We investigate sub-gap transport through a single-level quantum dot tunnel coupled to one superconducting and two normal-conducting leads. Despite the tendency of a large charging energy to suppress the equilibrium proximity effect, a finite Andreev current through the dot can be achieved in non-equilibrium situations. We propose two schemes to identify non-local Andreev transport. In one of them, the presence of strong Coulomb interaction leads to negative values of the non-local conductance as a clear signal of non-local Andreev transport.
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 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.
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 …
A normal metal source reservoir can load two electrons onto a double quantum dot in the spin-triplet configuration. We show that if the drain lead of the dot is a spin-singlet superconductor, these electrons cannot form a Cooper pair and are blockaded on the double dot. We call this phenomenon Andreev blockade because it arises due to suppressed Andreev reflections. We identify transport characteristics unique to Andreev blockade. Most significantly, it occurs for any occupation of the dot adjacent to the superconductor, in contrast with the well-studied Pauli blockade which requires odd occup…
The Andreev spectrum of a quantum dot embedded in a hybrid semiconductor-superconductor interferometer can be modulated by electrostatic gating, magnetic flux through the interferometer, and Zeeman splitting from in-plane magnetic field. We demonstrate parity transitions in the embedded quantum dot system, and show that the Zeeman-driven transition is accompanied by a 0-π transition in the superconducting phase across the dot. We further demonstrate that flux through the interferometer modulates both dot parity and 0-π transitions.
The charge of the subgap states in an Andreev quantum dot (AQD; this is a quantum dot inserted into a superconducting loop) is very sensitive to the magnetic flux threading the loop. We study the sensitivity of this device as a function of its parameters for the limit of a large superconducting gap. In our analysis, we account for the effects of a weak Coulomb interaction within the dot. We discuss the suitability of this setup as a device detecting weak magnetic fields.
We investigate local and nonlocal signatures of hybridization between a quantum dot state and an extended Andreev bound state (ABS) in a gate-defined InAs nanowire with multiple side probes. When a quantum dot in one of the side probes was hybridized with an ABS in the nanowire, a characteristic spectroscopic pattern was observed both locally, i.e., in the probe with the quantum dot, and nonlocally, in the tunnel conductance of a remote probe. Nonlocal signatures of hybridization reveal the extended nature of the ABS.
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…
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.
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…
We study an Andreev quantum dot, that is a quantum dot inserted in a superconducting ring, with several levels or conducting channels. We analyze the degeneracy of the ground state as a function of the phase difference and of the gate voltage and find its dependence on the Coulomb interaction within and between channels. We compute a (non integer) charge of the dot region and Josephson current. The charge-to-phase and current-to-gate voltage sensitivities are studied. We find that, even in the presence of Coulomb interaction between the channels, the sensitivity increases with the number of ch…
We investigate the Andreev transport through double-quantum-dot Cooper pair splitters with ferromagnetic leads. The analysis is performed with the aid of the real-time diagrammatic technique in the sequential tunneling regime. We study the dependence of the Andreev current, the differential conductance, and the tunnel magnetoresistance on various parameters of the model in both the linear and nonlinear response regimes. In particular, we analyze the spin-resolved transport in the crossed Andreev reflection regime, where a blockade of the current occurs due to enhanced occupation of the triplet…
We design and investigate an experimental system capable of entering an electron transport blockade regime in which a spin-triplet localized in the path of current is forbidden from entering a spin-singlet superconductor. To stabilize the triplet a double quantum dot is created electrostatically near a superconducting lead in an InAs nanowire. The dots are filled stochastically with electrons of either spin. The superconducting lead is a molecular beam epitaxy grown Al shell. The shell is etched away over a wire segment to make room for the double dot and the normal metal gold lead. The quantu…
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 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 …
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…
We propose a model for resonant Josephson tunneling through quantum dots that accounts for Cooper pair-breaking processes in the superconducting leads caused by a magnetic field or spin-flip scattering. The pair-breaking effect on the critical supercurrent $I_c$ and the Josephson current-phase relation $I(ϕ)$ is largely due to the modification of the spectrum of Andreev bound states below the reduced (Abrikosov-Gorkov) quasiparticle gap. For a quantum dot formed in a quasi-one-dimensional channel, both $I_c$ and $I(ϕ)$ can show a significant magnetic field dependence induced by pair breaking d…
