Magnetic gap effect on the tunneling conductance in a topological insulator ferromagnet/superconductor junction

The tunneling conductance on the surface of a topological-insulator-based ferromagnet/superconductor (F/S) structure is studied where S is an s-wave superconductor with superconducting order parameter ∼Δ. The conductance is calculated based on the BTK formalism. The magnetization in F is applied along the z-direction () in order to induce the energy-mass gaps (m) for the Dirac electrons in the F-region. In this work, the influence of energy gap due to the magnetic field in the F-region on the conductance is emphasized. The Fermi energy mismatch between F (EFF=EF) and S (EFS=EF+U), where the gate potential U is applied to the electrode on top of S, is also considered. As a result, a biased voltage V can cause the conductance switch at eV=Δ, depending on the value of the magnetic field. The conductance is found to be linearly dependent on either m or U. The slope of the curve can also be adjusted. This linear behavior in a topological-insulator-based F/S structure may be valuable for electronic applications of the linear-control-current devices. The tunneling conductances of the quasi-Dirac-particle in a topological-insulator-based F/S junction are quite different from those of a graphene-based F/S junction.     

Tunneling conductance in topological insulator ferromagnet/p-wave superconductor junctions

The tunneling conductance in topological insulator (TI) ferromagnet/p-wave superconductor (FM/pS) junction is studied based on the Blonder–Tinkham–Klapwijk (BTK) theory. The Fermi energy mismatch between FM and pS as well as the finite quasiparticle lifetime are considered. Three kinds of pairings p_x, p_y, and p_x+ip_y-waves for pS are chosen. It is found that the spectrum strongly depend on the magnetic gap, the gate potential, the quasiparticle lifetime as well as the type of the pair potential symmetry. The pair potential symmetry drastically affects the formation of the zero-energy bound states dependent on the magneto effect or the Fermi energy mismatch effect. The finite quasiparticle lifetime effect can suppress the Andreev resonant scattering process at eV=Δ₀ and smear the dips in the conductance.     

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)     

量子线/绝缘层/p波超导体结的隧道谱

用Bogoliubov-de Gennes方程来研究量子线/绝缘层/p波超导体结(q/I/p)中的准粒子输运过程，利用推广的Blonder，Tinkham和Klapwijk模型计算绝对零度和有限温度下q/I/p的一级谐波隧道谱.和量子线/绝缘层/d波超导体结的一级谐波隧道谱不同的是q/I/p的一级谐波隧道谱中存在零偏压电导峰.随着q/I/p中绝缘层的势垒散射增强，q/I/p的一级谐波隧道谱中零偏压电导峰变高.     

Differential conductance in normal-metal/insulator/metal/d-wave superconductor junction carrying a supercurrent

This paper applies the Bogoliubov--de Gennes equation and the Blonder--Tinkham--Klapwijk approach to study the oscillatory behaviour of differential conductance in a normal metal/insulator/metal/d-wave superconductor junction carrying a supercurrent I_s. We find that (i) a three-humped structure appears at a nearly critical supercurrent I_s and z ≈ 0.5 for the normal metal/insulator/metal/d_x² + y²-wave superconductor junction; (ii) the zero-bias conductance peak splits into two peaks with sufficiently large applied current for the normal metal/insulator/metal/d_xy-wave superconductor junction; (iii) the conductance spectrum exhibits oscillating behaviour with the bias voltage and the peaks of the resonances are suppressed by increasing supercurrent I_s.     

Tunneling conductance on surface of topological insulator ferromagnet/insulator/(s- or d-wave) superconductor junction: Effect of magnetically-induced relativistic mass

We investigate the tunneling conductance on the surface of topological insulator ferromagnet (F)/insulator (I)/superconductor (S) junction where superconducting type is either s- or d-wave paring. Topological insulators (TI) are insulating in bulk but conducting on the surface with the Dirac-fermion-like carriers. In contrast to the Dirac fermions in graphene, relativistic mass of the Dirac fermions in TI can be easily caused by applying magnetic field perpendicular to its surface. In this work, we emphatically focus on the effect of the magnetically-induced relativistic mass on the tunneling conductance of a TI-based F/I/S junction. We find that, due to the effect of spinless fermions as carriers in TI, the behavior of the tunneling conductance in a TI-based NIS junction resembles that in a nonmagnetic graphene-based NIS junction. In case of the d-wave paring F/I/S junction, increasing magnetically-induced relativistic mass changes the zero bias conductance dip (peak) to a zero bias conductance peak (dip). This behavior cannot be observed in a graphene-based F/I/S junction.     

