Josephson current in superconductor/ferromagnet/ superconductor junctions

The Bogoliubov-de Gennes equation and Nambu spinor Green's function approach are applied to studying the Josephson current in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions in the clean limit. It is found that the critical current exhibits a damped oscillation with the F thickness d, the oscillation period equal to 2πξ_F with ξ_F the coherence length of the F. The change of the critical current from positive to negative is determined by factor cosφ^′ with φ^′=d/ξ_F as the F-induced phase difference. The exponent decay of the critical current is close related to that of the superconductor order parameter in the F, both of them having the same decay length.     

Josephson current in superconductor/ferromagnet/superconductor junctions

By using the Bogoliubov–de Gennes equation and the Nambu spinor Greens function approach, we have theoretically studied the dc Josephson current and the coupling phase state of superconductor/ferromagnet/superconductor (SC/FM/SC) junctions, where the FM is of weak ferromagnetism. From the behavior of the temperature-dependent dc Josephson current (I_c), we confirm that such SC/FM/SC junction may change from 0-phase to π-phase state with increasing the temperature (T), for particular parameters of the thickness and the strength of ferromagnetism of the FM interlayer. We attribute such changement to an extra phase difference between the two SCs. The results are qualitatively consistent with an experiment [Phys. Rev. Lett. 86 (2001) 2427], which shows a sharp cusp structure on the I_c−T curves of Nb/Cu_0.48Ni_0.52/Nb junction for specific thickness of the Cu_0.48Ni_0.52, indicating the junction changes from 0-phase state at high temperatures to π-phase state at low temperatures.     

Josephson current in a clean superconductor normal-metal superconductor junction

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. Our results are able to account for the recent experimental results.     

Josephson current in a clean superconductor normal-metal superconductor junction

Based on a simple matrix method, we investigate the effects of Fermi vector mismatch and elastic barrier on the dc Josephoson current through a ballistic, normal, one-dimensional quantum channel in contact with two superconducting electrodes. Our results are able to account for the recent experimental results.     

Spontaneous Josephson spin current in triplet superconductor/ferromagnet/triplet superconductor junctions

This paper theoretically studies Josephson spin current through triplet superconductor/ferromagnet/triplet superconductor junctions. At the ferromagnet/superconductor interfaces, the ferromagnetic scattering potential gives rise to coupling between the Andreev bound states and lifts their spin degeneracy. These spin-split Andreev states carry the Josephson spin current through the junctions. The generated spin supercurrent can be controlled by the magnetization of a ferromagnetic thin layer and bias voltage across the junctions.     

Proximity-driven source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor voltage-biased Josephson junction

We theoretically investigate an opportunity to implement a source of highly spin-polarized ac current on the basis of superconductor/weak ferromagnet/superconductor (SFS) voltage-biased junction in the regime of essential proximity effect and calculate the current flowing through the probe electrode tunnel coupled to the ferromagnetic interlayer region. It is shown that while the polarization of the dc current component is generally small in case of weak exchange field of the ferromagnet, there is an ac component of the current in the system. This ac current is highly spin-polarized and entirely originated from the non-equilibrium proximity effect in the interlayer. The frequency of the current is controlled by the voltage applied to SFS junction. We discuss a possibility to obtain a source of coherent ac currents with a certain phase shift between them by tunnel coupling two probe electrodes at different locations of the interlayer region. The article is published in the original.     

Contribution of the triplet component of the supercurrent-carrying density of states to the Josephson current in a nonequilibrium superconductor/ferromagnet/superconductor junction

A weak link of two superconductors with s-type pairing through a ferromagnet has been theoretically investigated in the regime of a nonequilibrium spin-dependent distribution of electrons over energy levels in a ferromagnetic interlayer. It has been shown that, under the given conditions, the triplet component of the supercurrent-carrying density of states, which does not participate in the Josephson current transfer under equilibrium and spin-independent nonequilibrium conditions, is involved in the Josephson current transfer through the junction. In this case, the standard supercurrent transferred by the singlet component of the supercurrent-carrying density of states remains unchanged as compared to the case of the equilibrium distribution of electrons in the interlayer. An additional current transferred by the triplet component is controlled by a voltage that controls the specific shape and the degree of nonequilibrium of the electron distribution function in the interlayer. Depending on this controlling parameter, the additional current can substantially amplify or attenuate the standard supercurrent and also switch the junction between 0 and π states.     