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…
Andreev bound states (ABSs) are studied in quantum dot coupled to conventional BCS superconducting leads on the basis of effective slave boson Hamiltonian in an infinite-U (Coulomb interaction) limit followed by Green's function technique. From the relevant Green's function, density of states (DOS) is analyzed at different superconducting phase differences. On the basis of numerical computation, it is pointed out from DOS plot that ABSs (sub-gap states) arise due to the phase difference between left and right superconducting leads. Due to the dependence on superconducting phase difference, ABS…
We calculate the current as a function of applied voltage in non-topological s-wave superconductor-quantum dot-topological superconductor tunnel junction. We consider the type of TS which hosts two Majorana bound states (MBS) at the ends of a semiconductor quantum wire or of a chain of magnetic atoms in the proximity with s-wave superconductor. We find that the $I-V$ characteristic of such system in the regime of big voltages has a typical two dot shape and is ornamented by peaks of multiple Andreev reflections. We also consider the other options when the zero energy states are created by diso…
We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift charac…
Resonant tunneling through a quantum dot coupled to superconducting reservoirs in the presence of time-dependent external voltage has been studied. A general formula of the current is derived based on the nonequilibrium Green's function technique. Using this formula photon-assisted quasiparticle transport has been investigated for the quantum dot connected to superconductors. In addition, resonant Andreev transport through a strongly correlated quantum dot connected to a normal metallic lead and a superconducting lead is studied.
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…
We study the Andreev reflection (AR) in a three terminal mesoscopic hybrid system, in which two ferromagnets (F$_1$ and F$_2$) are coupled to a superconductor (S) through a quantum dot (QD). By using non-equilibrium Green function, we derive a general current formula which allows arbitrary spin polarizations, magnetization orientations and bias voltages in F$_1$ and F$_2$. The formula is applied to study both zero bias conductance and finite bias current. The current conducted by crossed AR involving F$_1$, F$_2$ and S is particularly unusual, in which an electron with spin $σ$ incident from o…
In modern experiments with hybrid superconducting (SC)/semiconducting nanowires the presence of zero-energy Andreev bound states (ABSs), characterized by a partial overlap of the Majorana wave functions, is a common problem that significantly complicates the detection of a genuine Majorana bound state (MBS). In this article, taking into account spatial inhomogeneity of experimentally investigated nanowire samples, we study interference transport features of a curved heterostructure in which two normal wires (or arms) are separated by a superconducting wire. Since Andreev reflection on the two …
We study the out-of-equilibrium current through a multilevel quantum dot contacted to two superconducting leads and in the presence of Rashba and Dresselhaus spin-orbit couplings, in the regime of strong dot-lead coupling. The multiple Andreev reflection (MAR) subgap peaks in the current voltage characteristics are found to be modified (but not suppressed) by the spin-orbit interaction, in a way that strongly depends on the shape of the dot confining potential. In a perfectly isotropic dot the MAR peaks are enhanced when the strength $α_R$ and $α_D$ of Rashba and Dresselhaus terms are equal. W…
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…
The quasi-bound states of a superconducting quantum dot that is weakly coupled to a normal metal appear as resonances in the Andreev reflection probability, measured via the differential conductance. We study the evolution of these Andreev resonances when an external parameter (such as magnetic field or gate voltage) is varied, using a random-matrix model for the $N\times N$ scattering matrix. We contrast the two ensembles with broken time-reversal symmetry, in the presence or absence of spin-rotation symmetry (class C or D). The poles of the scattering matrix in the complex plane, encoding th…
Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetrically attached to superconducting leads is studied via the perturbation expansion in the interaction strength. We find the exact asymptotic form of the spin-symmetric solution for the Andreev states continuously approaching the Fermi level. We thereby derive a critical interaction at which the Andreev states at zero temperature merge at the Fermi energy, being the upper bound for the $0-π$ transition. We show that the spin-symmetric solution becomes degenerate beyond this interaction, in the $π$ phase, and the Andre…
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 temper…
