We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign. Experimental signatures of the effect include a non-monotonic magnetoconductance curve and a transition from an insulator-like to a metal-like temperature dependence of the conductance. Our results are applicable to ballistic or disordered dots.
We study the transport properties of low-energy (quasi)particles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We consider four different geometrical setups and focus on the dependence of transport on the strength of an applied magnetic field. By solving the classical equations of motion for each setup we calculate the magnetoconductance in terms of transmission and reflection coefficients for both the normal and Andreev versions of the billiard, calculating in the latter the critical field value above which the outgoing current of holes…
We have measured the electromagnetic response of micron-size isolated mesoscopic GaAs/GaAlAs square dots down to temperature T=16mK, by coupling them to an electromagnetic micro-resonator. Both dissipative and non dissipative responses exhibit a large magnetic field dependent quantum correction, with a characteristic flux scale which corresponds to a flux quantum in a dot. The real (dissipative) magnetoconductance changes sign as a function of frequency for low enough density of electrons. The signal observed at frequency below the mean level spacing corresponds to a negative magnetoconductanc…
The magnetoconductance G in chaotic quantum dots at medium/high magnetic fluxes Phi is calculated by means of a tight binding Hamiltonian on a square lattice. Chaotic dots are simulated by introducing diagonal disorder on surface sites of L x L clusters. It is shown that when the ratio W/L is sufficiently large, W being the leads width, G increases steadily showing a maximum at a flux Phi_max ~ W. Bulk disordered ballistic cavities (with an amount of impurities proportional to L) does not show this effect. On the other hand, for magnetic fluxes larger than that for which the cyclotron radius i…
The mechanism of the magnetoconductance oscillations in junctions of a ballistic semiconductor and a superconductor is discussed. The oscillations appear when both the normal and the Andreev reflection occur at the interface. The interplay between the classical cyclotron motion of a quasiparticle and the phase shift caused by the magnetic field is the origin of the conductance oscillations.
We have studied the magnetoconductance of quantum dots with triangular symmetry and areas down to 0.2 square microns, made in a high mobility two-dimensional electron gas embedded in a GaAs-AlGaAs heterostructure. Semiclassical simulations show that the gross features in the measured magnetoconductance are caused by ballistic effects. Below 1 K we observe a strong periodic oscillation, which may be explained in terms of the Aharanov-Bohm flux quantization through the area of a single classical periodic orbit. From a numerical and analytical analysis of possible trajectories in hard- and soft-w…
Employing oval shaped quantum billiards connected by quantum wires as the building blocks of a linear quantum dot array, we calculate the ballistic magnetoconductance in the linear response regime. Optimizing the geometry of the billiards, we aim at a maximal finite- over zero-field ratio of the magnetoconductance. This switching effect arises from a relative phase change of scattering states in the oval quantum dot through the applied magnetic field, which lifts a suppression of the transmission characteristic for a certain range of geometry parameters. It is shown that a sustainable switchin…
Gapped excitation spectra of Andreev states are studied in one- and two-dimensional (1D and 2D) normal systems in superconducting contacts subject to a parallel magnetic field. In the ballistic regime, a specific interplay between magnetic field spin splitting and the effect of a screening supercurrent is found to preserve time-reversal symmetry for certain groups of Andreev states remaining gapped despite the presense of the magnetic field. In 1D wires such states can lead to a fractional thermal magnetoconductance equal to half of the thermal conductance quantum. In 2D systems the thermal ma…
We study resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We obtain a formula for the Andreev current and apply it to discuss the linear and non-linear transport in the nonperturbative regime, where the effects of the Kondo resonance on the two particle tunneling arise. In particular we notice an enhancement of the Kondo anomaly in the $I-V$ characteristics due to the superconducting electrode.
We show that the direction of coherent electron transport across a cyclic system of quantum dots or a cyclic molecule can be modulated by an external magnetic field if the cycle has an odd number of hopping sites, but the transport becomes completely symmetric if the number is even. These contrasting behaviors, which remain in the case of interacting electrons, are a consequence of the absence or presence of alternance symmetry in the system. These findings are relevant for the design of nanocircuits based on coupled quantum dots or molecular junctions.
