Resonant Andreev reflection in a normal-metal/quantum-dot/superconductor system with coupled Majorana bound states

Andreev reflection(AR) in a normal-metal/quantum-dot/superconductor(N–QD–S) system with coupled Majorana bound states(MBSs) is investigated theoretically. We find that in the N–QD–S system, the AR can be enhanced when coupling to the MBSs is incorporated. Fano line-shapes can be observed in the AR conductance spectrum when there is an appropriate QD–MBS coupling or MBS–MBS coupling. The AR conductance is always e~2/2h at the zero Fermi energy point when only QD–MBSs coupling is considered. In addition, the resonant AR occurs when the MBS–MBS coupling roughly equals to the QD energy level. We also find that an AR antiresonance appears when the QD energy level approximately equals to the sum of the QD–MBS coupling and the MBS–MBS coupling. These features may serve as characteristic signatures for the probe of MBSs.     

耦合Majorana束缚态T形双量子点中的Andreev反射

研究了连接在正常金属电极和超导电极之间的耦合Majorana束缚态(MBSs)T形双量子点结构中的Andreev反射.研究发现,对于T形双量子点结构,当入射能量等于边耦合量子点能级时Andreev反射电导出现Fano振荡,连接MBSs之后,零费米能附近出现一对新的Fano型振荡峰.如果忽略两个MBSs之间的相互作用,零费米能点的Andreev反射电导为定值1/2G_0(G_0=2e~2/h),不受量子点能级、双量子点之间耦合强度以及量子点与MBSs之间的耦合强度的影响.此外,在没有耦合MBSs的T形双量子点结构中,调节双量子点间的耦合强度可以使零费米能附近的Andreev反射电导出现由共振带向反共振带的转变,而耦合MBSs之后,又可以使反共振消失转而出现新的共振峰.     

Quantum transport through a multi-quantum-dot-pair chain side-coupled with Majorana bound states

We investigate the quantum transport properties through a special kind of quantum dot(QD) system composed of a serially coupled multi-QD-pair(multi-QDP) chain and side-coupled Majorana bound states(MBSs) by using the Green functions method,where the conductance can be classified into two kinds:the electron tunneling(ET) conductance and the Andreev reflection(AR) one.First we find that for the nonzero MBS-QDP coupling a sharp AR-induced zero-bias conductance peak with the height of e~2/h is present(or absent) when the MBS is coupled to the far left(or the other) QDP.Moreover,the MBS-QDP coupling can suppress the ET conductance and strengthen the AR one,and further split into two sub-peaks each of the total conductance peaks of the isolated multi-QDPs,indicating that the MBS will make obvious influences on the competition between the ET and AR processes.Then we find that the tunneling rate ΓLis able to affect the conductances of leads L and R in different ways,demonstrating that there exists a ΓL-related competition between the AR and ET processes.Finally we consider the effect of the inter-MBS coupling on the conductances of the multi-QDP chains and it is shown that the inter-MBS coupling will split the zero-bias conductance peak with the height of e~2/h into two sub-peaks.As the inter-MBS coupling becomes stronger,the two sub-peaks are pushed away from each other and simultaneously become lower,which is opposite to that of the single QDP chain where the two sub-peaks with the height of about e~2/2h become higher.Also,the decay of the conductance sub-peaks with the increase of the MBS-QDP coupling becomes slower as the number of the QDPs becomes larger.This research should be an important extension in studying the transport properties in the kind of QD systems coupled with the side MBSs,which is helpful for understanding the nature of the MBSs,as well as the MBS-related QD transport properties.     

Majorana fermion modulated nonequilibrium transport through double quantum dots

Nonequilibrium electronic transports through a double-QD-Majorana coupling system are studied with a purpose to extract the information to identify Majorana bound states (MBSs). It is found that MBSs can help form various transport processes, including the nonlocal crossed Andreev reflection, local resonant Andreev reflection, and cotunneling, depending on the relative position of two dot levels. These processes enrich the signature of average currents and noise correlations to probe the nature of MBSs. We further demonstrate the switching between the current peaks of crossed Andreev reflection and cotunneling, which is closely related to the nonlocal nature of Majorana fermions. We also propose effective physical pictures to understand these Majorana-assisted transports.     

