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Two-dimensional magnets and superconductors are emerging as tunable building-blocks for quantum computing and superconducting spintronic devices, and have been used to fabricate all two-dimensional versions of traditional devices, such as Josephson junctions. However, novel devices enabled by unique features of two-dimensional materials have not yet been demonstrated. Here, we present NbSe 2 /CrSBr van der Waals superconducting spin valves that exhibit infinite magnetoresistance and nonreciprocal charge transport. These responses arise from a unique metamagnetic transition in CrSBr, which controls the presence of localized stray fields suitably oriented to suppress the NbSe 2 superconductivity in nanoscale regions and to break time reversal symmetry. Moreover, by integrating different CrSBr crystals in a lateral heterostructure, we demonstrate a superconductive spin valve characterized by multiple stable resistance states. Our results show how the unique physical properties of layered materials enable the realization of high-performance quantum devices based on novel working principles., (© 2023. The Author(s).)

The macroscopic coherence in superconductors supports dissipationless supercurrents that could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions would enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called the superconducting (SC) diode effect. We demonstrate the strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish the nonvolatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge and surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens the door for novel technologies while revealing the ubiquity of the Meissner screening effect induced SC diode effect in superconducting films, and it should be eliminated with great care in the search for exotic superconducting states harboring finite-momentum Cooper pairing.

Breaking a correlated pair in a superconductor requires an even number of fermions providing at least twice the pairing energy Δ. Here, we show that a single tunneling electron can also excite a pair breaking excitation in a proximitized gold film in the presence of magnetic impurities. Combining scanning tunneling spectroscopy with theoretical modeling, we map the excitation spectrum of an Fe-porphyrin molecule on the Au/V(100) proximitized surface into a manifold of entangled Yu-Shiba-Rusinov and spin excitations. Pair excitations emerge in the tunneling spectra as peaks outside the spectral gap only in the strong coupling regime, where the presence of a bound quasiparticle in the ground state ensures the even fermion parity of the excitation. Our results unravel the quantum nature of magnetic impurities on superconductors and demonstrate that pair excitations unequivocally reveal the parity of the ground state.

Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ0 (where ϕ0=h/2e) as a fundamental period. If CPs' splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ0.

Diodes are key elements for electronics, optics, and detection. Their evolution towards low dissipation electronics has seen the hybridization with superconductors and the realization of supercurrent diodes with zero resistance in only one direction. Here, we present the quasi-particle counterpart, a superconducting tunnel diode with zero conductance in only one direction. The direction-selective propagation of the charge has been obtained through the broken electron-hole symmetry induced by the spin selection of the ferromagnetic tunnel barrier: a EuS thin film separating a superconducting Al and a normal metal Cu layer. The Cu/EuS/Al tunnel junction achieves a large rectification (up to ∼40%) already for a small voltage bias (∼200 μV) 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 (P) of the barrier and describe the quasi-ideal Shockley-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., (© 2022. The Author(s).)

We calculate the nonreciprocal critical current and quantify the supercurrent diode effect in two-dimensional Rashba superconductors with arbitrary disorder, using the quasiclassical Eilenberger equation. The nonreciprocity is caused by the helical superconducting state, which appears when both inversion and time-reversal symmetries are broken. In the absence of disorder, we find a very strong diode effect, with the nonreciprocity exceeding 40% at optimal temperatures, magnetic fields, and spin-orbit coupling. We establish that the effect persists even in the presence of strong disorder. We show that the sign of the diode effect changes as magnetic field and disorder are increased, reflecting the changes in the nature of the helical state.

A conventional superconductor sandwiched between two ferromagnets can maintain coherent equilibrium spin current. This spin supercurrent results from the rotation of odd-frequency spin correlations induced in the superconductor by the magnetic proximity effect. In the absence of intrinsic magnetization, the superconductor cannot maintain multiple rotations of the triplet component but instead provides a Josephson type weak link for the spin supercurrent. We determine the analog of the current-phase relation in various circumstances and show how it can be accessed in experiments on dynamic magnetization. In particular, concentrating on the magnetic hysteresis and the ferromagnetic resonance response, we show how the spin supercurrent affects the nonequilibrium dynamics of magnetization which depends on a competition between spin supercurrent mediated static exchange contribution and a dynamic spin pumping contribution. Depending on the outcome of this competition, a mode crossing in the system can either be an avoided crossing or mode locking.

