We revisit the problem of diffusive proximity systems involving superconductors and normal metals (or ferromagnets) with magnetic disorder. On the length scales much larger than its correlation length, the effect of sufficiently weak magnetic disorder may be incorporated as a local spin-flip term in the Usadel equations. We derive this spin-flip term in the general case of a three-dimensional disordered Zeeman-type field with an arbitrary correlation length. Three different regimes may be distinguished: pointlike impurities (the correlation length is shorter than the Fermi wavelength), medium-range disorder (the correlation length between the Fermi wavelength and the mean free path), and long-range disorder (the correlation length longer than the mean free path). We discuss the relations between these three regimes by using the three overlapping approaches: the Usadel equations, the non-linear sigma model, and the diagrammatic expansion. The expressions for the spin-flip rate agree with the existing results obtained in less general situations.
We show that quantum spin fluctuations in inhomogeneous ferromagnets drastically affect the Andreev reflection of electrons and holes at a ferromagnet-superconductor interface. As a result a strong long-range proximity effect appears, associated with electron-hole spin triplet correlations and persisting on a lenght scale typical for non-magnetic materials, but anomalously large for ferromagnets.
We present a theoretical study of the density of states and supercurrent in diffusive superconductor-normal metal-superconductor (SNS) junctions. In particular, we study the influence on these two equilibrium properties of both an arbitrary transparency of the SN interfaces and the presence of spin-flip scattering in the normal wire. We show that the minigap that is present in the spectrum of the diffusive wire is very sensitive to the interface transmission. More mportantly, we show that at arbitrary transparency the minigap replaces the Thouless energy as the relevant energy scale for the pr…
We reconsider the problem of the superconducting proximity effect in a diffusive ferromagnet bounded by tunneling interfaces, using spin-dependent boundary conditions. This introduces for each interface a phase-shifting conductance Gphi which results from the spin dependence of the phase shifts acquired by the electrons upon scattering on the interface. We show that Gphi strongly affects the density of states and supercurrents predicted for superconducting/ferromagnetic hybrid circuits. We show the relevance of this effect by identifying clear signatures of Gphi in the data of T. Kontos et al …
The theory of the I-V characteristics in diffusive superconductor/weak ferromagnet/superconductor (SFS) junction is developed. We show that the exchange field $h$ of the ferromagnet manifests itself as an additional conductance peak at $eV \sim Δ+h$ in the phase-coherent regime, when the Thouless energy is of the order of superconducting order parameter. The excess current exhibits non-monotonous dependence on the exchange field and non-trivial temperature behavior, which is strongly influenced by the temperature dependence of the exchange field.
We discuss the quasiparticle entropy and heat capacity of a dirty superconductor-normal metal-superconductor junction. In the case of short junctions, the inverse proximity effect extending in the superconducting banks plays a crucial role in determining the thermodynamic quantities. In this case, commonly used approximations can violate thermodynamic relations between supercurrent and quasiparticle entropy. We provide analytical and numerical results as a function of different geometrical parameters. Quantitative estimates for the heat capacity can be relevant for the design of caloritronic d…
Resonant proximity effect in the normal metal / insulator / diffusive ferromagnet / insulator / $s$- and d-wave superconductor (N/I/DF/I/S) junctions is studied for various regimes by solving the Usadel equation with the generalized boundary conditions. It is shown that the resonant proximity effect originating from the exchange field in DF layer strongly modifies the tunneling conductance and density of states.
Using a Scanning Tunneling Microscope (STM), we investigate the Local Density of States (LDOS) of artificially fabricated normal metal nano-structures in contact with a superconductor. Very low temperature local spectroscopic measurements (100 mK) reveal the presence of well defined subgap peaks at energy |E|<Delta in the LDOS at various positions of the STM tip. Although no clear correlations between the LDOS and the shape of the samples have emerged, some of the peak features suggest they originate from quasi-particle bound states within the normal metal structures (De Gennes St James states…
We present a theory of the current-voltage characteristics in diffusive superconductor-normal-metal-superconductor junctions. By solving the time-dependent Usadel equations we are able to describe the phase-coherent transport for arbitrary length of the normal wire. We show how the interplay between proximity effect and multiple Andreev reflections gives rise to a rich subgap structure in the conductance and how it is revealed in the non-equilibrium distribution function.
