Nonlocal thermoelectric effects and nonlocal Onsager relations in a three-terminal proximity-coupled superconductor-ferromagnet device

Observation of Magnetic State Dependent Thermoelectricity in Superconducting Spin Valves

Superconductor-ferromagnet tunnel junctions demonstrate giant thermoelectric effects that are being exploited to engineer ultrasensitive terahertz radiation detectors. Here, we experimentally observe the recently predicted complete magnetic control over thermoelectric effects in a superconducting spin valve, including the dependence of its sign on the magnetic state of the spin valve. The description of the experimental results is improved by the introduction of an interfacial domain wall in the spin filter layer interfacing the superconductor. Surprisingly, the application of high in-plane magnetic fields induces a double sign inversion of the thermoelectric effect, which exhibits large values even at applied fields twice the superconducting critical field.

Spin Seebeck effect mediated reversal of vortex-Nernst effect in superconductor-ferromagnet bilayers

We report on the observation of sign reversal of vortex-Nernst effect in epitaxial NbN/Fe bilayers deposited on MgO (001) substrates. Strong coupling between vortex magnetisation and ferromagnetic magnetisation at the NbN/Fe bilayer interface is presented. In NbN/Fe bilayer thin films an apparent sign reversal of vortex-Nernst signal under a temperature gradient with magnetic field and temperature is observed when the thickness of Fe is increased up to 5 nm. This reversal of the vortex-Nernst effect is associated with the enhancement of the spin Seebeck effects (SSE) near T_c due to coherence peak effect (CPE) and strong coupling of vortex magnetisation and ferromagnetic magnetisation at the interface of the NbN/Fe bilayer. The observed large SSE via inverse spin Hall effect (ISHE) is due to the CPE below and close to T_C, highlighting the high spin to charge conversion efficiency of NbN in this region. This work may contribute to the development of superconducting spintronic devices by engineering the coupling of the superconductor/ferromagnet interface.

Density of states in the presence of spin-dependent scattering in SF bilayers: a numerical and analytical approach

We present a quantitative study of the density of states (DOS) in SF bilayers (where S is a bulk superconductor and F is a ferromagnetic metal) in the diffusive limit. We solve the quasiclassical Usadel equations in the structure considering the presence of magnetic and spin-orbit scattering. For practical reasons, we propose the analytical solution for the density of states in SF bilayers in the case of a thin ferromagnet and low transparency of the SF interface. This solution is confirmed by numerical calculations using a self-consistent two-step iterative method. The behavior of DOS dependencies on magnetic and spin-orbit scattering times is discussed.

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.

Experimental and theoretical study of field-dependent spin splitting at ferromagnetic insulator-superconductor interfaces

We present a combined experimental and theoretical work that investigates the magnetic proximity effect at a ferromagnetic insulator-superconductor (FI-S) interface. The calculations are based on the boundary condition for diffusive quasiclassical Green's functions, which accounts for arbitrarily strong spin-dependent effects and spin mixing angles. The resulting phase diagram shows a transition from a first-order to a second-order phase transition for large spin mixing angles. The experimentally found differential conductance of an EuS-Al heterostructure is compared with the theoretical calculation. With the assumption of a uniform spin mixing angle that depends on the externally applied field, we find good agreement between theory and experiment. The theory depends only on very few parameters, mostly specified by the experimental setup. We determine the effective spin of the interface moments as J ≈ 0.74ℏ.

Superconducting spintronic tunnel diode

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.