Spin-dependent transport at heavy metal/magnetic insulator interfaces is at the origin of many phenomena at the forefront of spintronics research. A proper quantification of the different interfacial spin conductances is crucial for many applications. Here, we report the first measurement of the spin Hall magnetoresistance (SMR) of Pt on a purely ferromagnetic insulator (EuS). We perform SMR measurements in a wide range of temperatures and fit the results by using a microscopic model. From this fitting procedure, we obtain the temperature dependence of the spin conductances ( G s , G r , and G i ), disentangling the contribution of field-like torque ( G i ), damping-like torque ( G r ), and spin-flip scattering ( G s ). An interfacial exchange field of the order of 1 meV acting upon the conduction electrons of Pt can be estimated from G i , which is at least three times larger than G r below the Curie temperature. Our work provides an easy method to quantify this interfacial spin-splitting field, which plays a key role in emerging fields such as superconducting spintronics and caloritronics as well as topological quantum computation.

Recent experiments have shown that proximity with high-temperature superconductors induces unconventional superconducting correlations in graphene. Here, we demonstrate that those correlations propagate hundreds of nanometers, allowing for the unique observation of d-wave Andreev-pair interferences in YBa_{2}Cu_{3}O_{7}-graphene devices that behave as a Fabry-Perot cavity. The interferences show as a series of pronounced conductance oscillations analogous to those originally predicted by de Gennes-Saint-James for conventional metal-superconductor junctions. The present demonstration is pivotal to the study of exotic directional effects expected for nodal superconductivity in Dirac materials.

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 φ 0 across the wire, leading to the anomalous Josephson effect 1,2 . We apply an external in-plane magnetic field and, thereby, achieve continuous tuning of φ 0 . 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.

We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the spin-spin correlation functions of the local moments on the surface of the magnetic insulator. The magnetic-field and temperature dependence of the spin mixing conductances leads to a rich behavior of the resistance due to an interplay between the Hanle effect and the spin mixing at the interface. We describe an unusual negative magnetoresistance originating from a nonlocal Hanle effect. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it enables the spin Hall magnetoresistance effect to be used as a technique to study magnetism at interfaces.

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.

We investigate the transport properties of a junction consisting of an electron-hole bilayer in contact with normal and superconducting leads. The electron-hole bilayer is considered as a semimetal with two electronic bands. We assume that in the region between the contacts the system hosts an exciton condensate described by a BCS-like model with a gap Γ in the quasiparticle density of states. We first discuss how the subgap electronic transport through the junction is mainly governed by the interplay between two kinds of reflection processes at the interfaces: the standard Andreev reflection at the interface between the superconductor and the exciton condensate, and a coherent crossed reflection at the semimetal-exciton-condensate interface that converts electrons from one layer into the other. We show that the differential conductance of the junction shows a minimum at voltages of the order of Γ/e. Such a minimum can be seen as a direct hallmark of the existence of the gapped excitonic state.

The Josephson effect is a fundamental quantum phenomenon where a dissipationless supercurrent is introduced in a weak link between two superconducting electrodes by Andreev reflections. The physical details and topology of the junction drastically modify the properties of the supercurrent and a strong enhancement of the critical supercurrent is expected to occur when the topology of the junction allows an 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 described by any known conventional phenomenon of Josephson junctions. We consider these results in the context of topological superconductivity, and show that the observed critical supercurrent enhancement is compatible with a magnetic field-induced topological transition.

Multi-terminal superconducting Josephson junctions based on the proximity effect offer the opportunity to tailor non-trivial quantum states in nanoscale weak links. These structures can realize exotic topologies in several dimensions, for example, artificial topological superconductors that are able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here we report the realization of a three-terminal Josephson interferometer based on a proximized nanosized weak link. Our tunnelling spectroscopy measurements reveal transitions between gapped (that is, insulating) and gapless (conducting) states that are 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 indices, in much the same way that the interface between two insulators of different topologies is necessarily conducting. The topological numbers that characterize such gapped states are given by superconducting phase windings over the two loops that form the Josephson interferometer. As these gapped states cannot be transformed to one another continuously without passing through a gapless condition, they are topologically protected. The same behaviour is found for all of the points of the weak link, confirming that this topology is a non-local property. Our observation of the gapless state is pivotal for enabling phase engineering of different and more sophisticated artificial topological materials.

A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position-particle-hole-spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials.

We report measurements of a new type of magnetoresistance in Pt and Ta thin films. The spin accumulation created at the surfaces of the film by the spin Hall effect decreases in a magnetic field because of the Hanle effect, resulting in an increase of the electrical resistance as predicted by Dyakonov [Phys. Rev. Lett. 99, 126601 (2007)]. The angular dependence of this magnetoresistance resembles the recently discovered spin Hall magnetoresistance in Pt/Y(3)Fe(5)O(12) bilayers, although the presence of a ferromagnetic insulator is not required. We show that this Hanle magnetoresistance is an alternative simple way to quantitatively study the coupling between charge and spin currents in metals with strong spin-orbit coupling.