We study differential shot noise in mesoscopic diffusive normal-superconducting (NS) heterostructures at finite voltages where nonlinear effects due to the superconducting proximity effect arise. A numerical scattering-matrix approach is adopted. Through an NS contact, we observe that the shot noise shows a reentrant dependence on voltage due to the superconducting proximity effect but the differential Fano factor stays approximately constant. Furthermore, we consider differential shot noise in the structures where an insulating barrier is formed between normal and superconducting regions and …
We formulate a quantitative theory of non-local electron transport in three-terminal disordered ferromagnet-superconductor-ferromagnet structures. We demonstrate that magnetic effects have different implications: While strong exchange field suppresses disorder-induced electron interference in ferromagnetic electrodes, spin-sensitive electron scattering at superconductor-ferromagnet interfaces can drive the total non-local conductance negative at sufficiently low energies. At higher energies magnetic effects become less important and the non-local resistance behaves similarly to the non-magneti…
We study heat and charge transport through a normal diffusive wire coupled with a superconducting wire over the region smaller than the coherence length. Due to partial Andreev reflection of quasiparticles from the interface, the subgap thermal flow is essentially suppressed and approaches zero along with energy, which is specific for diffusive structures. Whereas the electric conductance shows conventional reentrance effect, the thermal conductance rapidly decreases with temperature which qualitatively explains the results of recent experiments. In the Andreev interferometer geometry, the the…
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference …
We study non-equilibrium Josephson effect and phase-dependent conductance in three-terminal diffusive interferometers with short arms. We consider strong proximity effect and investigate an interplay of dissipative and Josephson currents co-existing within the same proximity region. In junctions with transparent interfaces, the suppression of the Josephson current appears at rather large voltage, $eV\sim Δ$, and the current vanishes at $eV\geqΔ$. Josephson current inversion becomes possible in junctions with resistive interfaces, where the inversion occurs within a finite interval of the appli…
We employ the Keldysh formalism in the quasiclassical approximation to study transport in a diffusive superconductor. The resulting 4x4 transport equations describe the flow of charge and energy as well as the corresponding flow of spin and spin energy. Spin-flip scattering due to magnetic impurities is included. We find that the spin-flip length is renormalized in the superconducting case and propose an experimental system to measure the spin-accumulation in a superconductor.
Superconductor/ferromagnet/superconductor heterostructures exhibit a so-called long-range proximity effect provided some layers of conical magnet Holmium are included in the respective interface regions. The Ho layers lead to a spin-flip process at the interface generating equal-spin spin-triplet pairing correlations in the ferromagnet. These equal-spin spin-triplet pairing correlations penetrate much further into the heterostructure compared to the spin-singlet and unequal-spin spin-triplet correlations which occur in the absence of Ho. Here we present calculations of this effect based on the…
The inverse proximity effect, i.e. the induction of a magnetic moment in the superconductor in superconductor-ferromagnet (S/F) junctions is studied theoretically. We present a microscopic approach which combines a model Hamiltonian with elements of the well established quasiclassical theory. With its help we study systems with arbitrary degree of disorder, interface transparency and thickness of the layers. In the diffusive limit we recover the result of previous works: the direction of the induced magnetization $M$ is opposite to the one of the F layer. However, we show that in the ballistic…
We examine the effect of a spin-active interface on the symmetry of proximity-induced superconducting pairing amplitudes in topological insulators. We develop a model to investigate the leading order contribution to the pairing amplitude considering 3 different kinds of spin-active interfaces: 1) those that induce spin-dependent scattering phases, 2) those that flip the spin of incident electrons, and 3) interfaces that both induce spin-dependent phases and flip the spins of incident electrons. We find that in cases (1) and (3) odd-frequency triplet pairing is induced in the TI while for case …
The proximity effect between a superconductor and a highly diffusive two-dimensional metal was revealed in a Scanning Tunneling Spectroscopy experiment. The in-situ elaborated samples consisted of superconducting single crystalline Pb islands interconnected by a non-superconducting 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…
