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.     

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.     

Suppression of leakage effect of Majorana bound states in the T-shaped quantum-dot structure

We theoretically study the transport properties in the T-shaped double-quantum-dot structure, by considering the dot in the main channel to be coupled to the Majorana bound state(MBS) at one end of the topological superconducting nanowire.It is found that the side-coupled dot governs the effect of the MBS on the transport behavior. When its level is consistent with the energy zero point, the MBS contributes little to the conductance spectrum. Otherwise, the linear conductance exhibits notable changes according to the inter-MBS coupling manners. In the absence of inter-MBS coupling, the linear conductance value keeps equal to e~2/2 h when the level of the side-coupled dot departs from the energy zero point. However,the linear conductance is always analogous to the MBS-absent case once the inter-MBS coupling comes into play. These findings provide new information about the leakage effect of MBSs in quantum-dot structures.     

Electronic transport of a T-shaped double-quantum-dot system in the Coulomb blockade regime

We studied the electronic transport properties of a T-shaped double-quantum-dot system in the Coulomb blockade regime when the onsite Coulomb interaction parameters U ₁ and U ₂ have finite values in both component dots. Our analysis is done in the so-called beyond Hartree-Fock approximation that includes contributions related to both normal and mixed averages of various number-like operators in the system. We provide an analytic formula for the main’s dot Green function in the case of large onsite Coulomb interaction parameters (U ₁ = U ₂ → ∞), and find that with a good approximation, this limit is realized when the ratio U ₁/t = U ₂/t ≥ 30, t being the interdot electron tunneling between the two component dots of the structures. In the most general situation of the Coulomb blockade regime (U ₁ ≠ U ₂) the system conductivity presents two dips corresponding to the Fano-Kondo effect and the system’s shot noise and electronic current present a series of plateaus that should be visible in experimental setups.     

Transport through a quantum dot coupled to two Majorana bound states

We investigate electron transport inside a ring system composed of a quantum dot (QD) coupled to two Majorana bound states confined at the ends of a one-dimensional topological superconductor nanowire. By tuning the magnetic flux threading through the ring, the model system we consider can be switched into states with or without zero-energy modes when the nanowire is in its topological phase. We find that the Fano profile in the conductance spectrum due to the interference between bound and continuum states exhibits markedly different features for these two different situations, which consequently can be used to detect the Majorana zero-energy mode. Most interestingly, as a periodic function of magnetic flux, the conductance shows 2π periodicity when the two Majorana bound states are nonoverlapping (as in an infinitely long nanowire) but displays 4π periodicity when the overlapping becomes nonzero (as in a finite length nanowire). We map the model system into a QD–Kitaev ring in the Majorana fermion representation and affirm these different characteristics by checking the energy spectrum.     

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.     

Kondo transport through a quantum dot coupled with side quantum-dot structures

This paper investigates Kondo transport properties in a quadruple quantum dot (QD) based on the slave-boson mean field theory and the non-equilibrium Green’s function.In the quadruple QD structure one Kondo-type QD sandwiched between two leads is side coupled to two separate QD structures:a single-QD atom and a double-QD molecule.It shows that the conductance valleys and peaks always appear in pairs and by tuning the energy levels in three side QDs,the one-,two-,or three-valley conductance pattern can be obtained.Furthermore,it finds that whether the valley and the peak can appear is closely dependent on the specific values of the interdot couplings and the energy level difference between the two QDs in the molecule.More interestingly,an extra novel conductance peak can be produced by the coexistence of the two different kinds of side QD structures.     

Electronic transport through a periodic array of quantum-dot rings

Using the tight-binding approximation and the transfer matrix method, this paper studies the electronic transport properties through a periodic array of quantum-dot (QD) rings threaded by a magnetic flux. It demonstrates that the even--odd parity of the QD number in a single ring and the number of the QD rings in the array play a crucial role in the electron transmission. For a single QD ring, the resonance and antiresonance transmission depend not only on the applied magnetic flux but also on the difference between the number of QDs on the two arms of the ring. For an array of QD rings, the transmission properties are related not only to the even--odd parity of the number $N_{0}$ of QDs in the single ring but also to the even--odd parity of the ring number $N$ in the array. When the incident electron energy is aligned with the site energy, for the array of $N$ rings with $N_{0}={\rm odd}$ the antiresonance transmission cannot occur but the resonance transmission may occur and the transmission spectrum has $N$ resonance peaks ($N-1$ resonance peaks) in a period for $N={\rm odd}$ (for $N={\rm even}$). For the array of $N$ rings with $N_{0}={\rm even}$ the transmission properties depend on the flux threading the ring and the QD number on one arm of the ring. These results may be helpful in designing QD devices.     

Kondo correlations and Majorana bound states in a metal to quantum-dot to topological-superconductor junction

Electron transport through a normal-metal-quantum-dot-topological-superconductor junction is studied and reveals interlacing physics of Kondo correlations with two Majorana fermions bound states residing on the opposite ends of the topological superconductor. When the strength of the Majorana fermion coupling exceeds the temperature T, this combination of Kondo-Majorana fermion physics might be amenable for an experimental test: The usual peak of the temperature dependent zero bias conductance σ(V=0,T) splits and the conductance has a dip at T=0. The heights of the conductance side peaks decrease with magnetic field.     

