Local Andreev Reflection Research Articles

Majorana fermion modulated nonequilibrium transport through double quantum dots

Abstract 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.

Odd-even effect of transport through a chain of Majorana bound states in a T-shaped junction

We investigate the transport characteristics of a chain of Majorana bound states (MBSs) in a T-shaped junction, where two normal leads are coupled to the same terminate MBS. We find the apparent odd-even effect in the transport process. Namely, when the MBS number is odd, the conductance spectrum exhibits a peak in the zero-bias limit. Besides, the shot noise Fano factor in the zero-bias limit and the conductance maximum are related by equation with . Otherwise, in the case of even-numbered MBSs, at the zero-bias limit, the conductance encounters its zero value, and the relation between F0 and changes as . Further investigation shows that these two kinds of relations are caused by the different interplay mechanisms between the crossed Andreev reflection and the local Andreev reflection. In addition, it is observed that the fluctuation of the inter-MBS couplings contributes little to the transport results. We ascertain that these results are helpful for understanding the MBS signature in transport spectra.

Anomalous quantized conductance in a half-metal/topological superconductor/half-metal junction

The composite topological superconductor (TS), which is made of one-dimensional spin–orbit coupled nanowire with proximity-induced superconductivity from an s-wave superconductor, is not a pure p-wave superconductor, but has a suppressed s-wave pairing. We calculate the conductance spectrum of a half-metal/TS/half-metal junction in order to probe the pairing states and the spin texture of the p-wave pairing. It is found that, besides the regular quantized conductance peak contributed by Majorana fermions (MFs) when the half-metal magnetization is parallel to the MF spin, an anomalous quantized conductance peak exists when they are almost antiparallel. The physical origin is the MF-assisted local Andreev reflection to condense s-wave pairings. The anomalous quantized conductance is also confirmed by the Kitaev's p-wave model with a nonzero s-wave pairing. The findings might provide a new way to find the MF.

Coherent conductance and magnetoresistance in a topological insulator ferromagnet/superconductor/ferromagnet junction

We investigate theoretically the coherent conductance and magnetoresistance in a topological insulator ferromagnet/superconductor/ferromagnet (F/SC/F) junction with perpendicular magnetization. It is shown that there exists a large difference between the coherent conductance of the parallel and antiparallel magnetization configurations, which leads to a large magnetoresistance. The superconductor layer thickness dependence of the magnetoresistance is discussed in terms of the contributions of the local Andreev reflection, electron elastic cotunneling and crossed Andreev reflection to the parallel and antiparallel conductances.

Superconducting proximity effect in silicene: Spin-valley-polarized Andreev reflection, nonlocal transport, and supercurrent

We theoretically study the superconducting proximity effect in silicene, which features massive Dirac fermions with a tunable mass (band gap), and compute the conductance across a normal-superconductor (N-S) silicene junction, the nonlocal conductance of an N-S-N junction, and the supercurrent flowing in an S-N-S junction. It is demonstrated that the transport processes consisting of local and nonlocal Andreev reflection may be efficiently controlled via an external electric field owing to the buckled structure of silicene. In particular, we demonstrate that it is possible to obtain a fully spin-valley-polarized crossed Andreev reflection process without any contamination of elastic cotunneling or local Andreev reflection, in stark contrast to ordinary metals. It is also shown that the supercurrent flowing in the S-N-S junction can be fully spin-valley polarized and that it is controllable by an external electric field.

Numerical model of crossed Andreev reflection and charge imbalance

We present a numerical model of local and nonlocal transport properties in a lateral spin valve structure consisting of two magnetic electrodes in contact with a third perpendicular superconducting electrode. By considering the transport paths for a single electron incident at the local F/S interface---in terms of probabilities of crossed or local Andreev reflection, elastic cotunneling, or quasiparticle transport---we show that this leads to nonlocal charge imbalance. We compare this model with experimental data from an aluminum-permalloy (Al/Py) lateral spin valve geometry device and demonstrate the effectiveness of this simple approach in replicating experimental behavior.

Nonlocal noise cross correlation mediated by entangled Majorana fermions

Due to their nonlocality, qubits nested in Majorana bound states may be the key to realize decoherence-free quantum computation. Majorana bound states could be achieved at the ends of a one-dimensional topological superconductor. However, when the bound states couple directly to electron reservoirs their nonlocal correlation is quenched by local Andreev reflections. Here we propose a scheme to generate nonlocal noise cross correlation between two well-separated quantum dots, mediated by a pair of Majorana bound states. Both positive and negative cross correlations can be obtained by tuning the gate voltages applied to the dots. Within a limited range of finite temperatures, the cross correlation is not suppressed by thermal fluctuations. Furthermore, we show how the local Andreev reflections suppress the noise cross correlation when multiple dot energy levels are coupled to the Majorana bound states. The measurable cross correlation is expected to serve as a sensitive indicator for the generation of Majorana fermions.