We present an analytical study of the proximity effect in ferromagnet/superconductor (F/S) heterostructures, allowing for an arbitrary magnetic exchange energy as well as arbitrary impurity and spin-flip scattering rates within a quasiclassical approach. While previous studies mainly have focused on the clean or dirty limits, our results grant access to the regime of intermediate impurity concentrations, thus allowing us to probe the crossover from the clean to dirty limit. We find that in the crossover regime, all possible symmetry correlations of the proximity-induced anomalous Green's funct…
We study theoretically the electronic entropy and specific heat in diffusive superconductor-normal metal-superconductor (SNS) Josephson junctions. In particular, we consider the influence of non-idealities occurring in an actual experiment, such as the presence of barriers at the NS interfaces, the spin-flip and inelastic scattering in the N region and quasiparticle subgap states in the superconductors. We find that spin-flip and inelastic scattering do not have, for typical parameters values, a large effect. On the contrary, the presence of barriers suppresses the superconducting correlations…
Multiterminal Josephson junctions have recently been proposed as a route to artificially mimic topological matter with the distinct advantage that its properties can be controlled via the superconducting phase difference, giving rise to Weyl points in 4-terminal geometries. A key goal is to accurately determine when the system makes a transition from a gapped to non-gapped state as a function of the phase differences in the system, the latter effectively playing the role of quasiparticle momenta in conventional topological matter. We here determine the proximity gap phase diagram of diffusive …
Coupling a conventional s-wave superconductor to a ferromagnet allows, via the proximity effect, to generate superconducting triplet correlations. This feature can be employed to achieve a superconducting triplet spin-valve effect in superconductor-ferromagnet (SF) hybrid structures, for example by switching the magnetizations of the ferromagnets between parallel and antiparallel configurations in F1SF2 and SF1F2 trilayers, or in SF bilayers with both Rashba and Dresselhaus SOC. It was recently reported that geometric curvature can control the generation of long ranged triplets. We use this pr…
The injection of pure spin current into superconductors by the dynamics of a ferromagnetic contact is studied theoretically. Taking into account suppression of the order parameter at the interfaces (inverse proximity effect) and the energy-dependence of spin-flip scattering, we determine the temperature-dependent ferromagnetic resonance linewidth broadening. Our results agree with recent experiments in Nb|permalloy bilayers [C. Bell et al., arXiv:cond-mat/0702461].
Enhanced proximity effect by mid gap Andreev resonant state (MARS) in a diffusive normal metal / insulator / triplet superconductor (DN/TS) junction is studied based on the Keldysh-Nambu quasiclassical Green's function formalism. By choosing a p-wave superconductor as a typical example of TS, conductance of the junction and the spatial variation of quasiparticle local density of states (LDOS) in DN are calculated as the function of the magnitudes of the resistance $R_{d}$, Thouless energy in DN and the transparency of the insulating barrier. The resulting conductance spectrum has a zero bias c…
Boundary conditions in quasiclassical theory of superconductivity are of crucial importance for describing proximity effects in heterostructures between different materials. Although they have been derived for the ballistic case in full generality, corresponding boundary conditions for the diffusive limit, described by Usadel theory, have been lacking for interfaces involving strongly spin-polarized materials, such as e.g. half-metallic ferromagnets. Given the current intense research in the emerging field of superconducting spintronics, the formulation of appropriate boundary conditions for t…
We study the role of the superconducting proximity effect on the electron-phonon energy exchange in diffusive normal metals (N) attached to superconductors (S). The proximity effect modifies the spectral response of the normal metal, in particular the local density of states. This leads to a weakening of the electron-phonon energy relaxation. We show that the effect is easily observable with modern thermometry methods, and predict that it can be tuned in structures connected to multiple superconductors by adjusting the phase difference between superconducting order parameters at the two NS int…
We report on mutual proximity effects in d-wave superconductor/half-metal heterostructures which correspond to systems composed of high-Tc cuprates and manganite materials. In our study, proximity effects are induced by the interplay of two separate interface effects: spin-mixing (or rotation) surface scattering and spin-flip scattering. The surface spin-mixing scattering introduces spin-triplet pairing correlations in superconducting side; as a result, Andreev bound states are formed at energies within the superconducting gap. The spin-flip scattering introduces not only long range equal-spin…
