Majorana–Kondo interplay in a Majorana wire-quantum dot system with ferromagnetic contacts*

We consider a single-level quantum dot(QD)and a topological superconducting wire hosting Majorana bound states at its ends.By the equation of motion method,we give the analytical Green’s function of the QD in the noninteracting and the infinite interacting case.We study the effects of QD energy level and the spin polarization on the density of states(DOS)and linear conductance of the system.In the noninteracting case,the DOS resonance shifts with the change of energy level and it shows bimodal structure at large spin polarization strength.In the infinite interacting case,the up-spin linear conductance first increases and then decreases with the increase of spin polarization strength,but the down-spin is stable.However,the DOS shows a splitting phenomenon in the large energy level with the increase of spin polarization strength.This provides an interesting way to explore the physical properties of such spin dependent effect in the hybrid Majorana QD systems.     

Influence of Majorana doublet on transport through a quantum dot system with ferromagnetic leads

We investigate the electron transport through a quantum dot connected with two ferromagnetic leads, by coupling one Majorana doublet laterally to the quantum dot. It is found that Majorana doublet keeps the value of zero-bias conductance to be independent of the shift of structural parameters, including dot level, relative lead-magnetization direction, and magnetic field on the dot. Even in the cases of asymmetric dot-lead couplings, the zero-bias conductance is weakly dependent on the relative lead-magnetization direction. On the other hand, when Majorana doublet is replaced by Majorana singlet, the zero-bias conductance value becomes sensitive to the structural parameters. Via analyzing the respective particle motion processes, the different influences of Majorana doublet and singlet are explained. We believe that this work can be helpful for understanding the peculiar properties of Majorana doublet.     

Detection of spin current through a quantum dot with Majorana bound states

The spin transport properties are theoretically investigated when a quantum dot(QD) is side-coupled to Majorana bound states(MBSs) driven by a symmetric dipolar spin battery. It is found that MBSs have a great effect on spin transport properties. The peak-to-valley ratio of the spin current decreases as the coupling strength between the MBS and the QD increases. Moreover, a non-zero charge current with two resonance peaks appears in the system. In the extreme case where the dot–MBS coupling strength is strong enough, the spin current and the charge current are both constants in the non-resonance peak range. When considering the effect of the Zeeman energy, it is interesting that the resonance peak at the higher energy appears one shoulder. And the shoulder turns into a peak when the Zeeman energy is big enough. In addition, the coupling strength between the two MBSs weakens their effects on the currents of the system. These results are helpful for understanding the MBSs signature in the transport spectra.     

Spin valve effect and negative tunnel magnetoresistance in a quantum dot transistor

We study the spin polarized transport through a quantum dot transistor. It is shown that the interplay of large Coulomb interaction and optically induced spin accumulation gives rise to the spin valve effect over a range of bias. We also find negative tunnel magnetoresistance for system with ferromagnetic electrodes.     

Josephson current through a quantum dot molecule with a Majorana zero mode and Andreev bound states

Based on the Green's function method, we investigate the interplay between Majorana zero mode (MZM) and Andreev bound states (ABSs) in a quantum dot molecule side coupled to a topological superconducting nanowire with a pair of MZMs forming a Josephson junction. Since the strong electron–hole asymmetry induced by the nanowire with a topologically non-trivial phase, the MZM suppress the ABSs. The suppression induced by the MZM is robust against the Coulomb repulsion. The interplay between the MZM and the ABSs in Josephson junction presents a feasible experimental means for distinguish between the presence of MZM and ABSs.     