Spin-dependent Andreev reflection in a three-terminal Aharonov-Bohm interferometer with coherent indirect coupling

Within the framework of non-equilibrium Green’s functions, we investigate the spin-dependent Andreev reflection (AR) in a three-terminal Aharonov-Bohm interferometer with double quantum dot, taking account of the coherent indirect coupling via the superconducting reservoir. It is found that the time-reversal symmetry is broken by the crossed Andreev reflection (CAR) process, and moreover that the spin-value effect of the linear conductance, the spin-polarised AR current, and a pure spin current can be generated by means of the normal AR and the CAR. Expressions for the AR conductances (the transport coefficients) governing the AR properties of this system are derived analytically. The effect of the coherent indirect coupling on the conductance, the Andreev reflected tunneling magnetoresistance (ARTMR), and the spin-related current in the presence of the AR are amply analyzed. Our results indicate that the optimal properties of this system can be realised by tuning the external parameters.     

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.     

Fano‐Majorana Effect and Bound States in the Continuum on a Crossbar‐Shaped Quantum Dot Hybrid Structure

Transport properties are investigated through a crossbar‐shaped structure formed by a quantum dot (QD) coupled to two normal leads and embedded between two 1D topological superconductors (TSCs). Each TSC hosts Majorana‐bound states (MBSs) at its ends, which can interact between them with an effective coupling strength. A signature of bound states in continuum (BIC) is found in the MBSs spectral function. By allowing finite inter MBSs coupling, BICs splitting is observed and shows projection in transmission for asymmetric coupling case as quasi‐BICs. As a consequence, it is also shown that the Fano effect, arising from interference phenomena between MBSs hybridization trough QD, is observed with a half‐integer amplitude modulation. It is believed that the findings can help to better understand the properties of MBSs and their interplay with QDs.     

Kondo Resonance versus Fano Interference in Double Quantum Dots Coupled to a Two-Lead One-Ring System

We analyse the transport properties of a coupled double quantum dot （DQD） device with one of the dots （QD1） coupled to metallic leads and the other （QD2） embedded in an Aharonov-Bhom （A-B） ring by means of the slaveboson mean-field theory. It is found that in this system, the Kondo resonance and the Fano interference exist simultaneously, the enhancing Kondo effect and the increasing hopping of the QD2-Ring destroy the localized electron state in the QD2 for the QD1-leads, and accordingly, the Fano interference between the DQD-leads and the QD1-leads are suppressed. Under some conditions, the Fano interference can be quenched fully and the single Kondo resonance of the QD1-leads comes into being. Moreover, when the magnetic flux of the A-B ring is zero, the influence of the parity of the A-B ring on the transport properties is very weak, but this influence becomes more obvious with non-zero magnetic flux. Thus this model may be a candidate for future device applications.     

Effect of Intra-Dot Coulomb Interaction on Andreev Reflection in Normal-Metal/Quantum-Dot/Superconductor System

We investigate the effect of intra-dot Coulomb interaction on the Andreev reflection in a normal-metal/quantum-dot/superconductor (N-QD-S) system with multiple levels in the quantum dot, in the regime where the intra-dot interacting constant is comparable to the energy gap of superconducting lead. By using nonequilibrium Green function method, the averaged occupation of electrons in the quantum dot and the Andreev reflection (AR) current are studied. Comparing to the case of non-interacting quantum dot, the system shows significant changes for the averaged occupation of electrons in QD (〈n〉) and the AR current (I). (i) In the linear response regime, 〈n〉-V_g exhibits a two-step-like behavior; and the I-V_g shows two groups of peaks, separated by U and with equal heights, where V_g is the gate voltage and U denotes the intra-dot Coulomb interaction constant. (ii) For finite bias voltage, dips, superposed on the step-like 〈n〉-V_g curve, and the current peaks appear simultaneously, both originate from the AR processes. For V≥U/2, extra AR current peaks occur between the two groups of the peaks. Besides, the properties of the heights of the AR current peaks are more complicated.     