The conditions for the formation of zero-energy peak in the density of states (DOS) in the normal metal / insulator / diffusive ferromagnet / insulator / s-wave superconductor (N/I/DF/I/S) junctions are studied by solving the Usadel equations. The DOS of the DF is calculated in various regimes for different magnitudes of the resistance, Thouless energy and the exchange field of the DF, as well as for various resistances of the insulating barriers. The conditions for the DOS peak are formulated for the cases of weak proximity effect (large resistance of the DF/S interface) and strong proximity …
We present tunnel spectroscopy experiments on the proximity effect in lateral superconductor-normal metal-superconductor (SNS) Josephson junctions. Our weak link is embedded into a superconducting (S) ring allowing phase biasing of the Josephson junction by an external magnetic field. We explore the temperature and phase dependence of both the induced mini-gap and the modification of the density of states in the normal (N) metal. Our results agree with a model based on the quasiclassical theory in the diffusive limit. The device presents an advanced version of the superconducting quantum inter…
We study spin dependent phonomena in superconducting junctions in both ballistic and diffusive regimes. For ballistic junctions we study both ferromagnet / $s$- and d-wave superconductor junctions and two dimensional electron gas / s-wave superconductor junctions with Rashba spin-orbit coupling. It is shown that the exchange field alway suppresses the conductance while the Rashba spin-orbit coupling can enhance it. In the latter part of the article we study the diffusive ferromagnet / insulator / $s$- and d-wave superconductor junctions, where the proximity effect can be enhanced by the exchan…
We demonstrate two effects that occur in all diffusive superconducting-magnetic heterostructures with rotating magnetization: the reappearance of singlet $|0,0>$ correlations deep in the magnetic material and a cascade of $s=1$, $m=0, \pm 1$ components (in the two spin-$1/2$ basis $|s,m>$). We do so by examining the order parameter and Josephson current through a multilayer with five mutually perpendicular ferromagnets. The properties of the middle layer determine whether the current is due to $m=0$ or $m\neq 0$ contributions. We conclude that so-called long- and short-range components are pre…
We analyze the proximity effect of superconductor/ferromagnet nanostructures and point out that the scattering of quasiparticle of spin-triplet pairs by local magnetic moments leads to large resistance peak slightly below the superconducting transition temperature of the superconductor. Both the temperature and the magnitude of the resistance peak decrease with increasing magnetic field, which agree quite well with the experimental results reported in [Nature Phys. 6, 389 (2010)].
The Josephson Effect and Superconducting Proximity Effect were observed in Superconductor -Graphene-Superconductor (SGS) Josephson junctions with coherence lengths comparable to the distance between the superconducting leads. By comparing the measured temperature and doping dependence of the supercurrent and the proximity induced sub-gap features (multiple Andreev reflections) to theoretical predictions we find that, contrary to expectations, the ballistic transport model fails to describe the SGS junctions. In contrast, the diffusive junction model yields close quantitative agreement with the…
Current noise provides useful information on correlations important for transport properties of mesoscopic systems. Of particular interest, both experimentally and theoretically, are heterostructures of normal metals and superconductors. We use an extended Keldysh-Green's function approach to calculate the current correlations fully accounting for the superconducting proximity effect. The shot noise in diffusive wires shows a reentrant behaviour, similar to the reentrance effect of the conductance. At intermediate energies the effective charge (the ratio of the differential noise and different…
The description of the proximity effect in superconducting/ferromagnetic heterostructures requires to use spin-dependent boundary conditions. Such boundary conditions must take into account the spin dependence of the phase shifts acquired by electrons upon scattering on the boundaries of ferromagnets. The present article shows that this property can strongly affect the critical temperature and the energy dependence of the density of states of diffusive heterostructures. These effects should allow a better caracterisation of diffusive superconductor/ferromagnet interfaces.
We study the effect of spin-flip scattering on the density of states in a long diffusive S-N junction with transparent interface. We calculate the critical value of the spin-flip scattering rate at which the minigap closes and give the dependence of the minigap on the spin-flip rate. For the system we consider, the minigap and the critical spin-flip rate have the scale of the Thouless energy, and not of the superconducting gap.