Reprint of : Majorana fermion fingerprints in spin-polarised scanning tunnelling microscopy

We calculate the spatially resolved tunnelling conductance of topological superconductors (TSCs) based on ferromagnetic chains, measured by means of spin-polarised scanning tunnelling microscopy (SPSTM). Our analysis reveals novel signatures of MFs arising from the interplay of their strongly anisotropic spin-polarisation and the magnetisation content of the tip. We focus on the deep Yu–Shiba–Rusinov (YSR) limit where only YSR bound states localised in the vicinity of the adatoms govern the low-energy as also the topological properties of the system. Under these conditions, we investigate the occurrence of zero/finite bias peaks (ZBPs/FBPs) for a single or two coupled TSC chains forming a Josephson junction. Each TSC can host up to two Majorana fermions (MFs) per edge if chiral symmetry is preserved. Here we retrieve the conductance for all the accessible configurations of the MF number of each chain. Our results illustrate innovative spin-polarisation-sensitive experimental routes for arresting the MFs by either restoring or splitting the ZBP in a predictable fashion via: (i) weakly breaking chiral symmetry, e.g. by the SPSTM tip itself or by an external Zeeman field and (ii) tuning the superconducting phase difference of the TSCs, which is encoded in the 4π-Josephson coupling of neighbouring MFs.     

The effects of electric and magnetic fields on the current spin polarization and magnetoresistance in a ferromagnetic/organic semiconductor/ferromagnetic（FM/OSC/FM） system

From experimental results of spin polarized injection and transport in organic semiconductors(OSCs),we theoretically study the current spin polarization and magnetoresistance under an electric and a magnetic field in a ferromagnetic/organic semiconductor/ferromagnetic(FM/OSC/FM) sandwich structure according to the spin drift-diffusion theory and Ohm’s law.From the calculations,it is found that the interfacial current spin polarization is enhanced by several orders of magnitude through tuning the magnetic and electric fields by taking into account the specific characteristics of OSC.Furthermore,the effects of the electric and magnetic fields on the magnetoresistance are also discussed in the sandwich structure.     

Generating and reversing spin accumulation by temperature gradient in a quantum dot attached to ferromagnetic leads

We propose to generate and reverse the spin accumulation in a quantum dot (QD) by using the temperature difference between the two ferromagnetic leads connected to the dot. The electrons are driven purely by the temperature gradient in the absence of an electric bias and a magnetic field. In the Coulomb blockade regime, we find two ways to reverse the spin accumulation. One is by adjusting the QD energy level with a fixed temperature gradient, and the other is by reversing the temperature gradient direction for a fixed value of the dot level. The spin accumulation in the QD can be enhanced by the magnitudes of both the leads’ spin polarization and the asymmetry of the dot-lead coupling strengths. The present device is quite simple, and the obtained results may have practical usage in spintronics or quantum information processing.     

Universal transport properties of a quantum dot system with a laterally-coupled Majorana zero mode

We present a comprehensive analysis about the transport properties of a quantum dot (QD) system with a side-coupled Majorana zero mode. Our calculation result shows that when the coupling manners between the two leads and QDs are identical, the local Andreev reflection and the interlead normal tunneling have the same magnitude at the zero-bias limit. Accordingly, the zero-bias conductance value is always equal to e²/2h, which is exactly one half of the resonant-tunneling conductance. This result is independent of the level number and the level distribution in the single-QD case, and in the coupled-QD case it is irrelevant to the geometry of the QD molecule. The universal transport property is a powerful evidence for the feasibility to detect the MBSs based on a QD circuit. This result also means that the QD condition is not a key factor to achieve the detection. On the other hand, if the decoupling phenomenon appears, the Majorana zero mode may play a trivial role in contributing to the conductance property.     

Bulk—like contribution of tunnel magnetoresistance in magnetic tunnel junctions

We have demonstrated that the bulk-like contribution to tunnelling magnetoresistance (TMR) exists in the magnetic tunnel junctions, and is determined by the tunnelling characteristic length of the ferromagnetic electrodes. In the experiment, a wedge-shaped CoFe layer is inserted at the interface between the insulating barrier and the reference electrode. It is found that TMR ratio increases from 18% without CoFe layer to a saturation value of 26.5% when the CoFe thickness is about 2.3 nm. The tunnelling characteristic length, l_{tc}, can be obtained to be about 0.8 nm for CoFe materials.     

