Coulomb-assisted nonlocal electron transport between two pairs of Majorana bound states in a superconducting island

We investigate the nonlocal transport modulated by Coulomb interactions in devices comprising two interacting Majorana wires,where both nanowires are in proximity to a mesoscopic superconducting(SC)island.Each Majorana bound state(MBS)is coupled to one lead via a quantum dot with resonant levels.In this device,the nonlocal correlations can be induced in the absence of Majorana energy splitting.We find that the negative differential conductance and giant current noise cross correlation could be induced,due to the interplay between nonlocality of MBSs and dynamical Coulomb blockade effect.This feature may provide a signature for the existence of the MBSs.

Fano Resonances Can Provide Two Criteria to Distinguish Majorana Bound States from Other Candidates in Experiments

There are still debates on whether the observed zero energy peak in the experiment by Stevan et al. [Science 346 （2014） 602] reveals the existence of the long pursued Ala.jorana bound states （MBSs）. We propose that, by mounting two scanning tunneling microscopic tips on top of the topological superconducting chain and measuring the transmission spectrum between these two metallic tips, there are two kinds of characteristics on the spectrum that are caused by A.IBSs uniquely： One is symmetric peaks with respect to zero energy and the other is 4~r period caused by a nearby dosephson junction. The former refers to the fact that MBSs are eomposited by Alajorana fermions which distributed in the particle and hole subspaees equally. The latter is based on the well known 4w period of Josephson effect in topological superconductor. We think that such two characteristics can be used as criteria to distinguish MBSs from other candidates, such as impurities, Kondo effect and traditional Andreev bound states.

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.

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 e2/2h 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.

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.

Probing the Majorana bound states in a hybrid nanowire double-quantum-dot system by scanning tunneling microscopy

We propose an interferometer composing of a scanning tunneling microscope(STM),double quantum dots(DQDs),and a semiconductor nanowire carrying Majorana bound states(MBSs)at its ends induced by the proximity effect of an s-wave superconductor,to probe the existence of the MBSs in the dots.Our results show that when the energy levels of DQDs are aligned to the energy of MBSs,the zero-energy spectral functions of DQDs are always equal to 1/2,which indicates the formation of the MBSs in the DQDs and is also responsible for the zero-bias conductance peak.Our findings suggest that the spectral functions of the DQDs may be an excellent and convenient quantity for detecting the formation and stability of the spatially separated MBSs in quantum dots.

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.

Nonlinear Seebeck and Peltier effects in a Majorana nanowire coupled to leads

We theoretically study nonlinear thermoelectric transport through a topological superconductor nanowire hosting Majorana bound states(MBSs) at its two ends, a system named as Majorana nanowire(MNW). We consider that the MNW is coupled to the left and right normal metallic leads subjected to either bias voltage or temperature gradient. We focus our attention on the sign change of nonlinear Seebeck and Peltier coefficients induced by mechanisms related to the MBSs, by which the possible existence of MBSs might be proved. Our results show that for a fixed temperature difference between the two leads, the sign of the nonlinear Seebeck coefficient(thermopower) can be reversed by changing the overlap amplitude between the MBSs or the system equilibrium temperature, which are similar to the cases in linear response regime. By optimizing the MBS–MBS interaction amplitude and system equilibrium temperature, we find that the temperature difference may also induce sign change of the nonlinear thermopower. For zero temperature difference and finite bias voltage, both the sign and magnitude of nonlinear Peltier coefficient can be adjusted by changing the bias voltage or overlap amplitude between the MBSs. In the presence of both bias voltage and temperature difference, we show that the electrical current at zero Fermi level and the states induced by overlap between the MBSs keep unchanged, regardless of the amplitude of temperature difference. We also find that the direction of the heat current driven by bias voltage may be changed by weak temperature difference.

Thermoelectric signature of Majorana zero modes in a T-typed double-quantum-dot structure

The thermoelectric effect of the system is theoretically investigated,by coupling Majorana zero mode to the T-typed double-quantum-dot-structure in different ways.It is found that when a single Majorana zero mode is coupled to one of the quantum dots(QDs),the thermoelectric efficiency is suppressed due to the leakage of Majorana zero modes into the QDs.When the Majorana zero mode is coupled to QD2,the suppression of the thermoelectric efficiency is more serious than that of QD1.Furthermore,when two Majorana zero modes are introduced simultaneously,suppression of the thermoelectric effect still takes place.We believe that such results can be candidates for the detection of Majorana bound states and help us understand the role of Majorana zero mode in thermoelectricity.

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 whenφ=0,2πand a resonance shape whenφ=0.5πand 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.

多带笼目超导体CsV_(3)Sb_(5)衍生体系的可调磁通涡旋束缚态

Vortices and bound states offer an effective means of comprehending the electronic properties of superconductors.Recently,surface-dependent vortex core states have been observed in the newly discovered kagome superconductors CsV_(3)Sb_(5).Although the spatial distribution of the sharp zero energy conductance peak appears similar to Majorana bound states arising from the superconducting Dirac surface states,its origin remains elusive.In this study,we present observations of tunable vortex bound states(VBSs)in two chemically-doped kagome superconductors Cs(V_(1-x)Tr_(x))_(3)Sb_(5)(Tr=Ta or Ti),using low-temperature scanning tunneling microscopy/spectroscopy.The CsV_(3)Sb_(5)-derived kagome superconductors exhibit full-gap-pairing superconductivity accompanied by the absence of long-range charge orders,in contrast to pristine CsV_(3)Sb_(5).Zero-energy conductance maps demonstrate a field-driven continuous reorientation transition of the vortex lattice,suggesting multiband superconductivity.The Ta-doped CsV_(3)Sb_(5)displays the conventional cross-shaped spatial evolution of Caroli-de Gennes-Matricon bound states,while the Tidoped CsV_(3)Sb_(5)exhibits a sharp,non-split zero-bias conductance peak(ZBCP)that persists over a long distance across the vortex.The spatial evolution of the non-split ZBCP is robust against surface effects and external magnetic field but is related to the doping concentrations.Our study reveals the tunable VBSs in multiband chemically-doped CsV_(3)Sb_(5)system and offers fresh insights into previously reported Y-shaped ZBCP in a non-quantum-limit condition at the surface of kagome superconductor.