Effect of helical edge states on the tunneling conductance in ferromagnet/noncentrosymmetric superconductor junction

Helical edge states exist in the mixed spin-singlet and spin-triplet phase of a noncentrosymmetric (NCS) superconductor [Y. Tanaka, T. Yokoyama, A.V. Balatsky, N. Nagaosa, Phys. Rev. B 79, 060505(R) (2009)]. In this article we have considered a planar ferromagnetic metal/NCS superconductor tunnel junction and have studied the effect of these helical edge states which manifests itself through the charge and spin tunneling conductance across the junction. We have shown the behavior of conductance for the entire range of variation of γ = Δ _-/Δ ₊ where Δ _± are the order parameters in the positive and negative helicity bands of the NCS superconductor. There exists a competition between the Rashba parameter α and the exchange energy E _ex which is crucial for determining the variation of the conductance with the applied bias voltage across the junction. We have found a nonzero spin current across the junction which appears due to the exchange energy in the Ferromagnet and modulates with the bias voltage. It also changes its profile when the strength of the exchange energy is varied.     

Proximity effects in a superconductor/ferromagnet junction

A proximity effect in an s-wave superconductor/ferromagnet (SC/F) junction is theoretically studied using the second order perturbation theory for the tunneling Hamiltonian and Green's function method. We calculate a pair amplitude induced by the proximity effect in a weak ferromagnetic metal (FM) and a half-metal (HM). In the SC/FM junction, it is found that a spin-singlet pair amplitude (Ψ_s) and spin-triplet pair amplitude (Ψ_t) are induced in FM and both amplitudes depend on the frequency in the Matsubara representation. Ψ_s is an even function and Ψ_t is an odd function with respect to the Matsubara frequency (ω_n). In the SC/HM junction, we examine the proximity effects by taking account of magnon excitations in HM. It is found that the triplet-pair correlation is induced in HM. The induced pair amplitude in HM shows a damped oscillation as a function of the position and contains the terms of even and odd functions of ω_n as in the case of the SC/FM junction. We discuss that in our tunneling model the pair amplitude of even function of ω_n only contributes to a Josephson current.     

Josephson current in ferromagnetic d-wave superconductor/ferromagnetic d-wave superconductor junction

We solve a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, study the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor (S)/insulating layer (I)/d-wave S junction are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction depend to a great extent on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field can under certain conditions enhance the Josephson critical current in a d-wave S/I/d-wave S junction.     

超导体/铁磁体绝缘层-超导体隧道结的直流Josephson效应

在超导体铁磁体绝缘层超导体结(SFIS)中,运用BogoliubovdeGennes(BdG)方程和FurusakiTsukada(FT)电流公式,计算铁磁超导共存态的自洽方程和SFIS结中的直流Josephson电流.研究表明,铁磁超导态的磁交换能h对准粒子的Andreev反射有抑制作用,使得SFIS结中的直流Josephson电流随铁磁超导共存态的磁交换能h增大而减弱 关键词： S/F-I-S结 铁磁超导态 直流Josephson电流     

磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森效应

通过求解磁性d波超导中的能隙和磁交换能的自洽方程, 研究磁性d波超导/铁磁/磁性d波超导结中的约瑟夫森电流. 计算结果表明: 1)临界电流随中间的铁磁层厚度呈现出两种不同周期的振荡混合, 通过增强铁磁层中的磁交换能q₀和铁磁/磁性d波超导界面处的势垒强度z₀, 短周期分量可从长周期中分离出来, 反之, 通过降低q₀和z₀, 长周期分量可从短周期中分离出来; 2)在两边磁性d波超导的磁化方向取平行时, 在取一些特定的铁磁层厚度下, 磁性d波超导中的磁交换能可增强系统的临界电流. 关键词： 磁性d波超导体 铁磁体 约瑟夫森电流     

Josephson effect in SIFS with an inhomogeneous superconductor/ferromagnet interface

The Josephson effect in a superconductor-insulator-ferromagnet-superconductor structure with a stepwise change in the transparency of the superconductor/ferromagnet interface has been investigated within the formalism of the Usadel equations. It is shown that, at a certain thickness of the ferromagnet layer, this feature leads to the formation of a point contact with an anomalous dependence of the critical current on the external magnetic field.     

