Conductance in normal metal/insulator/ferromagnetic superconductor tunnel junctions

In this paper, the superconducting order parameter and the energy spectrum of the Bogoliubov excitations are obtained from the Bogoliubov-de Gennes equation for a ferromagnetic superconductor (FS). In the framework of the Blonder-Tinkham-Klapwijk model, we present the differential conductance of the normal metal/insulator/FS junctions. It is shown that the exchange energy h in the FS can lead to the Zeeman splitting of the conductance peaks and the energy difference between the two splitting peaks is equal to 2h. The observation of such Zeeman splitting in the conductance spectrum can be taken as evidence for the coexistence between superconductivity and ferromagnetism.     

NM/FI/NI/FI/NM新型双自旋过滤隧道结的隧穿电导和隧穿磁电阻

在NM/FI/FI/NM型双自旋过滤隧道结(此处NM为非磁金属层，FI为铁磁绝缘体或半导体层)的基础上，我们提出一种NM/FI/NI/FI/NM新型双自旋过滤隧道结(此处NI表示非磁绝缘体或半导体层). 插入NI层的目的是为了避免原双自旋过滤隧道结中相邻FI层界面处磁的耦合作用所导致的对隧穿磁电阻的不利影响. 在自由电子近似的基础上，利用转移矩阵方法，对NM/FI/NI/FI/NM新型双自旋过滤隧道结的隧穿电导、隧穿磁电阻与FI层及NI层厚度的变化关系以及随偏压的变化关系进行了理论研究.计算结果表明，在NM/FI/NI/FI/NM新型双自旋过滤隧道结中仍可以得到很大的TMR值. 关键词： 双自旋过滤隧道结 隧穿磁电阻 非磁绝缘(半导)体间隔层     

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.     

铁磁超导态/绝缘层/自旋三重态p波超导体结的直流Josephson电流

由Bogoliubov-de Gennes方程得到铁磁超导共存态(FS)的自洽方程，利用推广的Furusaki-Tsukada的电流公式计算了铁磁超导态/绝缘层/自旋三重态p波超导体(FS/I/p)结的直流Josephson电流随结的温度、相位差以及FS中磁交换能、结界面的势垒散射强度的变化关系.研究表明：FS中磁交换能、结界面的势垒散射均抑制FS/I/p结的直流Josephson电流.当自旋三重态超导体具有p_x波配对势时，自旋三重态超导体结的直流Josephson电流随结两侧相位差的振荡周期是π. 关键词： 铁磁超导态 自旋三重态超导体 p波超导体 直流Josephson电流     

Josephson effect in supercondutor/ferromagnetic semiconductor/superconductor junctions

Using a general expression for dc Josephson current, we study the Josephson effect in ballistic superconductor (SC)/ferromagnetic semiconductor (FS)/SC junctions, in which the mismatches of the effective mass and Fermi velocity between the FS and SC, spin polarization P in the FS, as well as strengths of potential scattering Z at the interfaces are included. It is shown that in the coherent regime, the oscillatory dependences of the maximum Josephson current on the FS layer thickness L and Josephson current on the macroscopic phase difference φ for the heavy and light holes, resulting from the spin splitting energy gained or lost by a quasiparticle Andreev-reflected at the FS/SC interface, are much different due to the different mismatches in the effective mass and Fermi velocity between the FS and the SC, which is related to the crossovers between positive (0) and negative (π) couplings or equivalently 0 and π junctions. Also, we find that, for the same reason, Z and P are required not to surpass different critical values for the Josephson currents of the heavy and light holes. Furthermore, it is found that, for the dependence of the Josephson current on φ, regardless of how L,Z, and P change, the Josephson junctions do not transit between 0 and π junctions for the light hole.     

Quantum point contact conductance in ferromagnetic semiconductor/superconductor junctions

An extended Blonder-Tinkham-Klapwijk approach is applied to study how the tunneling conductance in ferromagnetic semiconductor/s-wave superconductor (FS/SC) junction, where the FS region is a quantum wire, is manipulated by the mismatches of the effective mass between the FS and SC, spin polarization in the FS, as well as the strength of potential scattering at the interface. It is demonstrated that in the single-mode case they have different influences on the tunneling spectra.     