We present a theory of transport through interacting quantum dots coupled to normal and superconducting leads in the limit of weak tunnel coupling. A Josephson current between two superconducting leads, carried by first-order tunnel processes, can be established by non-equilibrium proximity effect. Both Andreev and Josephson current is suppressed for bias voltages below a threshold set by the Coulomb charging energy. A $π$-transition of the supercurrent can be driven by tuning gate or bias voltages.
In this paper, we investigate the transport through a T-shaped double quantum dot coupled to two normal metal leads left and right and a superconducting lead. Analytical expressions of Andreev transmission and local Density of States of the system at zero temperature have been obtained. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot. We report for first time the Fano effect produced by Andreev bound states in a side quantum dot. Our results show that as a consequence of quantum interference and proximity effect, the transmission …
Electron transport through the Corbino disk in graphene is studied in the presence of uniform magnetic fields. At the Dirac point, we observe conductance oscillations with the flux piercing the disk area $Φ_d$, characterized by the period $Φ_0=(2h/e)\ln(R_o/R_i)$, where $R_o$ ($R_i$) is the outer (inner) disk radius. The oscillations magnitude increase with the radii ratio and exceed 10% of the average conductance for $R_o/R_i\geqslant 5$ in the case of the normal Corbino setup, or for $R_o/R_i\geqslant 2.2$ in the case of the Andreev-Corbino setup. At a finite but weak doping, the oscillation…
We show that a quantum dot connected via tunnel barriers to superconducting leads traps a continuously tunable and hence fractional charge. The fractional charge on the island is due to particle-hole symmetry breaking and can be tuned via a gate potential acting on the dot or via changes in the phase difference across the island. We determine the groundstate, equilibrium, and excitation charges and show how to identify these quantities in an experiment.
We examine the voltage V and magnetic field B dependent Andreev conductance of a chaotic quantum dot coupled via point contacts to a normal metal and a superconductor. In the case where the contact to the superconductor dominates, we find that the conductance is consistent with the dot itself behaving as a superconductor-- it appears as though Andreev reflections are occurring locally at the interface between the normal lead and the dot. This is contrasted against the behaviour of an integrable dot, where for a similar strong coupling to the superconductor, no such effect is seen. The voltage …
We investigate the conductance statistics of a quantum-chaotic dot--a normal-metal grain--with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.
The Coulomb drag effect has been observed as a tiny current induced by both electron-hole asymmetry and interactions in normal coupled quantum dot devices. In the present work we show that the effect can be boosted by replacing one of the normal electrodes by a superconducting one. Moreover, we show that at low temperatures and for sufficiently strong coupling to the superconducting lead, the Coulomb drag is dominated by Andreev processes, is robust against details of the system parameters and can be controlled with a single gate voltage. This mechanism can be distinguished from single-particl…
We experimentally study the electrical transport properties of Ge/Si core/shell nanowire device with two superconducting leads in the Coulomb blockade regime. Anomalous zero field magnetoconductance peaks are observed for the first time at the gate voltages where Coulomb blockade oscillation peaks present. Many evidences indicate this feature is due to Andreev reflection enhanced phase coherent single hole tunneling through the quantum dot, which can be suppressed by an external magnetic field without destroying the superconducting states in the electrodes.
Quantum simulation is a way to study unexplored Hamiltonians by mapping them onto the assemblies of well-understood quantum systems such as ultracold atoms in optical lattices, trapped ions or superconducting circuits. Semiconductor nanostructures which form the backbone of classical computing hold largely untapped potential for quantum simulation. In particular, chains of quantum dots in semiconductor nanowires can be used to emulate one-dimensional Hamiltonians such as the toy model of a topological p-wave superconductor. Here we realize a building block of this model, a double quantum dot w…
Kitaev chain is a theoretical model of a one-dimensional topological superconductor with Majorana zero modes at the two ends of the chain. With the goal of emulating this model, we build a chain of three quantum dots in a semiconductor nanowire. We observe Andreev bound states in each of the three dots and study their magnetic field and gate voltage dependence. Theory indicates that triple dot states acquire Majorana polarization when Andreev states in all three dots reach zero energy in a narrow range of magnetic field. In our device Andreev states in one of the dots reach zero energy at a lo…
Andreev quantum dot (AQD) is a superconducting junction where Bogolyubov quasiparticles can be trapped in discrete Andreev levels. We investigate the feasibility of manipulating individual spin in an AQD. We show that AQD can be brought into spin-1/2 state. The coupling between spin and superconducting current facilitate manipulation and measurement of this state in comparison with common semiconductor quantum dots. We demonstrate that AQD's coupled inductively can serve as a solid-state base for universal quantum computing.
