The magnetization in a superconductor induced due to the inverse proximity effect is investigated in hybrid bilayers containing a superconductor and a ferromagnetic insulator or a strongly spin-polarized ferromagnetic metal. The study is performed within a quasiclassical Green function framework, wherein Usadel equations are solved with boundary conditions appropriate for strongly spin-polarized ferromagnetic materials. A comparison with recent experimental data is presented. The singlet to triplet conversion of the superconducting correlations as a result of the proximity effect with a ferromagnet is studied.
Superconductor/ferromagnet proximity effect has been studied for Pb/Co$_2$Cr$_{1-x}$Fe$_x$Al bilayers. Different substrate temperatures allowed us to prepare the Heusler alloy Co$_2$Cr$_{1-x}$Fe$_x$Al films with different degree of spin polarization of conduction band of the Heusler layer. We obtain a strong correlation between the dependence of the superconducting transition temperature on the Pb-layer thickness at fixed thickness of the Heusler layer and the degree of spin polarization in the ferromagnetic layer.
Scanning tunneling spectroscopy measurements conducted on epitaxially grown bilayers of half-metallic ferromagnetic La2/3Ca1/3MnO3 (LCMO) on superconducting (SC) (100)YBa2Cu3O7-delta (YBCO) reveal long-range penetration of superconducting order into the LCMO. This anomalous proximity effect manifests itself in the tunneling spectra measured on the LCMO layer as gaps and zero bias conductance peaks. Remarkably, these proximity-induced spectral features were observed for bilayers with LCMO thickness of up to 30 nm, an order of magnitude larger than the expected ferromagnetic coherence length in …
We show that quantum vortex-loop proliferation may be one possible explanation of the super-long-range proximity effect observed in an insulating underdoped cuprate, using the dual theory of quantum vortices. As a test of this scenario, we propose that a dual proximity effect experiment can confirm the superfluid motion of the quantum vortices in the vortex-proliferated insulator and can measure the divergent correlation lengths near the superconductor-insulator transition.
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.
We study the proximity effect in a ferromagnetic nanoparticle having a vortex magnetization pattern. We show that for axisymmetric system consisting of a circular particle and a magnetic vortex situated at the center of it no long range superconducting correlations are induced. It means that induced superconductivity is localized in the small area near the superconducting electrode. However, in the real systems axial symmetry can be broken by either a shift of the magnetic vortex from the origin or geometrical anisotropy of the ferromagnetic particle. In this case a long range proximity effect…
We study the proximity effect in superconductor - metallic or ferromagnetic Aharonov Bohm loop hybrid structures self consistently using the Bogoliubov-deGennes formalism within the two dimensional extended Hubbard model. We calculate the local density of states, the pair amplitude, and persistent currents as a function of several modulation parameters, the position around the loop, the exchange field, the magnetic flux through the loop, the loop size, and the chemical potential in the loop atoms. We find that the parameters above can modulate the proximity effect.
Considerable evidence for proximity-induced triplet superconductivity on the ferromagnetic side of a superconductor-ferromagnet (S-F) interface now exists; however, the corresponding effect on the superconductor side has hardly been addressed. We have performed scanning tunneling spectroscopy measurements on NbN superconducting thin films proximity coupled to the half-metallic ferromagnet La2/3Ca1/3MnO3 (LCMO) as a function of magnetic field. We have found that at zero and low applied magnetic fields the tunneling spectra on NbN typically show an anomalous gap structure with suppressed coheren…
We study peculiarities of proximity effect in clean superconductor -- ferromagnet structures caused by either spatial or momentum dependence of the exchange field. Even a small modulation of the exchange field along the quasiparticle trajectories is shown to provide a long range contribution to the supercurrent due to the specific interference of particle- and hole- like wave functions. The momentum dependence of the exchange field caused by the spin -- orbit interaction results in the long -- range superconducting correlations even in the absence of ferromagnetic domain structure and can expl…
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.