Role of Two-Dimensional Ising Superconductivity in the Nonequilibrium Quasiparticle Spin-to-Charge Conversion Efficiency

Nonequilibrium studies of two-dimensional (2D) superconductors (SCs) with Ising spin-orbit coupling are prerequisite for their successful application to equilibrium spin-triplet Cooper pairs and, potentially, Majorana Fermions. By taking advantage of the recent discoveries of 2D SCs and their compatibility with any other materials, we fabricate here nonlocal magnon devices to examine how such 2D Ising superconductivity affects the conversion efficiency of magnon spin to quasiparticle charge in superconducting flakes of 2H-NbSe₂ transferred onto ferrimagnetic insulating Y₃Fe₅O₁₂. Comparison with a reference device based on a conventionally paired superconductor shows that the Y₃Fe₅O₁₂-induced in-plane (IP) exchange spin-splitting in the NbSe₂ flake is hindered by its inherent out-of-plane (OOP) spin-orbit field, which, in turn, limits the transition-state enhancement of the spin-to-charge conversion efficiency. Our out-of-equilibrium study highlights the significance of symmetry matching between underlying Cooper pairs and exchange-induced spin-splitting for the giant transition-state spin-to-charge conversion and may have implications toward proximity-engineered spin-polarized triplet pairing via tuning the relative strength of IP exchange and OOP spin-orbit fields in ferromagnetic insulator/2D Ising SC bilayers.

Thermoelectric current in a graphene Cooper pair splitter

Generation of electric voltage in a conductor by applying a temperature gradient is a fundamental phenomenon called the Seebeck effect. This effect and its inverse is widely exploited in diverse applications ranging from thermoelectric power generators to temperature sensing. Recently, a possibility of thermoelectricity arising from the interplay of the non-local Cooper pair splitting and the elastic co-tunneling in the hybrid normal metal-superconductor-normal metal structures was predicted. Here, we report the observation of the non-local Seebeck effect in a graphene-based Cooper pair splitting device comprising two quantum dots connected to an aluminum superconductor and present a theoretical description of this phenomenon. The observed non-local Seebeck effect offers an efficient tool for producing entangled electrons.

Thermoelectricity due to the interplay of the nonlocal Cooper pair splitting and the elastic co-tunneling in normal metal-superconductor-normal metal structure is predicted. Here, the authors observe the non-local Seebeck effect in a graphene-based Cooper pair splitting device.

Giant Transition-State Quasiparticle Spin-Hall Effect in an Exchange-Spin-Split Superconductor Detected by Nonlocal Magnon Spin Transport

Although recent experiments and theories have shown a variety of exotic transport properties of nonequilibrium quasiparticles (QPs) in superconductor (SC)-based devices with either Zeeman or exchange spin-splitting, how a QP interplays with magnon spin currents remains elusive. Here, using nonlocal magnon spin-transport devices where a singlet SC (Nb) on top of a ferrimagnetic insulator (Y₃Fe₅O₁₂) serves as a magnon spin detector, we demonstrate that the conversion efficiency of magnon spin to QP charge via inverse spin-Hall effect (iSHE) in such an exchange-spin-split SC can be greatly enhanced by up to 3 orders of magnitude compared with that in the normal state, particularly when its interface superconducting gap matches the magnon spin accumulation. Through systematic measurements by varying the current density and SC thickness, we identify that superconducting coherence peaks and exchange spin-splitting of the QP density-of-states, yielding a larger spin excitation while retaining a modest QP charge-imbalance relaxation, are responsible for the giant QP iSHE. The latter exchange-field-modified QP relaxation is experimentally proved by spatially resolved measurements with varying the separation of electrical contacts on the spin-split Nb.

Writing 3D Nanomagnets Using Focused Electron Beams

Focused electron beam induced deposition (FEBID) is a direct-write nanofabrication technique able to pattern three-dimensional magnetic nanostructures at resolutions comparable to the characteristic magnetic length scales. FEBID is thus a powerful tool for 3D nanomagnetism which enables unique fundamental studies involving complex 3D geometries, as well as nano-prototyping and specialized applications compatible with low throughputs. In this focused review, we discuss recent developments of this technique for applications in 3D nanomagnetism, namely the substantial progress on FEBID computational methods, and new routes followed to tune the magnetic properties of ferromagnetic FEBID materials. We also review a selection of recent works involving FEBID 3D nanostructures in areas such as scanning probe microscopy sensing, magnetic frustration phenomena, curvilinear magnetism, magnonics and fluxonics, offering a wide perspective of the important role FEBID is likely to have in the coming years in the study of new phenomena involving 3D magnetic nanostructures.