We perform a comparative study of the quantum and classical transport probabilities of low-energy quasiparticles ballistically traversing normal and Andreev two-dimensional open cavities with a Sinai-billiard shape. We focus on the dependence of the transport on the strength of an applied magnetic field $B$. With increasing field strength the classical dynamics changes from mixed to regular phase space. Averaging out the quantum fluctuations, we find an excellent agreement between the quantum and classical transport coefficients in the complete range of field strengths. This allows an overall …
We have studied the Kondo quantum dot coupled to two superconducting leads and investigated the subgap Andreev states using the NRG method. Contrary to the recent NCA results [Clerk and Ambegaokar, Phys. Rev. B 61, 9109 (2000); Sellier et al., Phys. Rev. B 72, 174502 (2005)], we observe Andreev states both below and above the Fermi level.
We study an analytical model of a Rashba nanowire that is partially covered by and coupled to a thin superconducting layer, where the uncovered region of the nanowire forms a quantum dot. We find that, even if there is no topological superconducting phase possible, there is a trivial Andreev bound state that becomes pinned exponentially close to zero energy as a function of magnetic field strength when the length of the quantum dot is tuned with respect to its spin-orbit length such that a resonance condition of Fabry-Perot type is satisfied. In this case, we find that the Andreev bound state …
We study a strongly interacting quantum dot connected to a normal and to a superconducting lead. By means of the slave-boson technique we investigate the low temperature regime and discuss electrical transport through the dot. We find that the zero bias anomaly in the current-voltage characteristics which is associated to the occurance of the Kondo resonance in the quantum dot, is enhanced in the presence of superconductivity, due to resonant Andreev scattering.
We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with sub-gap-peaks at $|V_{sd}|=Δ/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $|V_{sd}|=2Δ/e$ for odd(even) occupation. We attribute the enhanced $Δ$-peak to an interplay between Kondo-correlations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for large Lyapunov exponent and the logarithmic reduction of the gap when the Eh…
We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and non-linear transport in the nonperturbative regime. New effects associated to the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the $I-V$ characteristics depends on the relative size of the gap energy and the Kondo temperature.
We present a numerical study of the emergence of Majorana and Andreev bound states in a system composed by two quantum dots, in which one of then is coupled to a conventional superconductor, SC1, and the other connects to a topological superconductor, SC2. By controlling the interdot coupling we can drive the system from a two single (uncoupled) quantum dots to a double (coupled) dot system configurations. We employ a recursive Green's function technique that provides us with numerically exact results for the local density of states of the system. We first show that in the uncoupled dot config…
Combining scattering matrix formalism with non-linear $σ$-model technique we analyze weak localization effects in arrays of chaotic quantum dots connected via barriers with arbitrary distribution of channel transmissions. With the aid of our approach we evaluate magnetoconductance of two arbitrarily connected quantum dots as well as of $N\times M$ arrays of identical quantum dots.