The ferromagnetic resonance of thin sputtered Ni80Fe20 films grown on Nb is measured. By varying the temperature and thickness of the Nb the role of the superconductivity on the whole ferromagnetic layer in these heterostructures is explored. The change in the spin transport properties below the superconducting transition of the Nb is found to manifest itself in the Ni80Fe20 layer by a sharpening in the resonance of the ferromagnet, or a decrease in the effective Gilbert damping co-efficient. This dynamic proximity effect is in contrast to low frequency studies in these systems, where the effe…
We investigate the effect of an inhomogeneous exchange field on the proximity effect in superconductor-ferromagnet hybrid structures within the quasi-classical theory of superconductivity. As an example we study the proximity effect in a superconductor-ferromagnet bilayer with an in-plane spiral magnetic order in the ferromagnet. This model simulates a multiple magnetic domain structure where the domain walls of the Néel type are of equal size as the domains. Triplet correlations are induced in the bilayer by the superconducting proximity effect, which are sensitive to the local quantization a…
We show that in multiband superconductors even small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in unusual response to low magnetic fields leading to phase separation into domains of a two-component Meissner states and vortex droplets.
We study theoretically the influence of ferromagnetic metals on a superconducting film in the clean limit. Using a self-consistent solution of the Bogoliubov--de Gennes equation for a ferromagnet-superconductor-ferromagnet double junction we calculate the pair potential and conductance spectra as a function of the superconducting layer thickness $d$ for different strengths of ferromagnets and interface transparencies. We find that the pair potential and the critical temperature are weakly perturbed by the exchange interaction and do not drop to zero for any finite $d$. On the other hand, for t…
We study proximity effects at ferromagnet superconductor interfaces by self-consistent numerical solution of the Bogoliubov-de Gennes equations for the continuum, without any approximations. Our procedures allow us to study systems with long superconducting coherence lengths. We obtain results for the pair potential, the pair amplitude, and the local density of states. We use these results to extract the relevant proximity lengths. We find that the superconducting correlations in the ferromagnet exhibit a damped oscillatory behavior that is reflected in both the pair amplitude and the local de…
We study heat transport in hybrid normal metal - superconductor - normal metal (NSN) structures. We find the thermal conductance of a short superconducting wire to be strongly enhanced beyond the BCS value due to inverse proximity effect. The measurements agree with a model based on the quasiclassical theory of superconductivity in the diffusive limit. We determine a crossover temperature below which quasiparticle heat conduction dominates over the electron-phonon relaxation.
The spread of the Cooper pairs into the ferromagnet in proximity coupled superconductor - ferromagnet (SF) structures is shown to cause a strong inverse electromagnetic phenomenon, namely, the long-range transfer of the magnetic field from the ferromagnet to the superconductor. Contrary to the previously investigated inverse proximity effect resulting from the spin polarization of superconducting surface layer, the characteristic length of the above inverse electrodynamic effect is of the order of the London penetration depth, which usually much larger than the superconducting coherence length…
It is shown that the order parameter $Δ$ induced in the normal part of superconductor-normal-superconductor proximity system is modulated in the magnetic field differently from vortices in bulk superconductors. Whereas $Δ$ turns zero at vortex centers, the magnetic structure of these vortices differs from that of Abrikosov's.
We examined the proximity effect in granular films made of Pb, a superconductor, and Ni, a ferromagnet, with various compositions. Slow decay of the critical temperature as a function of the relative volume concentration of Ni per sample was demonstrated by our measurements, followed by a saturation of T$_c$. Using an approximate theoretical description of our granular system in terms of a layered one, we show that our data can only be reasonably fitted by a multilayer model. This indicates the importance of the interplay between different ferromagnetic grains; when non-collinearly magnetized …
We study the perpendicular transport characteristics of small superconductor/ferromagnetic insulator/superconductor (YBa$_2$Cu$_3$O$_{7-x}$/LaMnO$_{3+δ}$/YBa$_2$Cu$_3$O$_{7-x}$) tunnel junctions. At a large bias voltage $V\sim 1$ V we observe a step-like onset of excess current that occurs below the superconducting transition temperature $T<T_c$ and is easily suppressed by a magnetic field. The phenomenon is attributed to a novel type of the superconducting proximity effect of non-equilibrium electrons injected into the conduction band of the ferromagnetic insulator via a Fowler-Nordheim tunne…
We consider superconductivity nucleation in multiply connected mesoscopic samples such as thin-walled cylinders or rings placed in electrical contact with a ferromagnet. The superconducting critical temperature and order parameter structure are studied on the basis of linearized Usadel equations. We suggest a mechanism of switching between the superconducting states with different vorticities caused by the exchange field and associated with the oscillatory behavior of the Cooper pair wave function in a ferromagnet.
