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.     

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.     

Josephson and Andreev transport through quantum dots

In this article, we review the state of the art on the transport properties of quantum dot systems connected to superconducting and normal electrodes. The review is mainly focused on the theoretical achievements, although a summary of the most relevant experimental results is also given. A large part of the discussion is devoted to the single-level Anderson-type models generalized to include superconductivity in the leads, which already contains most of the interesting physical phenomena. Particular attention is paid to the competition between pairing and Kondo correlations, the emergence of π-junction behavior, the interplay of Andreev and resonant tunneling, and the important role of Andreev bound states that characterized the spectral properties of most of these systems. We give technical details on the several different analytical and numerical methods which have been developed for describing these properties. We further discuss the recent theoretical efforts devoted to extend this analysis to more complex situations like multidot, multilevel or multiterminal configurations in which novel phenomena is expected to emerge. These include control of the localized spin states by a Josephson current and also the possibility of creating entangled electron pairs by means of non-local Andreev processes.     

Confined states in two-dimensional flat elliptic quantum dots and elliptic quantum wires

The energy spectrum and corresponding wave functions of a flat quantum dot with elliptic symmetry are obtained exactly. A detailed study is made of the effect of ellipticity on the energy levels and the corresponding wave functions. The analytical behavior of the energy levels in certain limiting cases is obtained.     

Selecting wave function states in open quantum dots

We study how wave function scarring in an open quantum dot is influenced as the strength of its environmental coupling is varied and show evidence for groups of wave function scars that recur periodically with gate voltage. The precise form of these scars is found to evolve with gate voltage, which we discuss in terms of the properties of the semi-classical orbits that give rise to the scars. We also provide convincing experimental evidence for a correlation between the scars and the oscillations observed in the conductance when the gate voltage is varied.     

Charged magneto-exciton states in semiconductor quantum dots

By embedding a layer of self-assembled quantum dots into a field-effect structure, we are able to control the exciton charge in a single dot. We present the results of photoluminescence experiments as a function of both charge and magnetic field. The results demonstrate a hierarchy of energy scales determined by quantization, the direct Coulomb interaction, the electron–electron exchange interaction, and the electron–hole exchange interaction. For excitons up to the triply charged exciton, the behavior can be understood from a model assuming discrete levels within the quantum dot. For the triply charged exciton, this is no longer the case. In a magnetic field, we discover a coherent interaction with the continuum states, the Landau levels associated with the wetting layer.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.     

Andreev reflection current through a molecule quantum dot in the presence of the electron-phonon interaction and the spin-flip scattering

With the aid of the nonequilibrium Green's function and the Lang-Firsov canonical transformation, we investigate the joint effects of a phononic environment and the spin-flip scattering on the Andreev reflection (AR) in a ferromagnet/single-molecular quantum dot/superconductor (FM/MQD/SC) system. In the presence of the strong electron-phonon interaction (EPI), it is found that the EPI strongly suppresses the AR current (called the Franck-Condon blockade). When the coherent spin-flip (similar to a transverse magnetic field) is taken into account within the MQD, the AR current is significantly enhanced, furthermore, the spin-polarized AR current or even the pure spin-polarized AR current can be generated. By tuning the system parameters, the amplitude and direction of the AR current can be changed, this provides an efficient mechanism for controlling the AR process.     

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.     

Enhancement of charge and spin Seebeck effect in triple quantum dots coupling to ferromagnetic and superconducting electrodes

We theoretically study the thermoelectric transport properties through a triple quantum dots (QDs) device with the central QD coupled to a ferromagnetic lead, a superconducting one, and two side QDs with spin-dependent interdot tunneling coupling. The thermoelectric coefficients are calculated in the linear response regime by means of nonequilibrium Green's function method. The thermopower is determined by the single-electron tunneling processes at the edge of superconducting gap. Near the outside of the gap edge the thermopower is enhanced while thermal conductance is suppressed, as a result, the charge figure of merit can be greatly improved as the gap appropriately increases. In the same way, charge figure of merit also can be greatly improved near the outside of the gap edge by adjusting interdot tunneling coupling and asymmetry coupling of the side QDs to central QD. Moreover, the appropriate increase of the interdot tunneling splitting and spin polarization of ferromagnetic lead not only can improve charge thermopower and charge figure of merit, but also can enhance spin thermopower and spin figure of merit. Especially, the interdot tunneling splitting scheme provides a method of controlling charge (spin) figure merit by external magnetic field.     