Crossed Andreev reflection in a quantum dot coupled to a topological superconducting single-stranded DNA

We investigate the crossed Andreev reflection (CAR) through a quantum dot (QD) coupled to topological superconducting single-stranded DNA (ssDNA). It is found that the topological nontrivial states appear in the QD due to leakage of the Majorana zero mode. Majorana zero mode can be identified by measuring the CAR. This device can be used as a Majorana zero mode detector that relies on the system parameters, such as the spin orbit coupling, the twist angle, molecular length. A high efficiency Cooper pair splitter can be realized by regulating the magnitude and direction of the gate voltage. In additions, the signature of CAR is robust against the Coulomb blockade and the disorder induced by distinct amino acids. This work provides an alternative method for detection of Majorana zero mode in ssDNA.     

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.     

Strong decays of the low-lying bottom strange baryons

Andreev reflection(AR) refers to the electron-hole conversion at the normal metal-superconductor interface. In a threedimensional metal with a spherical Fermi surface, retro(specular) AR can occur with the sign reversal of all three(a single)components of particle velocity. Here, we predict a novel type of AR with the inversion of two velocity components, dubbed"anomalous Andreev reflection"(AAR), which can be realized in a class of materials with a torus-shaped Fermi surface, such as doped nodal line semimetals. For its toroidal circle perpendicular to the interface, the Fermi torus doubles the AR channels and generates multiple AR processes. In particular, the AAR and retro AR are found to dominate electron transport in the light and heavy doping regimes, respectively. We show that the AAR visibly manifests itself as a ridge structure in the spatially resolved nonlocal conductance, in contrast to the peak structure for the retro AR. Our work opens a new avenue for the AR spectroscopy and offers a clear transport signature of the torus-shaped Fermi surface.     

Influence of Majorana Bound States in Quantum Rings

A quantum ring coupled to a 1D topological superconductor hosting Majorana bound states (MBSs) is investigated. The MBSs effects over the spectrum and persistent current along the quantum ring are studied. The spectra of the system are obtained by an exact numerical diagonalization of the Bogoliubov-de Gennes Hamiltonian in the Majorana representation. In addition, Green's function formalism is implemented for analytical calculations and obtained a switching condition in the MBSs fermionic parity. Three different patterns that could be obtained for the spatial separation of the MBSs, named: bowtie, diamond, and asymmetric, are reported here, which are present only in odd parity in the quantum ring, while only a single pattern (bowtie) is obtained for even parity. Those patterns are subject strictly to the switching condition for the MBSs. Besides, quantum ring with the presence of a Majorana zero mode presents gapped/gapless spectra in odd/even parity showing in the even case a subtle signature in the persistent current.     

Influence of intradot Coulomb correlations on the Andreev reflection in a ferromagnetic metal/quantum dot/superconductor hybrid junction

Spin-dependent tunneling through a quantum dot coupled to one ferromagnetic and onesuperconducting electrodes is studied in the Andreev reflection (AR) regime. Electricalconductance is calculated within the nonequilibrium Green function technique. Features ofthe AR current involved by the intradot Coulomb correlations (or the dot’s chargingenergy U) and in the presence of the Zeeman splitting of the dotdiscrete level are analyzed in both linear and nonlinear transport regimes. A newinterference effect due to AR is predicted to appear in the case of a weak on-dotrepulsion. Strong Coulomb correlations studied in nonequilibrium situation revealedsignificant modifications of the AR differential conductance occurring only in case ofspin-polarized transmission. Origin of a variety of the multipeak structure of theconductance for the system with the interacting quantum dot, as well as the conditions forthe perfect U-dependent AR transmission are also discussed.     