We suggest a mechanism which promotes the existence of a phase soliton -- topological defect formed in the relative phase of superconducting gaps of a two-band superconductor with s+- type of pairing. This mechanism exploits the proximity effect with a conventional s-wave superconductor which favors the alignment of the phases of the two-band superconductor which, in the case of s+- pairing, are pi-shifted in the absence of proximity. In the case of a strong proximity such effect can be used to reduce soliton's energy below the energy of a soliton-free state thus making the soliton thermodynam…
We report measurements of the critical temperature of YBCO-Co doped YBCO Superconductor-Normal bilayer films. Depending on the morphology of the S-N interface, the coupling between S and N layers can be turned on to depress the critical temperature of S by tens of degrees, or turned down so the layers appear almost totally decoupled. This novel effect can be explained by the mechanism of quasiparticle transmission into an anisotropic superconductor.
We investigate inverse proximity effects in a spin-triplet superconductor (TSC) interfaced with a ferromagnet (FM), assuming different types of magnetic profiles and chiral or helical pairings. The region of the coexistence of spin-triplet superconductivity and magnetism is significantly influenced by the orientation and spatial extension of the magnetization with respect to the spin configuration of the Cooper pairs, resulting into clearcut anisotropy signatures. A characteristic mark of the inverse proximity effect arises in the induced spin-polarization at the TSC interface. This is unexpec…
The discovery of noncentrosymmetric superconductors, such as CePt$_3$Si, and chiral superconductors, such as Sr$_2$RuO$_4$, calls for experimental methods to identify the presence of spin-triplet pairing. We here demonstrate a method which accomplishes this in an appealingly simple manner: a spin-sensitive proximity effect in a ferromagnet$\mid$triplet superconductor bilayer. It is shown how the orientation of the field can be used to unambiguously distinguish between different spin-triplet states. Moreover, the proximity effect becomes long-ranged in spite of the presence of an exchange field…
We show that in superlattices with alternating superconducting (S) and ferromagnetic (F) layers the spontaneous magnetic field induced in the superconducting layers due to the electromagnetic proximity effect becomes dramatically enhanced compared to the previously studied S/F bilayers. The effect reveals itself for the in-plane orientation of the magnetic moments both for ferromagnetic and anti-ferromagnetic ordering of the moments in the F layers. In the finite size samples the magnetic field decays from the sample surface towards the bulk of the structure, and the decay length strongly depe…
We study the proximity effect in good contacts between normal metals and high Tc (d-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity scattering in the two sides, s-wave pairing interaction in the normal metal side (attractive or repulsive), as well as subdominant s-wave paring in the superconductor side. For the [100] orientation, a real combination d+s of the order parameters is always found. The spectral signatures of the proximity effect in the normal metal includes a suppression of t…
Heterostructures made of itinerant ferromagnets and superconductors are studied. In contrast to most previous models, ferromagnetism is not enforced as an external Zeeman field but induced in a correlated single-band model (CSBM) that displays itinerant ferromagnetism as a mean-field ground state. This allows us to investigate the influence of an adjacent superconducting layer on the properties of the ferromagnet in a self-consistent Bogoliubov-de Gennes approach. The CSBM displays a variety features not present in the Zeeman exchange model that influence the behavior of order parameters close…
At the interface between a superconductor and a ferromagnetic metal spin-singlet Cooper pairs can penetrate into the ferromagnetic part of the heterostructure with an oscillating and decaying spin-singlet Cooper pair density. However, if the interface allows for a spin-mixing effect, equal-spin spin-triplet Cooper pairs can be generated that can penetrate much further into the ferromagnetic part of the heterostructure, known as the long-range proximity effect. Here, we present results of spin-mixing based on self-consistent solutions of the microscopic Bogoliubov-de Gennes equations incorporat…
We study the emergent proximity effect in mesoscopic circuits that involve a conventional superconductor and an unconventional pnictide superconductor separated by a diffusive normal or ferromagnetic wire. The focus is placed on revealing signatures of the proposed s+- state of pnictides from the proximity-induced density of states and Josephson current. We find analytically a universal result for the density of states that exhibits both the Thouless gap at low energies, and peculiar features near the superconducting gap edges at higher energies. The latter may be used to discriminate between …
We investigate the effects of Andreev bound states due to the unconventional pairing on the inverse proximity effect of ferromagnet/superconductor junctions. Utilizing quasiclassical Eilenberger theory, we obtain the magnetization penetrating into the superconductor. We show that in a wide parameter range the direction of the induced magnetization is determined by two factors: whether Andreev bound states are present at the junction interface and the sign of the spin-mixing angle. In particular, when Andreev bound states appear at the interface, the direction of the induced magnetization is op…