Controlling spin supercurrents via nonequilibrium spin injection

We propose a mechanism whereby spin supercurrents can be manipulated in superconductor/ferromagnet proximity systems via nonequilibrium spin injection. We find that if a spin supercurrent exists in equilibrium, a nonequilibrium spin accumulation will exert a torque on the spins transported by this current. This interaction causes a new spin supercurrent contribution to manifest out of equilibrium, which is proportional to and polarized perpendicularly to both the injected spins and the equilibrium spin current. This is interesting for several reasons: as a fundamental physical effect; due to possible applications as a way to control spin supercurrents; and timeliness in light of recent experiments on spin injection in proximitized superconductors.

Experimental Realization of a Quantum Dot Energy Harvester

We demonstrate experimentally an autonomous nanoscale energy harvester that utilizes the physics of resonant tunneling quantum dots. Gate-defined quantum dots on GaAs/AlGaAs high-electron-mobility transistors are placed on either side of a hot-electron reservoir. The discrete energy levels of the quantum dots are tuned to be aligned with low energy electrons on one side and high energy electrons on the other side of the hot reservoir. The quantum dots thus act as energy filters and allow for the conversion of heat from the cavity into electrical power. Our energy harvester, measured at an estimated base temperature of 75 mK in a He^{3}/He^{4} dilution refrigerator, can generate a thermal power of 0.13 fW for a temperature difference across each dot of about 67 mK.

Spin Splitting Induced in a Superconductor by an Antiferromagnetic Insulator

Inspired by recent feats in exchange coupling antiferromagnets to an adjacent material, we demonstrate the possibility of employing them for inducing spin splitting in a superconductor, thereby avoiding the detrimental, parasitic effects of ferromagnets employed to this end. We derive the Gor'kov equation for the matrix Green's function in the superconducting layer, considering a microscopic model for its disordered interface with a two-sublattice magnetic insulator. We find that an antiferromagnetic insulator with effectively uncompensated interface induces a large, disorder-resistant spin splitting in the adjacent superconductor. In addition, we find contributions to the self-energy stemming from the interfacial disorder. Within our model, these mimic impurity and spin-flip scattering, while another breaks the symmetries in particle-hole and spin spaces. The latter contribution, however, drops out in the quasiclassical approximation and thus, does not significantly affect the superconducting state.

Creation of equal-spin triplet superconductivity at the Al/EuS interface

In conventional superconductors, electrons of opposite spins are bound into Cooper pairs. However, when the superconductor is in contact with a non-uniformly ordered ferromagnet, an exotic type of superconductivity can appear at the interface, with electrons bound into three possible spin-triplet states. Triplet pairs with equal spin play a vital role in low-dissipation spintronics. Despite the observation of supercurrents through ferromagnets, spectroscopic evidence for the existence of equal-spin triplet pairs is still missing. Here we show a theoretical model that reveals a characteristic gap structure in the quasiparticle density of states which provides a unique signature for the presence of equal-spin triplet pairs. By scanning tunnelling spectroscopy we measure the local density of states to reveal the spin configuration of triplet pairs. We demonstrate that the Al/EuS interface causes strong and tunable spin-mixing by virtue of its spin-dependent transmission.

Andreev bound states at spin-active interfaces

Andreev bound states are ubiquitous in superconducting hybrid structures. They are formed near impurities, in Josephson junctions, in vortex cores and at interfaces. At spin-active superconductor-ferromagnet interfaces, Andreev bound states are formed due to spin-dependent scattering phases. Spin-dependent phase shifts are an important ingredient for the generation of triplet Cooper pairs in superconductor-ferromagnet hybrid structures. Spectroscopy of Andreev bound states is a powerful probe of superconducting order parameter symmetry, as well as spin-dependent interface scattering and the triplet proximity effect.This article is part of the theme issue 'Andreev bound states'.

