Bridge Field-Effect Transistor.

Superconducting field-effect transitor (SuFET) and Josephson field-effect transistor (JoFET) technologies take advantage of electric-field-induced control of charge-carrier concentration to modulate the channel superconducting properties. Despite the fact that the field-effect is believed to be ineffective for superconducting metals, recent experiments showed electric-field-dependent modulation of the critical current ( IC) in a fully metallic transistor. However, the grounding mechanism of this phenomenon is not completely understood. Here, we show the experimental realization of Ti-based Dayem bridge field-effect transistors (DB-FETs) able to control the IC of the superconducting channel. Our easy fabrication process for DB-FETs show symmetric full suppression of IC for applied critical gate voltages as low as VGC ≃ ±8 V at temperatures reaching about the 85% of the record critical temperature, TC ≃ 550 mK, for titanium. The gate-independent TC and normal-state resistance ( RN) coupled with the increase of resistance in the superconducting state ( RS) for gate voltages close to the critical value ( VGC) suggest the creation of field-effect induced metallic puddles in the superconducting sea. Our devices show extremely high values of transconductance (| gmMAX| ≃ 15 µA/V at VG ≃ ±6.5 V) and variations of Josephson kinetic inductance ( LK) with VG of 2 orders of magnitude. Therefore, the DB-FET appears as an ideal candidate for the realization of superconducting electronics, superconducting qubits, and tunable interferometers as well as photon detectors.

Phase-Tunable Josephson Thermal Router.

A fundamental aspect of electronics is the ability to distribute a charge current among different terminals. On the other hand, despite the great interest in dissipation, storage, and conversion of heat in solid state structures, the control of thermal currents at the nanoscale is still in its infancy. Here, we show the experimental realization of a phase-tunable thermal router able to control the spatial distribution of an incoming heat current, thus providing the possibility of tuning the electronic temperatures of two output terminals. This ability is obtained thanks to a direct current superconducting quantum interference device (dc SQUID), which can tune the coherent component of the electronic heat currents flowing through its Josephson junctions. By varying the external magnetic flux and the bath temperature, the SQUID allows us to regulate the size and the direction of the thermal gradient between two drain electrodes. Our results offer new opportunities for all microcircuits requiring an accurate energy management, including electronic coolers, quantum information architectures, and thermal logic components.