We apply the scattering matrix approach to the triplet proximity effect in superconductor-half metal structures. We find that for junctions that do not mix different orbital modes, the zero bias Andreev conductance vanishes, while the zero bias Josephson current is nonzero. We illustrate this finding on a ballistic half-metal--superconductor (HS) and superconductor -- half-metal -- superconductor (SHS) junction with translation invariance along the interfaces, and on HS and SHS systems where transport through the half-metallic region takes place through a single conducting channel. Our calcula…
We study a two-dimensional superconductor in close proximity to a two-dimensional metallic sheet. The electrons in the superconducting sheet are coupled to those in the metallic sheet by the Coulomb interaction only. We obtain an effective phase-only action for the superconductor by integrating out all the electronic degrees of freedom in the problem. The Coulomb drag of the normal electrons in the metallic sheet is found to make the spectrum of phase-fluctuations in the superconductor, dissipative at long wavelengths. The dissipative co-efficient $η$ is shown to be simply related to the norma…
We study the superconducting proximity effect between a conventional semiconductor and a disordered s-wave superconductor. We calculate the effective momentum relaxation rate in the semiconductor due to processes involving electron tunneling into a disordered superconductor and scattering off impurities. The magnitude of the effective disorder scattering rate is important for understanding the stability of the topological (chiral p-wave) superconducting state that emerges in the semiconductor, since disorder scattering has a detrimental effect and can drive the system into a non-topological st…
We study the proximity effect in SF'(AF)F'S and SF'(F)F'S planar junctions, where S is a clean conventional (s-wave) superconductor, while F' and middle layers are clean or moderately diffusive ferromagnets. Middle layers consist of two equal ferromagnets with antiparallel (AF) or parallel (F) magnetizations that are not collinear with magnetizations in the neighboring F' layers. We use fully self-consistent numerical solutions of the Eilenberger equations to calculate the superconducting pair amplitudes and the Josephson current for arbitrary thickness of ferromagnetic layers and the angle be…
We report the effect on the superconducting transition temperature (Tc) of a Nb film proximity coupled to the synthetic antiferromagnet Fe/{Cr/Fe}_(N-1). We find that there is a parity dependence of Tc on the total number of Fe layers, N; locally Tc is always a maximum when N is even, and a minimum when N is odd. The Fe electron mean free path and coherence length are indicative of dirty limit behavior; as such, we numerically model our data using the linearized Usadel equations with good correlation.
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…
We study theoretically the proximity effect in a ferromagnetic semiconductor with Rashba spin-orbit interaction. The exchange potential generates opposite-spin-triplet Cooper pairs which are transformed into equal-spin-triplet pairs by the spin-orbit interaction. In the limit of strong spin-orbit interaction, symmetry of the dominant Cooper pair depends on the degree of disorder in a ferromagnet. In the clean limit, spin-singlet $s$-wave Cooper pairs are the most dominant because the spin-momentum locking stabilizes a Cooper pair consisting of a time-reversal partner. In the dirty limit, on th…
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 fabricated three-dimensional disordered Pb-Cu granular structures, with various metal compositions. The typical grain size of both metals is smaller than the superconductor and normal metal coherence lengths, thus satisfying the Cooper limit. The critical temperature of the samples was measured and compared with the critical temperature of bilayers. We show how the proximity effect theories, developed for bilayers, can be modified for random mixtures and we demonstrate that our experimental data fit well the de Gennes weak coupling limit theory in the Cooper limit. Our results indicate that…
We present a study of the proximity effect and the inverse proximity effect in a superconductor$\mid$ferromagnet bilayer, taking into account several important factors which mostly have been ignored in the literature so far. These include spin-dependent interfacial phase shifts (spin-DIPS) and inhomogeneous textures of the magnetization in the ferromagnetic layer, both of which are expected to be present in real experimental samples. Our approach is numerical, allowing us to access the full proximity effect regime. In Part I of this work, we study the superconducting proximity effect and the r…
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…
A strong mutual influence of superconductors (S) and ferromagnetic (F) conductors in hybrid F/S (Ni/Al) nanostructures is observed. The magnitude of a proximity-induced conductance on the F-side is more than two orders larger than that predicted by theory. Re-entrance of the superconductors to the normal state reciprocated by changes on the F-side has been found in low applied magnetic fields with new peaks in the differential resistance as an effect of the saturation magnetisation. An analysis has been developed providing a base for a numerical description of the system. PACS numbers: 74.50.+…
Thin film junctions and bilayers of the doped topological insulator $\rm Bi_2Se_3$ and the s-wave superconductor NbN were found to exhibit conductance spectra with prominent zero bias and coherence peaks. Various tunneling models with different pair potentials have failed to fit our data, except for the triplet $p_x+ip_y$ pair potential, which breaks time reversal symmetry, but yielded reasonably good fits. This provides evidence for proximity induced triplet superconductivity in the $\rm Bi_2Se_3$ layer near the interface with the NbN film.