Effects of Majorana bound states on dissipation and charging in a quantum resistor-capacitor circuit

We investigate the effects of Majorana bound states on the ac response of a quantum resistor-capacitor circuit which is composed of a topological superconducting wire whose two ends are tunnel-coupled to a lead and a spinless quantum dot, respectively. The Majorana states formed at the two ends of the wire are found to suppress completely or enhance greatly the dissipation, depending on the strength of the overlap between two Majorana modes and/or the dot level. We compare the relaxation resistance and the quantum capacitance of the system with those of non-Majorana counterparts to find that the effects of the Majorana state on the ac response are genuine and cannot be reproduced in ordinary fermionic systems.     

Spin-polarized current and tunnel magnetoresistance in heterogeneous single-barrier magnetic tunnel junctions

Current in heterogeneous tunnel junctions is studied in the framework of the parabolic conduction-band model. The developed model of the electron tunneling takes explicitly into account the difference of effective masses between ferromagnetic and insulating layers and between conduction subbands. Calculations for Fe/MgO/Fe-like structures have shown the essential impact of effective mass differences in regions (constituents) of the structure on the tunnel magnetoresistance of the junction.     

Phase-and spin-dependent manipulation of leakage of Majorana mode into double quantum dot

We present a phase-and spin-dependent manipulation of leakage of a Majorana mode into a double quantum dot. We study the density of states(DOS) to show the effect of phase change factor on the Majorana leakage into(out) of a double quantum dot. The DOS is derived from the Green's function of the quantum dot by the equation of motion method, and exhibits a formant structure when φ = 0, 2π and a resonance shape when φ = 0.5π and 1.5π. Also, it changes more strongly under the spin-polarized coefficient than the non-polarized lead. Such a theoretical model can be modified to explore the spin-dependent effect in the hybrid Majorana quantum dot system.     

Flux-dependent tunnel magnetoresistance in parallel-coupled double quantum dots

The tunnel magnetoresistance (TMR) in an Aharonov–Bohm interferometer with two quantum dots inserted in its arms, which is attached to ferromagnetic leads with parallel and antiparallel magnetic configurations, is theoretically studied by means of the nonequilibrium Green’s function technique. We pay particular attention to the influence of an applied magnetic flux on the characteristics of the TMR. In the linear response regime (the external bias voltage V→0) and when the electrons are free from intradot Coulomb interaction, the magnetic flux only changes the peak or dip positions of the TMR. But in the presence of intradot Coulomb repulsion, its peak or dip positions, signs and magnitude are tuned by the magnetic flux. For the nonlinear response regime (V≠0), the TMR is symmetric with respect to zero bias voltage and the magnetic flux can influence its magnitude, signs and the peak positions regardless of the existence of intradot Coulomb interaction. The behavior of the TMR is interpreted in terms of the quantum interference (Fano) effect.     

Tunnel magnetoresistance in alumina, magnesia and composite tunnel barrier magnetic tunnel junctions

Using magnetron sputtering, we have prepared Co-Fe-B/tunnel barrier/Co-Fe-B magnetic tunnel junctions with tunnel barriers consisting of alumina, magnesia, and magnesia-alumina bilayer systems. The highest tunnel magnetoresistance ratios we found were 73% for alumina and 323% for magnesia-based tunnel junctions. Additionally, tunnel junctions with a unified layer stack were prepared for the three different barriers. In these systems, the tunnel magnetoresistance ratios at optimum annealing temperatures were found to be 65% for alumina, 173% for magnesia, and 78% for the composite tunnel barriers. The similar tunnel magnetoresistance ratios of the tunnel junctions containing alumina provide evidence that coherent tunneling is suppressed by the alumina layer in the composite tunnel barrier.     