We study the proximity-induced superconducting correlations as well as the local density of states of a ferromagnet, in a ferromagnet/s-wave superconductor heterostructure. We include the effects of spin-flip scattering, non-ideal interfaces, and the presence of impurities in the sample. We employ the quasiclassical theory of superconductivity, solving the Usadel equation with emphasis on obtaining transparent analytical results. As our main result, we report that in a certain parameter regime the spatial oscillations of the anomalous (superconducting) part of the Green's function induced in t…
The presence of a spin-flip potential at the interface between a superconductor and a ferromagnetic metal allows for the generation of equal-spin spin-triplet Cooper pairs. These Cooper pairs are compatible with the exchange interaction within the ferromagnetic region and hence allow for the long-range proximity effect through a ferromagnet or half-metal. One suitable spin-flip potential is provided by incorporating the conical magnet Holmium (Ho) into the interface. The conical magnetic structure is characterised by an opening angle $α$ with respect to the crystal $c$-axis and a turning (or p…
We find that the dependence on temperature and magnetic field of the electrical resistance of diffusive ferromagnetic nano-wires measured with superconducting electrodes changes drastically with the distance, $L$, between the ferromagnet/superconductor contacts, however is remarkably similar for the wires with the same $L$ ranging from 300 nm to 1000 nm, prepared under identical conditions. The result gives an evidence for the long-range superconductor-induced changes in transport properties of ferromagnetic nano-wires.
We experimentally investigated the current noise in diffusive Superconductor/Normal metal/Superconductor junctions with lengths between the superconducting coherence length xi_Delta and the phase coherence length L_Phi of the normal metal (xi_Delta < L < L_Phi). We measured the shot noise over a large range of energy covering both the regimes of coherent and incoherent multiple Andreev reflections. The transition between these two regimes occurs at the Thouless energy where a pronounced minimum in the current noise density is observed. Above the Thouless energy, in the regime of incoherent mul…
We present microscopic, self-consistent calculations of the superconducting order parameter and pairing correlations near the interface of an $s$-wave superconductor and a three-dimensional topological insulator with spin-orbit coupling. We discuss the suppression of the order parameter by the topological insulator and show that the equal-time pair correlation functions in the triplet channel, induced by spin-flip scattering at the interface, are of $p_x\pm i p_y$ symmetry. We verify that the spectrum at sub-gap energies is well described by the Fu-Kane model. The sub-gap modes are viewed as i…
The long-range proximity effect in superconductor/ferromagnet (S/F) hybrid nano-structures is observed if singlet Cooper pairs from the superconductor are converted into triplet pairs which can diffuse into the fer- romagnet 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 con- densate 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 …
The Josephson effect in superconductor / diffusive ferromagnet / superconductor (SFS) junctions is studied using the recursive Green function method in the regime of large exchange energy in a ferromagnet. Motivated by recent experiment [R. S. Keizer, et. al., Nature 439, 825 (2006)] we also address the case of superconductor / diffusive half metal / superconductor junctions. The pairing function in spin-singlet and triplet channels, the Josephson current and their mesoscopic fluctuations are calculated. We show that the spin-flip scattering at the junction interfaces opens the Josephson chann…
We study the transport properties of a quasi-two-dimensional diffusive normal metal film attached to a superconductor. We demonstrate that the properties of such films can essentially differ from those of quasi-one-dimensional systems: in the presence of the proximity induced superconductivity in a sufficiently wide film its conductance may not only increase but also decrease with temperature. We develop a quantitative theory and discuss the physical nature of this effect. Our theory provides a natural explanation for recent experimental findings referred to as the ``anomalous proximity effect…
We present a numerical study of the density of states in a ferromagnet/superconductor junction and the Josephson current in a superconductor/ferromagnet/superconductor junction in the diffusive limit by solving the Usadel equation with Nazarov's boundary conditions. Our calculations are valid for an arbitrary interface transparency and arbitrary spin-dependent scattering rate, which allows us to explore the entire proximity-effect regime. We first investigate how the proximity-induced anomalous Green's function affects the density of states in the ferromagnet for several values of the exchange…