We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while in NbTiN/InSb devices Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite …
Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this work, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to indiv…
We investigate quantum noise effect on the transportation of nonlocal Cooper pairs accross the realistic Andreev entangler which consists of an s-wave superconductor coupled to two small quantum dots at resonance which themselves are coupled to normal leads. The noise emerges due to voltage fluctuations felt by the electrons residing on the two dots as a result of the finite resistances in the gate leads or of any resistive lead capacitively coupled to the dots. In the ideal noiseless case, the setup provides a trustable source of mobile and nonlocal spin-entangled electrons and the transport …
We investigate the correlation functions of mesoscopic electronic transport in open chaotic quantum dots with finite tunnel barriers in the crossover between Wigner-Dyson ensembles. Using an analytical stub formalism, we show the emergence of a depletion/amplification of conductance fluctuations as a function of tunnel barriers, for both parametric variations of electron energy or magnetoconductance fields. Furthermore, even for pure Dyson ensembles, correlation functions of conductance fluctuations in chaotic quantum dots can exhibit anti-correlation. Experimental support to our findings is p…
We study the transport through side-coupled double quantum dots, connected to normal and superconducting (SC) leads with a T-shape configuration. We find, using the numerical renormalization group, that the Coulomb interaction suppresses SC interference in the side dot, and enhances the conductance substantially in the Kondo regime. This behavior stands in total contrast to a wide Kondo valley seen in the normal transport. The SC proximity penetrating into the interfacial dot pushes the Kondo clouds, which screens the local moment in the side dot, towards the normal lead to make the singlet bo…
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-j…
We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with de…
We study the sub-gap spectrum and the transport properties of a double quantum dot coupled to metallic and superconducting leads. The coupling of both quantum dots to the superconducting lead induces a non-local pairing in both quantum dots by the Andreev reflection processes. Additionally, we obtain two channels of Cooper pair tunneling into a superconducting lead. In such a system, the direct tunneling process (by one of two dots) or the crossed tunneling process (by both quantum dots at the same time) is possible. We consider the dependence of the Andreev transmittance on an inter-dot tunne…
We present a real-time diagrammatic theory for transport through interacting quantum dots tunnel coupled to normal and superconducting leads. Our formulation describes both the equilibrium and non-equilibrium superconducting proximity effect in a quantum dot. We study a three-terminal transistor geometry, consisting of a single-level quantum dot tunnel coupled to two phase-biased superconducting leads and one voltage-biased normal lead. We compute both the Josephson current between the two superconductors and the Andreev current in the normal lead, and analyze their switching on and off as wel…
The Andreev transport through a quantum dot coupled to two external ferromagnetic leads and one superconducting lead is studied theoretically by means of the real-time diagrammatic technique in the sequential and cotunneling regimes. We show that the tunnel magnetoresistance (TMR) of the Andreev current displays a nontrivial dependence on the bias voltage and the level detuning, and can be described by analytical formulas in the zero temperature limit. The cotunneling processes lead to a strong modification of the TMR, which is most visible in the Coulomb blockade regime. We find a zero-bias a…
We study the spin-resolved subgap transport in a triple quantum-dot system coupled to one superconducting and two ferromagnetic leads. We examine the Andreev processes in the parallel and antiparallel alignments of ferromagnets magnetic moments in both the linear and nonlinear response regimes. The emphasis is put on the analysis of the current cross-correlations between the currents flowing through the left and right arms of the device and relevant electron waiting time distributions. We show that both quantities can give an important insight into the subgap transport processes and their anal…
We study the transport properties of a hybrid nanostructure composed of a ferromagnet, two quantum dots, and a superconductor connected in series. By using the non-equilibrium Green's function approach, we have calculated the electric current, the differential conductance and the transmittance for energies within the superconductor gap. In this regime, the mechanism of charge transmission is the Andreev reflection, which allows for a control of the current through the ferromagnet polarization. We have also included interdot and intradot interactions, and have analyzed their influence through a…
We study charge transport through a topological superconductor with a pair of Majorana end states, coupled to leads via quantum dots with resonant levels. The non-locality of the Majorana bound states opens the possibility of crossed Andreev reflection with nonlocal shot noise, due to the injection of an electron into one end of the superconductor followed by the emission of a hole at the other end. In the space of energies of the two resonant quantum dot levels, we find a four peaked clover-like pattern for the strength of noise due to crossed Andreev reflection, distinct from the single elli…
Quantum transport through an impurity-free Corbino disk in bilayer graphene is investigated analytically, by the mode-matching method for effective Dirac equation, in the presence of uniform magnetic fields. Similarly as in the monolayer case (see Refs. [1,2]), conductance at the Dirac point shows oscillations with the flux piercing the disk area $Φ_D$ characterized by the period $Φ_0=2\,(h/e)\ln(R_{\rm o}/R_{\rm i})$, where $R_{\rm o}$ ($R_{\rm i}$) is the outer (inner) disk radius. The oscillations magnitude depends either on the radii ratio or on the physical disk size, with the condition f…
We demonstrate several new electron transport phenomena mediated by Andreev bound states (ABSs) that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state transition S-QD systems can occur. We ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity ex…
Hybrid devices combining quantum dots with superconductors are important building blocks of conventional and topological quantum-information experiments. A requirement for the success of such experiments is to understand the various tunneling-induced non-local interaction mechanisms, namely, crossed Andreev reflection, elastic cotunneling, and direct interdot tunneling, that are present in the device. Here, we provide a theoretical study of a simple device which consists of two quantum dots and a superconductor tunnel-coupled to the dots, often called a Cooper-pair splitter. We study the three…
Shape-averaged magnetoconductance (weak localization) is used for the first time to obtain the electron phase coherence time $τ_ϕ$ in open ballistic GaAs quantum dots. Values for $τ_ϕ$ in the range of temperature T from 0.335 to 4 K are found to be independent of dot area, and are not consistent with the $τ_ϕ \propto T^{-2}$ behavior expected for isolated dots. Surprisingly, $τ_ϕ(T)$ agrees quantitatively with the predicted dephasing time for disordered two-dimensional electron systems.