Josephson current through a ferromagnetic semiconductor/semiconductor/ferromagnetic semiconductor structure

We theoretically calculate the Josephson current for two superconductor/ferromagnetic semiconductor (SC/FS) bilayers separated by a semiconductor (SM) layer. It is found that the critical Josephson current I_C in the junction is strongly determined by not only the relative orientations of the effective exchange field of the two bilayers and scattering potential strengths at the interfaces but also the kinds of holes (the heavy or light) in the two FS layers. Furthermore, a robust approach to measuring the spin polarization P for the heavy and light holes is presented.     

Spin dependent Andreev reflection in ferromagnetic semiconductor/d-wave superconductor ballistic junction

The Andreev reflection (AR) probability and transmission of quasiparticles in ferromagnetic semiconductor/d-wave superconductor (FS/DS) ballistic junctions are studied based on an extended Blonder–Tinkham–Klapwijk (BTK) theory. It is shown that the dependence of AR probability and pair potential on the spin orientation of incident quasiparticles for the heavy holes is much different from that for light holes due to the different mismatches in the effective mass and Fermi velocity between FS and DS. The junction conductance is dominated by the quasiparticles which undergo AR processes with the largest probability, and this provides a method for measuring the spin polarization in FS.     

Asymmetric d-wave superconducting topological insulator in proximity with a magnetic order

In the framework of the Dirac–Bogoliubov–de Gennes formalism, we investigate the transport properties in the surface of a 3-dimensional topological insulator-based hybrid structure, where the ferromagnetic and superconducting orders are simultaneously induced to the surface states via the proximity effect. The superconductor gap is taken to be spin-singlet d-wave symmetry. The asymmetric role of this gap respect to the electron–hole exchange, in one hand, affects the topological insulator superconducting binding excitations and, on the other hand, gives rise to forming distinct Majorana bound states at the ferromagnet/superconductor interface. We propose a topological insulator N/F/FS junction and proceed to clarify the role of d-wave asymmetry pairing in the resulting subgap and overgap tunneling conductance. The perpendicular component of magnetizations in F and FS regions can be at the parallel and antiparallel configurations leading to capture the experimentally important magnetoresistance (MR) of junction. It is found that the zero-bias conductance is strongly sensitive to the magnitude of magnetization in FS region $m_{zfs}$ and orbital rotated angle α of superconductor gap. The negative MR only occurs in zero orbital rotated angle. This result can pave the way to distinguish the unconventional superconducting state in the relating topological insulator hybrid 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.     

Spin-dependent proximity effects in ferromagnetic semiconductor/superconductor structures

Proximity effects in normal metal/insulator/ferromagnetic semiconductor/superconductor (NM/I/FS/SC) and NM/I/SC/FS junctions are studied based on an extended Blonder-Tinkham-Klapwijk (BTK) theory. It is found that the magnitude of the proximity effects depends to a great extent on the mismatches of the effective mass and band between the FS and SC. For NM/I/FS/SC junction, the transition of the tunneling conductance from “0” to “π” state is determined by the mass, magnetic exchange energy in FS and the thickness of FS. For NM/I/SC/FS junctions, the conductance spectrum is spin-dependent, indicating a local coexistence of weak ferromagnetism and s-wave superconductivity.     

Universal behaviors of magnon-mediated spin transport in disordered nonmagnetic metal-ferromagnetic insulator heterostructures

We numerically investigate magnon-mediated spin transport through nonmagnetic metal/ferromagnetic insulator (NM/FI) heterostructures in the presence of Anderson disorder, and discover universal behaviors of the spin conductance in both one-dimensional (1D) and 2D systems. In the localized regime, the variance of logarithmic spin conductance σ²(lnG_T) shows a universal linear scaling with its average ⟨lnG_T⟩, independent of Fermi energy, temperature, and system size in both 1D and 2D cases. In 2D, the competition between disorder-enhanced density of states at the NM/FI interface and disorder-suppressed spin transport leads to a non-monotonic dependence of average spin conductance on the disorder strength. As a result, in the metallic regime, average spin conductance is enhanced by disorder, and a new linear scaling between spin conductance fluctuation rms(G_T) and average spin conductance G_T is revealed which is universal at large system width. These universal scaling behaviors suggest that spin transport mediated by magnon in disordered 2D NM/FI systems belongs to a new universality class, different from that of charge conductance in 2D normal metal systems.     