Out-of-equilibrium spin transport in mesoscopic superconductors

The excitations in conventional superconductors, Bogoliubov quasi-particles, are spin-[Formula: see text] fermions but their charge is energy-dependent and, in fact, zero at the gap edge. Therefore, in superconductors (unlike normal metals) spin and charge degrees of freedom may be separated. In this article, we review spin injection into conventional superconductors and focus on recent experiments on mesoscopic superconductors. We show how quasi-particle spin transport and out-of-equilibrium spin-dependent superconductivity can be triggered using the Zeeman splitting of the quasi-particle density of states in thin-film superconductors with small spin-mixing scattering. Finally, we address the spin dynamics and the feedback of quasi-particle spin imbalances on the amplitude of the superconducting energy gap.This article is part of the theme issue 'Andreev bound states'.

Theory of Andreev bound states in S-F-S junctions and S-F proximity devices

Andreev bound states are an expression of quantum coherence between particles and holes in hybrid structures composed of superconducting and non-superconducting metallic parts. Their spectrum carries important information on the nature of the pairing, and determines the current in Josephson devices. Here, I focus on Andreev bound states in systems involving superconductors and ferromagnets with strong spin-polarization. I provide a general framework for non-local Andreev phenomena in such structures in terms of coherence functions, and show how the latter link wave function and Green-function based theories.This article is part of the theme issue 'Andreev bound states'.

Oscillatory Nernst effect in Pt|ferrite|cuprate-superconductor trilayer films

Although magnetism and superconductivity hardly coexist in a single material, recent advances in nanotechnology and spintronics have brought to light their interplay in magnetotransport in thin-film heterostructures. Here, we found a periodic oscillation of Nernst voltage with respect to magnetic fields in Pt|LiFe₅O₈ (Pt|LFO) bilayers grown on a cuprate superconductor YBa₂Cu₃O_7−x (YBCO). At high temperatures above the superconducting transition temperature (T_C) of YBCO, spin Seebeck voltages originating in Pt|LFO layers are observed. As temperature decreases well below T_C, the spin Seebeck voltage is suppressed and unconventional periodic voltage oscillation as a function of magnetic fields appears; such an oscillation emerging along the Hall direction in the superconducting state has not been observed yet. Dynamics of superconducting vortices pinned by surface precipitates seems responsible for the oscillatory Nernst effect.

Optimal Quantum Interference Thermoelectric Heat Engine with Edge States

We show theoretically that a thermoelectric heat engine, operating exclusively due to quantum-mechanical interference, can reach optimal linear-response performance. A chiral edge state implementation of a close-to-optimal heat engine is proposed in an electronic Mach-Zehnder interferometer with a mesoscopic capacitor coupled to one arm. We demonstrate that the maximum power and corresponding efficiency can reach 90% and 83%, respectively, of the theoretical maximum. The proposed heat engine can be realized with existing experimental techniques and has a performance robust against moderate dephasing.

Triplet Cooper pairs induced in diffusive s-wave superconductors interfaced with strongly spin-polarized magnetic insulators or half-metallic ferromagnets

Interfacing superconductors with strongly spin-polarized magnetic materials opens the possibility to discover new spintronic devices in which spin-triplet Cooper pairs play a key role. Motivated by the recent derivation of spin-polarized quasiclassical boundary conditions capable of describing such a scenario in the diffusive limit, we consider the emergent physics in hybrid structures comprised of a conventional s-wave superconductor (e.g. Nb, Al) and either strongly spin-polarized ferromagnetic insulators (e.g. EuO, GdN) or halfmetallic ferromagnets (e.g. CrO₂, LCMO). In contrast to most previous works, we focus on how the superconductor itself is influenced by the proximity effect, and how the generated triplet Cooper pairs manifest themselves in the self-consistently computed density of states (DOS) and the superconducting critical temperature T_c. We provide a comprehensive treatment of how the superconductor and its properties are affected by the triplet pairs, demonstrating that our theory can reproduce the recent observation of an unusually large zero-energy peak in a superconductor interfaced with a half-metal, which even exceeds the normal-state DOS. We also discuss the recent observation of a large superconducting spin-valve effect with a T_c change ~1 K in superconductor/half-metal structures, in which case our results indicate that the experiment cannot be explained fully by a long-ranged triplet proximity effect.