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.     

Magnetoresistance in the ferromagnet/insulator/ferromagnet tunnel junction

Recently experiments and theories show that the tunnel magnetoresistance （TMR） does not only depend on the ferromagnetic metal electrodes but also on the insulator. Considering the rough-scattering effect and spin-flip effect in the insulator, this paper investigates the TMR ratio in a ferromagnet/insulator/ferromagnet （FM/I/FM） tunnelling junction by using Slonczewsik＇s model. A more general expression of TMR ratio as a function of barrier height, interface roughness and spin-flip effect is obtained. In lower barrier case, it shows that the TMR ratio depends on the roughscattering effect and spin-flip effect.     

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.     

Spin Josephson current in a ferromagnet/noncentrosymmetric superconductor junction

We investigate the equilibrium spin transport in a ferromagnet/noncentrosymmetric superconductor (FM/NCS) junction where the NCS has a dominant triplet order parameter and helical edge state. Based on the symmetry analysis and numerical calculation, we demonstrate that there is a nonzero spin supercurrent flowing in the junction, which stems from the exchange coupling between the FM magnetization and triplet Cooper-pair spin. It is also found that a transverse spin current other than the helical edge spin current is flowing along the interface of the junction, and its polarization is related to the longitudinal spin supercurrent. Besides, an equilibrium Hall current is also shown to flow along the junction’s interface due to the broken time-reversal symmetry from the FM.     

Ferromagnetic insulator effects in ferromagnetic semiconductor/ferromagnetic insulator/p-wave superconductor junctions

The effect of the ferromagnetic insulator on tunneling conductance in ferromagnetic semiconductor/ferromagnetic insulator/p-wave superconductor (FS/FI/P) junctions is studied based on a scattering theory. Three kinds of pairings for the P side are chosen: p_x, p_{y ,}p_x+ip_y waves. It is shown that the spin filtering effect originating from the exchange field in the FI strongly modifies the normalization conductance. Many novel features including the zero-bias conductance dip and splitting are exhibited for fixed spin polarization in the FS. The tunneling spectrum for the heavy holes is much different from that for the light holes due to the different mismatches in the effective mass and Fermi velocity between FS and P.     

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.     

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.     

Twofold spin-triplet pairing states and tunneling conductance in ferromagnet/ferromagnet/iron pnictide superconductor heterojunctions

By applying an extended eight-component Bogoliubov–de Gennes equation, we study theoretically the tunneling conductance in clean ferromagnet/ferromagnet/iron pnictide superconductor (FM/FM/iron-based SC) heterojunctions. Under the condition of noncollinear magnetizations, twofold novel Andreev reflections exist due to the existence of two bands in the SC, in which the incident electron and the two Andreev-reflected holes, belonging to the same spin subband, form twofold spin-triplet pairing states near the FM/iron-based SC interface. It is shown that the conversions of the conductance not only between the zero-bias peak and valley at zero energy but also between the peaks and dips at two gap energies are strongly dependent on both the interband coupling strength in the SC and the spin polarization in the FM. The qualitative differences from tunneling into a conventional s$s$-wave SC are also presented, which may help with experimentally probing and identifying the antiphase s$s$-wave pairing symmetry in the iron-based SC.     

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.     

正常金属/自旋三重态p波超导体结隧道谱的奇异性

利用Blonder，Tinkham和Klapwijk理论计算了正常金属/绝缘层/正常金属/自旋三重态的p波超导体结的隧道谱和平均电流.计算结果表明：在自旋三重态p波超导结的隧道谱中存在零偏压电导峰、零偏压电导凹陷和双凹陷结构，并有微分电导随偏压震荡的现象出现，在I-V曲线上出现电流台阶.这些结果在理论上支持Sr₂RuO₄的超导态是自旋三重态p波超导态. 关键词： 自旋三重态超导体 p波超导体 隧道谱     

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.     

Switching effects in superconductor/ferromagnet/superconductor graphene junctions

The Josephson effect in the superconductor/ferromagnet/superconductor （SFS） graphene Josephson junction is studied using the Dirac Bogoliubov-de Gennes （DBdG） formalism. It is shown that the SFS graphene junction drives 0–π transition with the increasing of p=h0L/vF？, which captures the effects of both the exchange field and the length of the junction; the spin-down current is dominant. The 0 state is stable for p 〈 pc （critical value pc ≈ 0.80） and the π state is stable for p 〉 pc, where the free energy minima are at φg=0 and φg=π, respectively. The coexistence of the 0 and π states appears in the vicinity of pc.