Quantum modulation effect in a graphene-based magnetic tunnel junction

The electronic (quantum) transport in a NG/F_B/FG tunnel junction (where NG, F_B and FG are a normal graphene layer, a ferromagnetic barrier connected to a gate and a ferromagnetic graphene layer, respectively) is investigated. The motions of the electrons in the graphene layers are taken to be governed by the Dirac Equation. Parallel (P) and antiparallel alignment (AP) of the magnetizations in the barrier and in the ferromagnetic graphene are considered. Our work focuses on the oscillation of the electrical conductance (Gq), of the spin conductance (Gs) and of the tunneling magneto resistance (TMR) of this magnetic tunnel junction. We find that, the quantum modulation due to the effect of the exchange field in F_B will be seen in the plots the conductance and of the TMR as functions of the thickness of ferromagnetic barrier (L). The period of two multiplied sinusoidal terms of the modulation are seen to be controlled by varying the gate potential and the exchange field of the F_B layer. The phenomenon, a quantum beating, is built up with two oscillating spin conductance components which have different periods of oscillation related to the splitting of Dirac's energies in the F_B region. The amplitudes of oscillations of Gq, Gs and TMR are not seen to decrease as the thickness increases. The decaying behaviors seen in the conventional transport through an insulator do not appear.     

Magneto transport on the surface of a topological insulator spin valve

The effects of the magnetization on the transport properties of a ferromagnet/barrier/ferromagnet spin valve fabricated with a topological insulator are studied. We consider two types of junctions, (i) an F₁/normal barrier (NB)/F₂ junction and (ii) an F₁/magnetic barrier (FB)/F₂ junction. The junctions in both cases lie in the xy-plane with the magnetizations in both ferromagnetic regions, F₁ and F₂ aligned in the z-direction. The charge carriers in the topological insulator have a Dirac like energy spectrum of a massive relativistic particle with the magnetization M playing the role of the mass. The gap opening is a special magneto feature of topological insulators. In an anti parallel alignment of the two magnetizations, the mass of the carriers is negative in the region where M is in the negative direction. The negative mass leads the behaviors of the magneto transport properties and the tunneling magneto resistance of these junctions to be quite different from those of graphene-based spin values.     

Spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator junction: The role of interface

The spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator (TI) junction is investigated numerically. It is shown that the transport properties of the hybrid junction strongly depend on the interface shape. For the junction with two sharp interfaces, a nonzero spin conductance can be generated besides the spin-split energy windows. Moreover, the axial symmetries of the in-plane spin conductance amplitude are broken. The underlying physics is attributed to the sharp-interface-induced quantum interference effect. However, for the hybrid junction with two smooth interfaces, a non-zero spin conductance can only be achieved in the spin-split energy windows. Further, the axial symmetries of the in-plane spin conductance amplitude recover. These findings may not only benefit to further apprehend the spin-dependent edge states transport in the hybrid TI junctions but also provide some theoretical bases to the application of the topological spintronics devices.     

Magnetic disorder induced enhanced magneto-resistance in La0.5Sr0.5Co1−xRuxO3

We observe a sharp increase in negative magneto-resistance ratio up to 40% for x=0.1, in La_0.5Sr_0.5Co_1−xRu_xO₃ which is due to the magnetic disorder induced by an anti-ferromagnetic interaction between Co and Ru ions. We also observe a metal to insulator and a ferromagnetic to anti-ferromagnetic transition for 0≤x≤0.3. Ruthenium (IV) ion disrupts an intermediate spin state of cobalt (Co³⁺:t_2g⁵e_g¹), forcing a double exchange mediated ferromagnetic state to an anti-ferromagnetic spin state for x≥0.2.     