Spectrum of Andreev bound states in Josephson junctions with a ferromagnetic insulator

Ferromagnetic-insulator (FI) based Josephson junctions are promising candidates for a coherent superconducting quantum bit as well as a classical superconducting logic circuit. Recently the appearance of an intriguing atomic-scale 0–π$0–\pi$ transition has been theoretically predicted. In order to uncover the mechanism of this phenomena, we numerically calculate the spectrum of Andreev bound states in a FI barrier by diagonalizing the Bogoliubov–de Gennes equation. We show that Andreev spectrum drastically depends on the parity of the FI-layer number L   and accordingly the π(0)$\pi (0)$ state is always more stable than the 0 (π$\pi$) state if L is odd (even).     

Tunable supercurrent in a parallel double quantum dot system

The supercurrent through an Aharonov-Bohm interferometer containing two parallel quantum dots connected with two superconductor leads is investigated theoretically. The possibility of controlling the supercurrent is explored by tuning the quantum dot energy levels and the total magnetic flux. By tuning the energy levels, both quantum dots can be in the on-resonance or off-resonance states, and thus the optimal modulation of the supercurrent can be achieved. The supercurrent sign does not change by simply varying the quantum dot energy levels. However, by tuning the magnetic flux, the supercurrent can oscillate from positive to negative, which results in the π-junction transition.     

A pure spin-current injector of semiconductor quantum dots with Andreev reflection and Rashba spin-orbit coupling

We propose a four-terminal device consisting of two parallel quantum dots with Rashba spin-orbit interaction (RSOI), coupled to two side superconductor leads and two common ferromagnetic leads, respectively. The two ferromagnetic leads and two quantum dots form a ring threaded by Aharonov-Bohm (AB) flux. This device possesses normal quasiparticle transmission between the two ferromagnetic leads, and normal and crossed Andreev reflections providing conductive holes. For the appropriate spin polarization of the ferromagnetic leads, RSOI and AB flux, the pure spin-up (or spin-down) current without net charge current in the right lead, which is due to the equal numbers of electrons and holes with the same spin-polarization moving along the same direction, can be obtained by adjusting the gate voltage, which may be used in practice as a pure spin-current injector.     

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.     

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.     

Zeeman effect and magnetic anomalies in narrow-gap semiconductor quantum dots

We present a systematic theoretical study, based on the Kane–Weiler 8×8 k·p model, of the linear Zeeman splitting introduced by the interaction between the angular momentum and the magnetic field which can give a measure of the non-linear Zeeman effect associated with interband coupling and diamagnetic contributions. The conduction and valence bands g-factors are calculated for InSb spherical and semi-spherical quantum dots. The calculations of the g-factors showed an almost linear dependence, for the ground state, on the magnetic field. We have also found that the strong magnetic field dependence as well as the dependence on the dot size of the effective spin splitting can be unambiguously attributed to the strength of the inter-level mixing.     

Spin-dependent Fano effect through parallel-coupled double quantum dots

Based on the nonequilibrium Green' function method, the spin-dependent Fano effect through parallel-coupled double quantum dots has been investigated by taking account of both Rashba spin-orbit interaction and intradot Coulomb interaction. It is shown that the quantum interference through the bonding, antibonding states and through their Coulomb blockade counterparts may result in two Breit-Wigner resonances and two Fano resonances in the conductance spectra. Moreover, the Fano lineshape of the two spin components can be modulated by Rashba spin-orbit interaction when the magnetic flux is switched on.     

Time-dependent transport through a quantum dot with the over-dot (bridge) additional tunneling channel

The time-dependent electron transport through a quantum dot with the additional over-dot (bridge) tunneling channel within the evolution operator technique has been studied. The microwave field applied to the leads and quantum dot has been considered and influence of the time-dependent shift of corresponding energy levels on the quantum dot charge and current flowing in the system, its time-averaged values and derivatives of the average current with respect to the gate and source–drain bias voltages have been investigated. The influence of the over-dot tunneling channel on the photon-assisted tunneling has been also studied.