Spin Seebeck effect and thermoelectric phenomena in superconducting hybrids with magnetic textures or spin-orbit coupling

We theoretically consider the spin Seebeck effect, the charge Seebeck coefficient, and the thermoelectric figure of merit in superconducting hybrid structures including either magnetic textures or intrinsic spin-orbit coupling. We demonstrate that large magnitudes for all these quantities are obtainable in Josephson-based systems with either zero or a small externally applied magnetic field. This provides an alternative to the thermoelectric effects generated in high-field (~1 T) superconducting hybrid systems, which were recently experimentally demonstrated. The systems studied contain either conical ferromagnets, spin-active interfaces, or spin-orbit coupling. We present a framework for calculating the linear thermoelectric response for both spin and charge of a system upon applying temperature and voltage gradients based on quasiclassical theory which allows for arbitrary spin-dependent textures and fields to be conveniently incorporated.

Nonlinear thermoelectric effects in high-field superconductor-ferromagnet tunnel junctions

Background: Thermoelectric effects result from the coupling of charge and heat transport and can be used for thermometry, cooling and harvesting of thermal energy. The microscopic origin of thermoelectric effects is a broken electron-hole symmetry, which is usually quite small in metal structures. In addition, thermoelectric effects decrease towards low temperatures, which usually makes them vanishingly small in metal nanostructures in the sub-Kelvin regime. Results: We report on a combined experimental and theoretical investigation of thermoelectric effects in superconductor/ferromagnet hybrid structures. We investigate the dependence of thermoelectric currents on the thermal excitation, as well as on the presence of a dc bias voltage across the junction. Conclusion: Large thermoelectric effects are observed in superconductor/ferromagnet and superconductor/normal-metal hybrid structures. The spin-independent signals observed under finite voltage bias are shown to be reciprocal to the physics of superconductor/normal-metal microrefrigerators. The spin-dependent thermoelectric signals in the linear regime are due to the coupling of spin and heat transport, and can be used to design more efficient refrigerators.

Spin manipulation in nanoscale superconductors

The interplay of superconductivity and magnetism in nanoscale structures has attracted considerable attention in recent years due to the exciting new physics created by the competition of these antagonistic ordering phenomena, and the prospect of exploiting this competition for superconducting spintronics devices. While much of the attention is focused on spin-polarized supercurrents created by the triplet proximity effect, the recent discovery of long range quasiparticle spin transport in high-field superconductors has rekindled interest in spin-dependent nonequilibrium properties of superconductors. In this review, the experimental situation on nonequilibrium spin injection into superconductors is discussed, and open questions and possible future directions of the field are outlined.

Observation of Thermoelectric Currents in High-Field Superconductor-Ferromagnet Tunnel Junctions

We report on the experimental observation of spin-dependent thermoelectric currents in superconductor-ferromagnet tunnel junctions in high magnetic fields. The thermoelectric signals are due to a spin-dependent lifting of the particle-hole symmetry, and are found to be in excellent agreement with recent theoretical predictions. The maximum Seebeck coefficient inferred from the data is about -100  μV/K, much larger than commonly found in metallic structures. Our results directly prove the coupling of spin and heat transport in high-field superconductors.

Resolving thermoelectric "paradox" in superconductors

For almost a century, thermoelectricity in superconductors has been one of the most intriguing topics in physics. During its early stages in the 1920s, the mere existence of thermoelectric effects in superconductors was questioned. In 1944, it was demonstrated that the effects may occur in inhomogeneous superconductors. Theoretical breakthrough followed in the 1970s, when the generation of a measurable thermoelectric magnetic flux in superconducting loops was predicted; however, a major crisis developed when experiments showed puzzling discrepancies with the theory. Moreover, different experiments were inconsistent with each other. This led to a stalemate in bringing theory and experiment into agreement. With this work, we resolve this stalemate, thus solving this long-standing "paradox," and open prospects for exploration of novel thermoelectric phenomena predicted recently.