Possible mechanism for tunneling magnetoresistance in La0.9Ba0.1MnO3/Nb-doped SrTiO3 p-n junctions

The observed tunneling magnetoresistance (TMR) effect in La_0.9Ba_0.1MnO₃ (LBMO)/Nb-doped SrTiO₃ (Nb-STO) p⁺-n junctions is investigated and a possible mechanism responsible for the TMR generation is proposed by taking into account the dynamic spin accumulation and paramagnetic magnetization in the Nb-STO layer. Because of carrier diffusion across the dynamic domain boundaries in the Nb-STO layer and spin disordering in the LBMO layer, the tunneling resistance through the junction is high at zero magnetic field. The spin disordering is suppressed upon applying a non-zero magnetic field, which results in the spin-polarized tunneling in this ferromagnetic/depletion layer/dynamic ferromagnetic sandwiched structure and thus the observed TMR effect. The dependence of the TMR effect on the domain size in the LBMO layer, the tunneling current and temperature as well is explained, qualitatively consistent with the experimental observation.     

Electrically controllable conductance and tunneling magnetoresistance through a topological insulator quantum well coupled to ferromagnetic electrodes

We theoretically investigate the electrically controllable conductance and tunneling magnetoresistance (TMR) through a two-dimensional topological insulator (TI) quantum well sandwiched between ferromagnetic (FM) electrodes in the method of nonequilibrium Green’s function (GF). It is demonstrated that the inter-edge tunnelings modulated conductance for spin-up and spin-down carriers presents an opposite tend with the polarization of the FM electrodes. The system TMR from the spin-valve effect is observed to be up to 65,000 %, as can be significantly suppressed and enhanced by the backscattering and spin-dephasing effect of the inter-edge spin-conserving and spin-flipping tunneling, respectively, other than the quite different energy-dependent oscillation behavior. The obtained results may provide a deeper understanding of the TI edge states and be used to design a dissipationless spintronic device based on TIs.     

Spin transistor and quantum spin Hall-effects in CdBxF2−x–p-CdF2–CdBxF2−x sandwich nanostructures

Planar CdB_xF_2−x–p-CdF₂–CdB_xF_2−x sandwich nanostructures prepared on the surface of the n-type CdF₂ bulk crystal are studied to register the spin transistor and quantum spin Hall-effects. The current–voltage characteristics of the ultra-shallow p⁺–n junctions verify the CdF₂ gap, 7.8 eV, and the quantum subbands of the 2D holes in the p-type CdF₂ quantum well confined by the CdB_xF_2−xδ-barriers. The temperature and magnetic field dependencies of the resistance, specific heat and magnetic susceptibility demonstrate the high temperature superconductor properties for the CdB_xF_2−xδ-barriers. The value of the superconductor energy gap, 2Δ = 102.06 meV, determined by the tunneling spectroscopy method appears to be in a good agreement with the relationship between the zero-resistance supercurrent in superconductor state and the conductance in normal state, πΔ/e, at the energies of the 2D hole subbands. The results obtained are evidence of the important role of the multiple Andreev reflections in the creation of the high spin polarization of the 2D holes in the edged channels of the sandwich device. The high spin hole polarization in the edged channels is shown to identify the mechanism of the spin transistor and quantum spin Hall-effects induced by varying the top gate voltage, which is revealed by the first observation of the Hall quantum conductance staircase.     

Bound states induced by a ferromagnetic delta-layer inserted into a three-dimensional topological insulator

We report on theoretical study of the bound electron states induced by a ferromagnetic delta-layer embedded into a narrow-band-gap semiconductor of the Bi₂Se₃-type which is a three-dimensional topological insulator with large spin-orbit coupling. We make use of an effective Hamiltonian taking into account the inverted band structure of the semiconductor host at the ?? point and describe the properties of the in-gap bound states: energy spectrum, characteristic length and spin polarization. We highlight a role of these states for a magnetic proximity effect in digital magnetic heterostructures based on the Bi₂Se₃-type semiconductors.