We present theoretical results on the interplay of magnetic and superconducting orders in diffusive ferromagnet-superconductor-ferromagnet trilayers. The induced triplet superconducting correlations throughout the trilayer lead to an induced spin magnetization. We include self-consistency of the order parameter in the superconducting layer at arbitrary temperatures, arbitrary interface transparency, and any relative orientation of the exchange fields in the two ferromagnets. We propose to use the torque on the trilayer in an external magnetic field as a probe of the presence of triplet correla…
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 pre…
We present a general theory of the superconductive proximity effect in disordered normal--superconducting (N-S) structures, based on the recently developed Keldysh action approach. In the case of the absence of interaction in the normal conductor we reproduce known results for the Andreev conductance G_A at arbitrary relation between the interface resistance R_T and the diffusive resistance R_D. In two-dimensional N-S systems, electron-electron interaction in the Cooper channel of normal conductor is shown to strongly affect the value of G_A as well as its dependence on temperature, voltage an…
We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present a complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superc…
Using an approach based on quasiclassical Green's functions we present a theoretical study of transport in mesoscopic S/N structures in the diffusive limit. The subgap conductance in S/N structures with barriers (zero bias and finite bias anomalies) are discused. We also analyse the temperature dependence of the conductance variation $δS(T)$ for a Andreev interferometer. We show that besides the well know low temperature maximum a second maximum near $T_c$ may appear. We present the results of studies on the Josephson effect in 4 terminal S/N/S contacts and on the possible sign reversal of the…
We investigate heat and charge transport through a diffusive SIF1F2N tunnel junction, where N (S) is a normal (superconducting) electrode, I is an insulator layer and F1,2 are two ferromagnets with arbitrary direction of magnetization. The flow of an electric current in such structures at subgap bias is accompanied by a heat transfer from the normal metal into the superconductor, which enables refrigeration of electrons in the normal metal. We demonstrate that the refrigeration efficiency depends on the strength of the ferromagnetic exchange field h and the angle α between the magnetizations o…
We present a general theory of the proximity effect in junctions between diffusive normal metals (DN) and unconventional superconductors in the framework of the quasiclassical Green's function formalism. Various possible symmetry classes in a superconductor are considered which are consistent with the Pauli principle: even-frequency spin-singlet even-parity (ESE) state, even-frequency spin-triplet odd-parity (ETO) state, odd-frequency spin-triplet even-parity (OTE) state and odd-frequency spin-singlet odd-parity (OSO) state. For each of the above four cases symmetry and spectral properties of …
We report the design and measurement of Superconducting/normal/superconducting (SNS) proximity DC squids in the long junction limit, i.e. superconducting loops interrupted by two normal metal wires roughly a micrometer long. Thanks to the clean interface between the metals, at low temperature a large supercurrent flows through the device. The dc squid-like geometry leads to an almost complete periodic modulation of the critical current through the device by a magnetic flux, with a flux periodicity of a flux quantum h/2e through the SNS loop. In addition, we examine the entire field dependence,…
Charge transport in the diffusive normal metal (DN) / insulator / $s$- and $% d $-wave superconductor junctions is studied in the presence of magnetic impurities in DN in the framework of the quasiclassical Usadel equations with the generalized boundary conditions. The cases of $s$- and d-wave superconducting electrodes are considered. The junction conductance is calculated as a function of a bias voltage for various parameters of the DN metal: resistivity, Thouless energy, the magnetic impurity scattering rate and the transparency of the insulating barrier between DN and a superconductor. It …
The proximity effect, quasiparticle transport, and local magnetic moment in ferromagnet--d-wave superconductor junctions with {110}-oriented interface are studied by solving self-consistently the Bogoliubov-de Gennes equations within an extended Hubbard model. It is found that the proximity induced order parameter oscillates in the ferromagnetic region. The modulation period is shortened with the increased exchange field while the oscillation amplitude is depressed by the interfacial scattering. With the determined superconducting energy gap, a transfer matrix method is proposed to compute the…
In diffusive Josephson junctions the phase-difference $ϕ$ between the superconductors strongly influences the spectroscopic features of the layer separating them. The observation of a uniform minigap and its phase modulation were only recently experimentally reported, demonstrating agreement with theoretical predictions up to now - a vanishing minigap at $ϕ=π$. Remarkably, we find that in the presence of intrinsic spin-orbit coupling a giant proximity effect due to spin-triplet Cooper pairs can develop at $ϕ=π$, in complete contrast to the suppressed proximity effect without spin-orbit couplin…