Crossed Andreev reflection in a zigzag graphene nanoribbon-superconductor junction

We investigate the crossed Andreev reflection (CAR) in a zigzag graphene nanoribbon/superconductor/nanoribbon junction. It is shown that when the zigzag chain number of the ribbon is even and only the zero-energy mode is involved in transport either the elastic cotunneling or the local Andreev reflection could be entirely suppressed by using a gate voltage whereas a sizable CAR is achieved. When one of the ribbon leads is magnetized not only is the CAR exclusive, but also the spin state of the CAR transmission is nonlocally controllable. The physical origin is the peculiar valley selection rule in the even zigzag graphene nanoribbon. The ideal Cooper-pair splitting in the proposed device holds for all applied bias in the superconducting energy gap.

Adiabatic pumping in a double-dot Cooper-pair beam splitter

We study adiabatic pumping through a double quantum dot coupled to normal and superconducting leads. For this purpose a perturbation expansion in the tunnel coupling between the dots and the normal leads is performed and processes underlying the pumping current are discussed. Features of crossed Andreev reflection are investigated in the average pumped charge and related to local Andreev reflection in a single quantum dot. In order to distinguish Cooper-pair splitting from quasiparticle pumping, we compare the properties of Cooper-pair pumping with single-electron pumping in a system with only normal leads. The dependence on the average dot level and the coupling asymmetry turn out to be the main distinguishing features. This is contrasted with the linear conductance for which it is more difficult to distinguish single-particle from Cooper-pair transport.

Local and nonlocal Andreev reflections in double barrier junctions

We study spin dependent charge transport through a junction, consisting of a superconductor connected to two normal or spin-polarized electrodes. Special attention is paid to a process known as a crossed or nonlocal Andreev reflection. The nonlocal reflection occurs when an incident electron (hole) from one electrode, injected with a subgap energy onto o superconducting layer, transforms into an Andreev hole (electron) in the second lead. When two electrons (holes), forming a Cooper pair, come from the same electrode, the process of the Andreev reflection is local. The coherent spin polarized transport in ferromagnet/superconductor/ferromagnet (F/S/F) double barrier junctions is analyzed using the Bogolubov-de Gennes (BdG) equation with appropriate boundary conditions. We calculate and discuss probabilities of the normal, local and crossed Andreev reflections, as well as probability of the elastic co-tunneling. These processes contribute to tunneling current when the distance between the magnetic electrodes is comparable to the superconducting coherence length. The dependence of the tunneling charge transport on the strength of the exchange field in the ferromagnetic electrodes, and on the height of the tunnel barriers are presented. We also discuss the local and nonlocal spin quantum entanglements of quasiparticle pairs induced by the Andreev reflections in the junction.

Splitting of a Cooper Pair by a Pair of Majorana Bound States

We propose a method to probe the nonlocality of a pair of Majorana bound states by crossed Andreev reflection, which is the injection of an electron into one bound state followed by the emission of a hole by the other (equivalent to the splitting of a Cooper pair). We find that, at sufficiently low excitation energies, this nonlocal scattering process dominates over local Andreev reflection involving a single bound state. As a consequence, the low-temperature and low-frequency fluctuations deltaI(i) of currents into the two bound states i=1, 2 are maximally correlated: deltaI_1deltaI_2[over ]=deltaI_i(2).[over ].

Crossed Andreev Reflection in a Graphene Bipolar Transistor

We investigate the crossed Andreev reflections between two graphene leads connected by a narrow superconductor. When the leads are, respectively, of the n and p type, we find that electron elastic cotunneling and local Andreev reflection are both eliminated even in the absence of any valley-isospin or spin polarizations. We further predict oscillations of both diagonal and cross conductances as a function of the distance between the graphene-superconductor interfaces.

Thouless energy of a superconductor from non local conductance fluctuations

We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections ``internal'' to the superconductor.

Sign of the crossed conductances at a ferromagnet/superconductor/ferromagnet double interface

Crossed conductance in hybrid Ferromagnet / Superconductor / Ferromagnet (FSF) structures results from the competition between normal transmission and Andreev reflection channels. Crossed Andreev reflection (CAR) and elastic cotunneling (EC) between the ferromagnets are dressed by local Andreev reflections, which play an important role for transparent enough interfaces and intermediate spin polarizations. This modifies the simple result previously obtained at lowest order, and can explain the sign of the crossed resistances in a recent experiment [D. Beckmann {\sl et al.}, cond-mat/0404360]. This holds both in the multiterminal hybrid structure model (where phase averaging over the Fermi oscillations is introduced ``by hand'' within the approximation of a single non local process) and for infinite planar interfaces (where phase averaging naturally results in the microscopic solution with multiple non local processes).