Antiresonance and decoupling in electronic transport through parallel-coupled quantum-dot structures with laterally-coupled Majorana zero modes

We theoretically investigate the electronic transport through a parallel-coupled multi-quantum-dot system, in which the terminal dots of a one-dimensional quantum-dot chain are embodied in the two arms of an Aharonov–Bohm interferometer. It is found that in the structures of odd(even) dots, all their even(odd) molecular states have opportunities to decouple from the leads, and in this process antiresonance occurs which are accordant with the odd(even)-numbered eigenenergies of the sub-molecule without terminal dots. Next when Majorana zero modes are introduced to couple laterally to the terminal dots, the antiresonance and decoupling phenomena still co-exist in the quantum transport process. Such a result can be helpful in understanding the special influence of Majorana zero mode on the electronic transport through quantum-dot systems.     

Coulomb interaction and quantum transport through a coherent scatterer

An interplay between charge discreteness, coherent scattering, and Coulomb interaction yields nontrivial effects in quantum transport. We derive a real-time effective action and an equivalent quantum Langevin equation for an arbitrary coherent scatterer and evaluate its current-voltage characteristics in the presence of interactions. Within our model, at large conductances G0 and low T (but outside the instanton-dominated regime), the interaction correction to G0 saturates and causes conductance suppression by a universal factor which depends only on the type of the conductor.     

Electronic transport through a quantum ring coupled to ferromagnetic leads

We study the spin-dependent transport through a one-dimensional quantum ring with taking both the Rashba spin--orbit coupling (RSOC) and ferromagnetic leads into consideration. The linear conductance is obtained by the Green's function method. We find that due to the quantum interference effect arising from the RSOC-induced spin precession phase and the difference in travelling phase between the two arms of the ring, the conductance becomes spin-polarized even in the antiparallel magnetic configuration of the two leads, which is different from the case in single conduction channel system. The linear conductance, the spin polarization and the tunnel magnetoresistance are periodic functions of the two phases, and can be efficiently tuned by the structure parameters.     

嵌入T型耦合双量子点介观A-B环系统的显著Fano 效应

利用平均场近似理论,研究了一个嵌入T型弱耦合双量子点的介观环系统的基态性质. 结果表明,体系中复杂的基态性质源于Kondo效应与Fano效应相互竞争. 当介观环的尺寸达到足以产生完全Kondo共振时,随双量子点间耦合强度的增强,尖锐的持续电流峰出现了,且越发显著,这说明体系中存在着显著的Fano 效应. 但介观环的Kondo共振持续电流峰值却几乎不发生变化,这为测定Kondo 屏蔽云提供了一个新的可能模型. 关键词： 耦合量子点 持续电流 Kondo效应 Fano 效应     

Electron transport through a quantum-dot superlattice

Miniband electron transport through a laterally-confined superlattice is investigated using the balance equation approach. Up to 15 subbands with intraband and interband impurity and phonon scatterings are included. The nonlinear drift velocity and electron temperature, calculated as functions of the applied electric field for systems of varying degrees of confinement, exhibit significant subband effects, and the cross-over from one-dimensional to three-dimensional behavior.     

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.     

Majorana bound state of a Bogoliubov-de Gennes-Dirac Hamiltonian in arbitrary dimensions

We study a Majorana zero-energy state bound to a hedgehog-like point defect in a topological superconductor described by a Bogoliubov-de Gennes (BdG)-Dirac type effective Hamiltonian. We first give an explicit wave function of a Majorana state by solving the BdG equation directly, from which an analytical index can be obtained. Next, by calculating the corresponding topological index, we show a precise equivalence between both indices to confirm the index theorem. Finally, we apply this observation to reexamine the role of another topological invariant, i.e., the Chern number associated with the Berry curvature proposed in the study of protected zero modes along the lines of topological classification of insulators and superconductors. We show that the Chern number is equivalent to the topological index, implying that it indeed reflects the number of zero-energy states. Our theoretical model belongs to the BDI class from the viewpoint of symmetry, whereas the spatial dimension d of the system is left arbitrary throughout the paper.     

Demonstrating nonlocality-induced teleportation through Majorana bound states in a semiconductor nanowire

It was predicted by Tewari et al. (2008) [15] that a teleportation-like electron transfer phenomenon is one of the novel consequences of the existence of Majorana fermion, because of the inherently nonlocal nature. In this work we consider a concrete realization and measurement scheme for this interesting behavior, based on a setup consisting of a pair of quantum dots which are tunnel-coupled to a semiconductor nanowire and are jointly measured by two point-contact detectors. We analyze the teleportation dynamics in the presence of measurement back-action and discuss how the teleportation events can be identified from the current trajectories of strong response detectors.     

The influence of Coulomb interaction on transport through mesoscopic two-barrier structures

We investigate the influence of the Coulomb interaction on the energy spectrum of a finite number of electrons in a geometrically confined quantum mechanical system. The spectrum is calculated numerically using the Slater determinants of the one-electron states as basis set. It is found to be dominated by the Coulomb repulsion when the system is large. Coulomb and exchange matrix elements for a given combination of four one-electron states are of the same order of magnitude. As a consequence, the energy difference between the ground states of the (N+1)- and theN-electron system is an order of magnitude smaller than each of the matrix elements, although being much larger than the separation of the one-electron energy levels. We discuss the importance of the interaction effects for the explanation of the recently observed resonant behavior of the electronic transport through quantum dots.     

Electronic transport through tetrahedron-structured DNA-like system

We theoretically investigate the electronic transport properties of a multi-terminal tetrahedronstructured DNA under a uniform magnetic field. Based on a tight-binding model, the current and nonlocal resistance are calculated under different situations by employing the Landauer–Büttiker formula. Our results indicate that the current displays a clear sign of interference in the presence of the magnetic field and can be mainly divided into three patterns, as demonstrated by the Fourier transformation. Furthermore, the tetrahedron-structured DNA can be used as a molecular switch. The underlying physical mechanisms are analyzed for the various phenomena observed in this threedimensional DNA interferometer.