We describe far-from-equilibrium nonlocal transport in a diffusive superconducting wire with a Zeeman splitting, taking into account different spin relaxation mechanisms. We demonstrate that due to the Zeeman splitting, an injection of current in a superconducting wire creates spin accumulation that can only relax via thermalization. This effect leads to a long-range spin accumulation detectable in the nonlocal signal. Our model gives a qualitative explanation and provides accurate fits of recent experimental results in terms of realistic parameters.

We have studied mesoscopic Josephson junctions formed by highly n-doped InAs nanowires and superconducting Ti/Pb source and drain leads. The current-voltage properties of the system are investigated by varying temperature and external out-of-plane magnetic field. Superconductivity in the Pb electrodes persists up to ∼7 K and with magnetic field values up to 0.4 T. Josephson coupling at zero backgate voltage is observed up to 4.5 K and the critical current is measured to be as high as 615 nA. The supercurrent suppression as a function of the magnetic field reveals a diffraction pattern that is explained by a strong magnetic flux focusing provided by the superconducting electrodes forming the junction.

The concept of thermophase refers to the appearance of a phase gradient inside a superconductor originating from the presence of an applied temperature bias across it. The resulting supercurrent flow may, in suitable conditions, fully counterbalance the temperature-bias-induced quasiparticle current therefore preventing the formation of any voltage drop, i.e., a thermovoltage, across the superconductor. Yet, the appearance of a thermophase is expected to occur in Josephson-coupled superconductors as well. Here, we theoretically investigate the thermoelectric response of a thermally biased Josephson junction based on a ferromagnetic insulator. In particular, we predict the occurrence of a very large thermophase that can reach π/2 across the contact for suitable temperatures and structure parameters; i.e., the quasiparticle thermal current can reach the critical current. Such a thermophase can be several orders of magnitude larger than that predicted to occur in conventional Josephson tunnel junctions. In order to assess experimentally the predicted very large thermophase, we propose a realistic setup realizable with state-of-the-art nanofabrication techniques and well-established materials, based on a superconducting quantum interference device. This effect could be of strong relevance in several low-temperature applications, for example, for revealing tiny temperature differences generated by coupling the electromagnetic radiation to one of the superconductors forming the junction.

We show that a huge thermoelectric effect can be observed by contacting a superconductor whose density of states is spin split by a Zeeman field with a ferromagnet with a nonzero polarization. The resulting thermopower exceeds kB/e by a large factor, and the thermoelectric figure of merit ZT can far exceed unity, leading to heat engine efficiencies close to the Carnot limit. We also show that spin-polarized currents can be generated in the superconductor by applying a temperature bias.

Spin selectivity in a ferromagnet results from a difference in the density of up- and down-spin electrons at the Fermi energy as a consequence of which the scattering rates depend on the spin orientation of the electrons. This property is utilized in spintronics to control the flow of electrons by ferromagnets in a ferromagnet (F1)/normal metal (N)/ferromagnet (F2) spin valve, where F1 acts as the polarizer and F2 the analyser. The feasibility of superconducting spintronics depends on the spin sensitivity of ferromagnets to the spin of the equal spin-triplet Cooper pairs, which arise in superconductor (S)-ferromagnet (F) heterostructures with magnetic inhomogeneity at the S-F interface. Here we report a critical temperature dependence on magnetic configuration in current-in-plane F-S-F spin valves with a holmium spin mixer at the S-F interface providing evidence of a spin selectivity of the ferromagnets to the spin of the triplet Cooper pairs.

Magnetization noncollinearity in ferromagnet-superconductor (F/S) heterostructures is expected to enhance the superconducting transition temperature (T(c)) according to the domain-wall superconductivity theory, or to suppress T(c) when spin-triplet Cooper pairs are explicitly considered. We study the proximity effect in F/S structures where the F layer is a Sm-Co/Py exchange-spring bilayer and the S layer is Nb. The exchange-spring contains a single, controllable and quantifiable domain wall in the Py layer. We observe an enhancement of superconductivity that is nonmonotonic as the Py domain wall is increasingly twisted via rotating a magnetic field, different from theoretical predictions. We have excluded magnetic fields and vortex motion as the source of the nonmonotonic behavior. This unanticipated proximity behavior suggests that new physics is yet to be captured in the theoretical treatments of F/S systems containing noncollinear magnetization.