Spin-polarized supercurrents for spintronics: a review of current progress

During the past 15 years a new field has emerged, which combines superconductivity and spintronics, with the goal to pave a way for new types of devices for applications combining the virtues of both by offering the possibility of long-range spin-polarized supercurrents. Such supercurrents constitute a fruitful basis for the study of fundamental physics as they combine macroscopic quantum coherence with microscopic exchange interactions, spin selectivity, and spin transport. This report follows recent developments in the controlled creation of long-range equal-spin triplet supercurrents in ferromagnets and its contribution to spintronics. The mutual proximity-induced modification of order in superconductor-ferromagnet hybrid structures introduces in a natural way such evasive phenomena as triplet superconductivity, odd-frequency pairing, Fulde-Ferrell-Larkin-Ovchinnikov pairing, long-range equal-spin supercurrents, [Formula: see text]-Josephson junctions, as well as long-range magnetic proximity effects. All these effects were rather exotic before 2000, when improvements in nanofabrication and materials control allowed for a new quality of hybrid structures. Guided by pioneering theoretical studies, experimental progress evolved rapidly, and since 2010 triplet supercurrents are routinely produced and observed. We have entered a new stage of studying new phases of matter previously out of our reach, and of merging the hitherto disparate fields of superconductivity and spintronics to a new research direction: super-spintronics.

Novel non-local effects in three-terminal hybrid devices with quantum dot

We predict non-local effect in the three-terminal hybrid device consisting of the quantum dot (QD) tunnel coupled to two normal and one superconducting reservoirs. It manifests itself as the negative non-local resistance and results from the competition between the ballistic electron transfer (ET) and the crossed Andreev scattering (CAR). The effect is robust both in the linear and non-linear regimes. In the latter case the screening of charges and the long-range interactions play significant role. We show that sign change of the non-local conductance depends on the subgap Shiba/Andreev states, and it takes place even in absence of the Coulomb interactions. The effect is large and can be experimentally verified using the four probe setup. Since the induced non-local voltage changes sign and magnitude upon varying the gate potential and/or coupling of the quantum dot to the superconducting lead, such measurement could hence provide a controlled and precise method to determine the positions of the Shiba/Andreev states. Our predictions ought to be contrasted with non-local effects observed hitherto in the three-terminal planar junctions where the residual negative non-local conductance has been observed at large voltages, related to the Thouless energy of quasiparticles tunneling through the superconducting slab.

Long-range spin accumulation from heat injection in mesoscopic superconductors with Zeeman splitting

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.

Very large thermophase in ferromagnetic Josephson junctions

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.

The interface between superconductivity and magnetism: understanding and device prospects

Ferromagnetism and conventional singlet superconductivity can be regarded as competing ordering phenomena. A considerable body of theoretical work over the past twenty years has predicted that at interfaces between the two systems competition or coupling between superconducting and magnetic phenomena are possible. Despite the very short lengthscales over which some of the phenomena exist, many of these predictions have been experimentally realized. The aim of this topical review is to provide an overview of the experimental position and to discuss the potential developments and applications of existing results.

Charge and spin transport in mesoscopic superconductors

BACKGROUND

Non-equilibrium charge transport in superconductors has been investigated intensely in the 1970s and 1980s, mostly in the vicinity of the critical temperature. Much less attention has been paid to low temperatures and the role of the quasiparticle spin.

RESULTS

We report here on nonlocal transport in superconductor hybrid structures at very low temperatures. By comparing the nonlocal conductance obtained by using ferromagnetic and normal-metal detectors, we discriminate charge and spin degrees of freedom. We observe spin injection and long-range transport of pure, chargeless spin currents in the regime of large Zeeman splitting. We elucidate charge and spin transport by comparison to theoretical models.

CONCLUSION

The observed long-range chargeless spin transport opens a new path to manipulate and utilize the quasiparticle spin in superconductor nanostructures.

Predicted very large thermoelectric effect in ferromagnet-superconductor junctions in the presence of a spin-splitting magnetic field

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.