We propose an all-electrical experimental setup to detect and manipulate the amplitude of odd-frequency pairing in a double quantum dot. Odd-frequency pair amplitude is induced from the breakdown of orbital symmetry when Cooper pairs are injected in the double dot with electrons in different dots. When the dot levels are aligned with the Fermi energy, i.e., on resonance, nonlocal Andreev processes are directly connected to the presence of odd-frequency pairing. Therefore, their amplitude can be manipulated by tuning the level positions. Detection of nonlocal Andreev processes by conductance me…
We study the conductance of normal-superconducting quantum dots with strong spin-orbit scattering, coupled to a source reservoir using a single-mode spin-filtering quantum point contact. The choice of the system is guided by the aim to study triplet Andreev reflection without relying on half metallic materials with specific interface properties. Focusing on the zero temperature, zero-bias regime, we show how dephasing due to the presence of a voltage probe enables the conductance, which vanishes in the quantum limit, to take nonzero values. Concentrating on chaotic quantum dots, we obtain the …
Within random matrix theory for quantum dots, both the dot's one-particle eigenlevels and the dot-lead couplings are statistically distributed. While the effect of the latter on the conductance is obvious and has been taken into account in the literature, the statistical distribution of the one-particle eigenlevels is generally replaced by a picket-fence spectrum. Here we take the random matrix theory eigenlevel distribution explicitly into account and observe significant deviations in the conductance distribution and magnetoconductance of closed quantum dots at experimentally relevant tempera…
Dephasing of one-particle states in closed quantum dots is analyzed within the framework of random matrix theory and Master equation. Combination of this analysis with recent experiments on the magnetoconductance allows for the first time to evaluate the dephasing times of closed quantum dots. These dephasing times turn out to depend on the mean level spacing and to be significantly enhanced as compared with the case of open dots. Moreover, the experimental data available are consistent with the prediction that the dephasing of one-particle states in finite closed systems disappears at low eno…
We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson …
We report on measurements of the magnetoconductance of an open circular InGaAs quantum dot between 1.3K and 204K. We observe two types of magnetoconductance fluctuations: universal conductance fluctuations (UCFs), and 'focusing' fluctuations related to ballistic trajectories between openings. The electron phase coherence time extracted from UCFs amplitude is larger than in GaAs/AlGaAs quantum dots and follows a similar temperature dependence (between T^-1 and T^-2). Below 150K, the characteristic length associated with 'focusing' fluctuations shows a slightly different temperature dependence f…
The Kondo effect in coupled quantum dots is investigated theoretically under magnetic fields. We show that the magnetoconductance (MC) illustrates peak structures of the Kondo resonant spectra. When the dot-dot tunneling coupling $V_C$ is smaller than the dot-lead coupling $Δ$ (level broadening), the Kondo resonant levels appear at the Fermi level ($E_F$). The Zeeman splitting of the levels weakens the Kondo effect, which results in a negative MC. When $V_{C}$ is larger than $Δ$, the Kondo resonances form bonding and anti-bonding levels, located below and above $E_F$, respectively. We observe …
We investigate electronic transport in a three-terminal hybrid system, composed by an interacting quantum dot tunnel coupled to one superconducting, one ferromagnetic, and one normal lead. Despite the tendency of the charging energy to suppress the superconducting proximity effect when the quantum dot is in equilibrium, the non-equilibrium proximity effect can give rise to a large Andreev current. The presence of the ferromagnet can lead to a finite spin accumulation on the dot. We find that the interplay of the Andreev current and spin accumulation can generate a pure spin current, with no as…