铁磁多层膜中的力致磁电阻效应

通过研究外应力场下铁磁多层膜系统中的自旋结构,讨论了系统磁电阻对外应力的依赖关系.结果表明,外应力能够诱发磁电阻效应,且其磁电阻紧密依赖于外应力的大小和方向.一般地对铁磁性层间耦合,其磁电阻与外应力之间的关系紧密地依赖于两铁磁层的磁致伸缩系数以及磁晶各向异性之差异.具体地,大小一定的外应力由磁易轴向磁难轴旋转的过程中,磁电阻先缓慢增大后急剧减小,在磁难轴附近变化较敏锐,并出现峰值.外应力方向一定时,磁电阻随应力的增大先敏锐增强后缓慢减小,且应力方向偏离磁易轴越远,变化趋势越显著.特别地,当外应力完全垂直于磁易轴时,应力大小的变化会引起磁电阻翻倍.而外应力场介于8πM/5≤H_λ≤18πM/5时,磁电阻会随应力的旋转单调上升,并在磁难轴附近急剧增强,产生GMR效应;对反铁磁性层间耦合,其GMR效应对应力大小和方向的响应近似地相反于铁磁性层间耦合情形. 关键词： 铁磁/非磁/铁磁三层膜 自旋结构 磁电阻 应力场     

Negative tunnelling magnetoresistance in spin filtering magnetic junctions with spin-orbit coupling

We present theoretical calculations of spin transport in spin filtering magnetic tunnelling junctions based on the Landauer-Buttiker formalism and taking into account the spin-orbit coupling(SOC).It is shown that spin-flip scattering induced by SOC is stronger in parallel alignment of magnetization of the ferromegnet barrier(FB) and the ferromagnetic electrode than that in antiparallel case.The increase of negative tunnelling magnetoresistance with bias is in agreement with recent experimental observation.     

A theorem for the existence of Majorana fermion modes in spin-orbit-coupled semiconductors

We prove an index theorem for the existence of Majorana zero modes in a semiconducting thin film with a sizable spin-orbit coupling when it is adjacent to an s-wave superconductor. The theorem, which is analogous to the Jackiw-Rebbi index theorem for the zero modes in mass domain walls in one-dimensional Dirac theory, applies to vortices with odd flux-quantum in a semiconducting film in which s-wave superconductivity and a Zeeman splitting are induced by proximity effect. The momentum space construction of the zero-mode solution presented here is complementary to the approximate real space solution of the Bogoliubov-de Gennes equations at a vortex core (Sau et al., arXiv:0907.2239 [17]), proving the existence of non-degenerate zero-energy Majorana excitations and the resultant non-Abelian topological order in the semiconductor heterostructure. With increasing magnitude of the proximity-induced pairing potential, the non-Abelian superconducting state makes a topological quantum phase transition to an ordinary s-wave superconducting state which no topological order.     

Thermoelectric effects in a double quantum dot system weakly coupled to ferromagnetic leads

Thermoelectric effects through a serial double quantum dot system weakly coupled to ferromagnetic leads are analyzed. Formal expressions of electrical conductance, thermal conductance, and thermal coefficient are obtained by means of Hubbard operators. The results show that although the thermopower is independent of the polarization of the leads, the figure of merit is reduced by an increase of polarization. The influences of temperature and interdot tunneling on the figure of merit are also investigated, and it is observed that increase of the interdot tunneling strength results in reduction of the figure of merit. The effect of temperature on the thermal conductance is also analyzed.     

磁性隧道结的隧穿磁电阻效应及其研究进展

文章概括地介绍了磁性隧道结（MTJs）的隧穿磁电阻（TMR）效应的产生机理和特点,主要用途和研究背景以及最近几年的研究进展和现状.对用Al2O3和MgO做绝缘势垒层的MTJs进行了对比,指出用MgO做绝缘势垒层的MTJs的优点.文章还阐明了交换偏置自旋阀（EB-SV）型MTJs的问题和不足,以及新兴的赝自旋阀（PSV）型MTJs的优势.文章最后总结了用于MTJs的各种铁磁层和绝缘势垒层材料,并对TMR材料今后的研究和开发作了展望.