The proximity effect between a superconductor and a highly diffusive two-dimensional metal is revealed in a scanning tunneling spectroscopy experiment. The in situ elaborated samples consist of superconducting single crystalline Pb islands interconnected by a nonsuperconducting atomically thin disordered Pb wetting layer. In the vicinity of each superconducting island the wetting layer acquires specific tunneling characteristics which reflect the interplay between the proximity-induced superconductivity and the inherent electron correlations of this ultimate diffusive two-dimensional metal. The observed spatial evolution of the tunneling spectra is accounted for theoretically by combining the Usadel equations with the theory of dynamical Coulomb blockade; the relevant length and energy scales are extracted and found in agreement with available experimental data.

The long-range proximity effect in superconductor-ferromagnet (S/F) hybrid nanostructures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the ferromagnet over large distances. It is commonly believed that this happens only in the presence of magnetic inhomogeneities. We show that there are other sources of the long-range triplet component (LRTC) of the condensate and establish general conditions for their occurrence. As a prototypical example, we consider first a system where the exchange field and spin-orbit coupling can be treated as time and space components of an effective SU(2) potential. We derive a SU(2) covariant diffusive equation for the condensate and demonstrate that an effective SU(2) electric field is responsible for the long-range proximity effect. Finally, we extend our analysis to a generic ferromagnet and establish a universal condition for the LRTC. Our results open a new avenue in the search for such correlations in S/F structures and make a hitherto unknown connection between the LRTC and Yang-Mills electrostatics.

We present a microscopic theory of the effect of a microwave field on the supercurrent through a quantum point contact of arbitrary transmission. Our theory predicts that (i) for low temperatures and weak fields, the supercurrent is suppressed at certain values of the superconducting phase, (ii) at strong fields, the current-phase relation is strongly modified and the current can even reverse its sign, and (iii) at finite temperatures, the microwave field can enhance the critical current of the junction. Apart from their fundamental interest, our findings are also important for the description of experiments that aim at the manipulation of the quantum state of atomic point contacts.

The observation of very large microwave-enhanced critical currents in superconductor-normal-metal-superconductor (SNS) junctions at temperatures well below the critical temperature of the electrodes has remained without a satisfactory theoretical explanation for more than three decades. Here we present a theory of the supercurrent in diffusive SNS junctions under microwave irradiation based on the quasiclassical Green's function formalism. We show that the enhancement of the critical current is due to the energy redistribution of the quasiparticles in the normal wire induced by the electromagnetic field. The theory provides predictions across a wide range of temperatures, frequencies, and radiation powers, both for the critical current and the current-phase relationship.

We study theoretically the electronic and transport properties of a diffusive superconductor-normal metal-superconductor junction in the presence of a perpendicular magnetic field. We show that the field dependence of the critical current crosses over from the well-known Fraunhofer pattern in wide junctions to a monotonic decay when the width of the normal wire is smaller than the magnetic length xi(H)=square root Phi(0)/H, where H is the magnetic field and Phi(0) the flux quantum. We demonstrate that this behavior is a direct consequence of the magnetic vortex structure appearing in the normal region and predict how this structure is manifested in the local density of states.

We demonstrate that in multilayered superconductor-ferromagnet structures a noncollinear alignment of the magnetizations of different ferromagnetic layers generates a triplet superconducting condensate which is odd in frequency. This triplet condensate coexists in the superconductors with the conventional singlet one but decays very slowly in the ferromagnet, which should lead to a large Josephson effect between the superconductors separated by the ferromagnet. Depending on the mutual direction of the ferromagnetic moments, the Josephson coupling can be both of 0 and of pi type.

We analyze the proximity effect in a superconductor/ferromagnet (S/F) structure with a local inhomogeneity of the magnetization in the ferromagnet near the S/F interface. We demonstrate that not only the singlet but also the triplet component of the superconducting condensate is induced in the ferromagnet due to the proximity effect. The singlet component penetrates into the ferromagnet over a short length xi(h) = sqrt[D/h] ( h is the exchange field and D the diffusion coefficient), whereas the triplet component penetrates over a long length sqrt[D/epsilon] and leads to a significant increase of the ferromagnet conductance below the superconducting critical temperature Tc.

We calculate the dc Josephson current for two superconductor/ferromagnet (S/F) bilayers separated by a thin insulating film. It is demonstrated that the critical Josephson current I(c) in the junction strongly depends on the relative orientation of the effective exchange field h of the bilayers. We found that in the case of an antiparallel orientation I(c) increases at low temperatures with increasing h and at zero temperature has a singularity when h equals the superconducting gap Delta. This striking behavior contrasts with the suppression of the critical current by the magnetic moments aligned in parallel and is an interesting new effect of the interplay between superconductors and ferromagnets.