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…
We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of spin-triplet Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. The additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and r…
We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scatter…
We study the influence of the configuration of the majority and minority spin subbands of electron spectra on the properties of atomic-scaled superconductor-ferromagnet S-F-S and F-S-F hybrid structures. At low temperatures, the S/F/S junction is either a 0 or junction depending on the energy shift between S and F materials and the anisotropy of the Fermi surfaces. We found that the spin switch effect in F/S/F system can be reversed if the minority spin electron spectra in F metal is of the hole-like type.
The effect of proximity of the magnetism of the Pr-based manganite (Pr0.6Sr0.4MnO3) on the superconductivity of Bi-based high-temperature superconductor (Bi1.75Pb0.25Sr2Ca2Cu3O10+d) was studied based on the results obtained from the magnetotransport and magnetization measurements. Decrease in the values of the upper critical field (HC2(0)) and an increase in the width of the superconducting transition (Delta TC) of Bi1.75Pb0.25Sr2Ca2Cu3O10+d were observed in proximity with the manganite. The combined effect of magnetic exchange interaction arising from the manganite, the leakage of Cooper-pair…
We investigate transport properties of a trilayer made of a d-wave superconductor connected to two ferromagnetic electrodes. Using Keldysh formalism we show that crossed Andreev reflection and elastic cotunneling exist also with d-wave superconductors. Their properties are controlled by the existence of zero energy states due to the anisotropy of the d-wave pair potential.
Proximity-induced superconductivity in a 3D topological insulator represents a new avenue for observing zero-energy Majorana fermions inside vortex cores. Relatively small gaps and low transition temperatures of conventional s-wave superconductors put the hard constraints on these experiments. Significantly larger gaps and higher transition temperatures in cuprate superconductors might be an attractive alternative to considerably relax these constraints, but it is not clear whether the proximity effect would be effective in heterostructures involving cuprates and topological insulators. Here, …
In this paper we present scanning tunneling microscopy of Bi$_2$Se$_3$ with superconducting Nb deposited on the surface. We find that the topologically protected surface states of the Bi$_2$Se$_3$ leak into the superconducting over-layer, suggesting a dual topological proximity effect. Coupling between theses states and the Nb states leads to an effective pairing mechanism for the surface states, leading to a modified model for a topological superconductor in these systems. This model is consistent with fits between the experimental data and the theory.
Superconductor-ferromagnet-superconductor Josephson junctions are known to exist in the $0$ and $π$ states with the transitions between them controlled by the temperature and ferromagnetic interlayer thickness. We demonstrate that these transitions can be controlled also by the external magnetic field directed perpendicular to the layers. By varying the ratio of diffusion coefficients in superconducting and ferromagnetic layers, these field-controlled transitions can be made detectable for arbitrary large value of the exchange energy in the ferromagnet. We also show that the $0$-$π$ transition…
The physics of superconductor-ferromagnet hybrid structures
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（高等经济学院）；Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University（莫斯科国立大学索别利钦核物理研究所）；Technical University of Moldova（摩尔多瓦技术大学）
We predict a novel type of Josephson effect to occur in triplet superconductor - ferromagnet - triplet superconductor Josephson junctions. We show that the Josephson current, I_J, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d-vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional temperature dependence of I_J in which I_J changes sign with increasing temperature
In this communication we consider generalities of the proximity effect in a contact between a conventional $s$-wave superconductor (S) nano-island and a thin film of a topological insulator (TI). A local hybridization coupling mechanism is considered and a corresponding model is corroborated that captures not only the induced unconventional superconductivity in a TI, but also predicts the spreading of topologically protected surface states into the superconducting over-layer. This dual nature of the proximity effect leads specifically to a modified description of topological superconductivity …