光学微盘腔与三能级量子点系统中的模耦合研究

用一种全量子理论方法研究了波导、光学微盘腔与三能级量子点耦合系统的动力学过程,求出其耦合后的透射模和反射模的解析解. 由于微腔表面粗糙引起反向散射,在微腔内形成两简并回音壁耦合共振模,其耦合率为β;量子点的两激发态分别以耦合率g₁,g₂与回音壁耦合共振模产生耦合. 在实数空间里,得出透射光谱和反射光谱的数值解,这些三能级模型结果比二能级模型结果更接近真实光学微盘腔系统,能更好地显示耦合系统的动力学特性. 关键词： 模耦合 光学微盘腔 三能级量子点 全量子理论     

Majorana fermion realization and relevant transport processes in a triple-quantum dot system

Nonequilibrium electronic transports through a system hosting three quantum dots hybridized with superconductors are investigated. By tuning the relative positions of the dot levels, we illustrate the existence of Majorana fermions and show that the Majorana feimions will either survive separately on single dots or distribute themselves among different dots with tunable probabilities. As a result, different physical mechanisms appear, including local Andreev reflection(LAR),cross Andreev reflection(CAR), and cross resonant tunneling(CRT). The resulting characteristics may be used to reveal the unique properties of Majorana fermions. In addition, we discuss the spin-polarized transports and find a pure spin current and a spin filter effect due to the joint effect of CRT and CAR, which is important for designing spintronic devices.     

Intradot spin-flip Andreev reflection tunneling through a ferromagnet-quantum dot-superconductor system with ac field

We investigate Andreev reflection (AR) tunneling through a ferromagnet-quantum dot-superconductor (F-QD-S) system in the presence of an external ac field. The intradot spin-flip scattering in the QD is involved. Using the nonequilibrium Green function and BCS quasiparticle spectrum for superconductor, time-averaged AR conductance is formulated. The competition between the intradot spin-flip scattering and photon-assisted tunneling dominates the resonant behaviors of the time-averaged AR conductance. For weak intradot spin-flip scattering strengths, the AR conductance shows a series of equal interval resonant levels. However, the single-peak at main resonant level develops into a well-resolved double-peak resonance at a strong intradot spin-flip scattering strength. Remarkable, multiple-photon-assisted tunneling that generates photonic sideband peaks with a variable interval has been found. In addition, the AR conductance-bias voltage characteristic shows a transition between the single-peak to double-peak resonance as the ratio of the two tunneling strengths varies.     

Nonlocal Andreev reflection with Rashba spin-orbital interaction in a triple-quantum-dot ring

We theoretically studied the nonlocal Andreev reflection with Rashba spin-orbital interaction in a triple-quantumdot(QD) ring,which is introduced as Rashba spin-orbital interaction to act locally on one component quantum dot.It is found that the electronic current and spin current are sensitive to the systematic parameters.The interdot spin-flip term does not play a leading role in causing electronic and spin currents.Otherwise the spin precessing term leads to shift of the peaks of the the spin-up and spin-down electronic currents in different directions and results in the spin current.Moreover,the spin-orbital interaction suppresses the nonlocal Andreev reflection,so we cannot obtain the pure spin current.     

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.     

How to distinguish between specular and retroconfigurations for Andreev reflection in graphene rings

We numerically investigate Andreev reflection in a graphene ring with one normal conducting and one superconducting lead by solving the Bogoliubov-de Gennes equation within the Landauer-Büttiker formalism. By tuning chemical potential and bias voltage, it is possible to switch between regimes where electron and hole originate from the same band (retroconfiguration) or from different bands (specular configuration) of the graphene dispersion, respectively. We find that the dominant contributions to the Aharonov-Bohm conductance oscillations in the subgap transport are of period h/2e in retroconfiguration and of period h/e in specular configuration, confirming the predictions obtained from a qualitative analysis of interfering scattering paths. Because of the robustness against disorder and moderate changes to the system, this provides a clear signature to distinguish both types of Andreev reflection processes in graphene.