Spin-polarized quasiparticle transport in ferromagnet/insulator/p-wave superconductor junction

We have studied the tunneling conductance in ferromagnet/insulator/p-wave superconductor junctions, taking into account the rough interface scattering effect. We find that there exist zero-bias conductance peaks and single-minimum structure in tunneling spectroscopy. As the exchange energy increases, the Andreev reflection is always suppressed and the differential conductance decreases. The differential conductance depends on the barrier strength and the roughness at the interface. Supported by the Natural Science Foundation of Jiangsu Higher Education Institutions, China (Grant No. 06KJB140009)     

0-pi Transitions in a superconductor/chiral ferromagnet/superconductor junction induced by a homogeneous cycloidal spiral

We study the pi phase in a superconductor-ferromagnet-superconductor Josephson junction, with a ferromagnet showing a cycloidal spiral spin modulation with in-plane propagation vector. Our results reveal a high sensitivity of the junction to the spiral order and indicate the presence of 0-pi quantum phase transitions as function of the spiral wave vector. We find that the chiral magnetic order introduces chiral superconducting triplet pairs that strongly influence the physics in such Josephson junctions, with potential applications in nanoelectronics and spintronics.     

Spin transport properties in ferromagnet/superconductor junctions on topological insulator

The spin-dependent Andreev reflection is investigated theoretically by analyzing the electronic transport in a thin-film topological insulator (TI) ferromagnet/superconductor (FM/SC) junction. The tunneling conductance and shot noise are calculated based on the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk theory. It is found that the magnetic gap in ferromagnet can enhance the Andreev retro-reflection but suppress the specular Andreev reflection. The gate potential applied to the electrode on top of superconductor can enhance the two types of reflections. There is a transition between the two types of reflections at which both the tunneling conductance and differential shot noise become zero. These results provide a method to realize and detect experimentally the intra-band specular Andreev reflection in thin film TI-based FM/SC structures.     

Ferromagnetic features of zero-bias conductance peaks in a ferromagnet/insulator/superconductor junction

We present a general formula for tunneling conductance in ballistic ferromagnet/ferromagnetic insulator/superconductor junctions where the superconducting state has the opposite spin pairing symmetry. The formula shows, correctly, that ferromagnetism has been induced by the effective mass difference between up- and down-spin electrons. This effectively mass mismatched ferromagnet and a standard Stoner ferromagnet have been employed in this paper. As an application of the formulation, we have studied the tunneling effect for junctions including a spin-triplet p-wave superconductor, where we choose a normal insulator for the insulating region, although our formula can be used for a ferromagnetic insulator. Then, we have been able to devote our attention to features of a ferromagnetic metal. The conductance spectra show a clear difference between the two ferromagnets depending upon the method of normalization of the conductance. In particular, an essential difference is seen in the zero-bias conductance peaks, reflecting the characteristics of each ferromagnet. From the obtained results, we suggest that the measurements of the tunneling conductance in the junction provide us with useful information about the mechanism of itinerant ferromagnetism in metals.     

Response of spin-accumulated ferromagnet/superconductor/ferromagnet double tunnel junction to applied magnetic field

Tunneling current in a ferromagnet/superconductor/ferromagnet double tunnel junction induces a nonequilibrium spin accumulation in the superconductor. We study theoretically the response of such a system to applied magnetic field. We show that the interplay between the magnetic field and the spin accumulation could lead to novel bias voltage dependence and magnetic field dependence of the superconducting gap function, and bring in anomalous asymmetry in the spin-dependent transport. Our study also indicates a possible application of the spin injection.     

Magnetization-dependent shift in ferromagnet/superconductor/ferromagnet trilayers with a strong ferromagnet

We have measured the superconducting transition temperature Tc of Ni/Nb/Ni trilayers when the magnetizations of the two outer Ni layers are parallel (P) and antiparallel (AP). The largest difference in occurs when the Nb thickness is just above the critical thickness at which superconductivity disappears completely. We have observed a difference in Tc between the P and AP states as large as 41 mK--a significant increase over earlier results in samples with higher Tc and with a CuNi alloy in place of the Ni. Our result also demonstrates that strong elemental ferromagnets are promising candidates for future investigations of ferromagnet/superconductor heterostructures.     

Zeeman effects on Josephson current in d-wave superconductor/d-wave superconductor junctions

This paper solves a self-consistent equation for the d-wave superconducting gap and the effective exchange field in the mean-field approximation, and studies the Zeeman effects on the d-wave superconducting gap and thermodynamic potential. The Josephson currents in the d-wave superconductor(S)/insulating layer(I)/d-wave S junctions are calculated as a function of the temperature, exchange field, and insulating barrier strength under a Zeeman magnetic field on the two d-wave Ss. It is found that the Josephson critical currents in d-wave S/d-wave S junction to a great extent depend on the relative orientation of the effective exchange field of the two S electrodes, and the crystal orientation of the d-wave S. The exchange field under certain conditions can enhance the Josephson critical current in a d-wave S/I/d-wave S junction.