We propose a three-terminal structure to probe robust signatures of Majorana zero modes. This structure consists of a quantum dot coupled to the normal metal, s-wave superconducting and Majorana Y-junction leads. The zero-bias differential conductance at zero temperature of the normal-metal lead peaks at $2e^{2}/h$, which will be deflected after Majorana braiding. This quantized conductance can entirely arise from the Majorana-induced crossed Andreev reflection, protected by the energy gap of the superconducting lead. We find that the effect of thermal broadening is significantly suppressed wh…
We consider a quantum dot with mechanical degrees of freedom which is coupled to superconducting electrodes. A Josephson current is generated by applying a phase difference. In the absence of coupling to vibrations, this setup was previously proposed as a detector of magnetic flux and we wish here to address the effect of the phonon coupling to this detection scheme. We compute the charge on the quantum dot and determine its dependence on the phase difference in the presence of phonon coupling and Coulomb interaction. This allows to identify regions in parameter space with the highest charge t…
We study the three terminal S-QD-S-QD-S Josephson junction biased with commensurate voltages. In the absence of an applied voltage, the Andreev bound states on each quantum dot hybridize forming an `Andreev molecule'. However, understanding of this system in a non-equilibrium setup is lacking. Applying a dc voltage on the bijunction makes the system time-periodic, and the equilibrium Andreev bound states evolve into a ladder of resonances with a finite lifetime due to multiple Andreev reflections (MAR). Starting from the time-periodic Bogoliubov-de Gennes equations we map the problem to a tigh…
Sub-gap transport properties of a quantum dot (QD) coupled to two superconducting and one metallic leads are studied theoretically, solving the time-dependent equation of motion by the Laplace transform technique. We focus on time-dependent response of the system induced by a sudden switching on the QD-leads couplings, studying the influence of initial conditions on the transient currents and the differential conductance. We derive analytical expressions for measurable quantities and find that they oscillate in time with the frequency governed by the QD-superconducting lead coupling and acquir…
Phonon-assisted electronic tunnelings through a vibrating quantum dot embedded between normal and superconducting leads are studied in the Kondo regime. In such a hybrid device, with the bias applied to the normal lead, we find a series of Kondo sidebands separated by half a phonon energy in the differential conductance, which are distinct from the phonon-assisted sidebands previously observed in the conventional Andreev tunnelings and in systems with only normal leads. These Kondo sidebands originate from the Kondo-Andreev cooperative cotunneling mediated by phonons, which exhibit a novel Kon…
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 …
Andreev bound state spectroscopy of a quantum-dot-based Aharonov-Bohm interferometer with superconducting terminals
Institute of Physics, Czech Academy of Sciences（捷克科学院物理研究所）；Jožef Stefan Institute（约泽夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）
I discuss thermoelectric properties of a quantum dot coupled to one normal and one superconducting lead in the presence of Kondo effect and Andreev scattering. I will focus on conductance, thermal conductance, thermopower and related quantities like thermoelectric figure of merit which is a direct measure of the usefulness of the system for applications and Wiedemann-Franz ratio which indicates if the system is in the Fermi liquid state. I will show that the superconductivity strongly modifies the thermal properties of the system. In particular, the thermopower is strongly enhanced near the su…
We study the dc-current transport in a voltage biased superconductor-chaotic dot-superconductor junction with an induced proximity effect(PE) in the dot. It is found that for a Thouless energy $E_{Th}$ of the dot smaller than the superconducting energy gap $Δ$, the PE is manifested as peaks in the differential conductance at voltages of order $E_{Th}$ away from the even subharmonic gap structures $eV \approx 2(Δ\pm E_{Th})/2n$. These peaks are insensitive to temperatures $kT \ll Δ$ but are suppressed by a weak magnetic field. The current for suppressed PE is independent of $E_{Th}$ and magneti…
Electrostatic charging affects the many-body spectrum of Andreev states, yet its influence on their microwave properties has not been elucidated. We developed a circuit quantum electrodynamics probe that, in addition to transition spectroscopy, measures the microwave susceptibility of different states of a semiconductor nanowire weak link with a single dominant (spin-degenerate) Andreev level. We found that the microwave susceptibility does not exhibit a particle-hole symmetry, which we qualitatively explain as an influence of Coulomb interaction. Moreover, our state-selective measurement reve…
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…
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 study influence of the phonon modes on a subgap spectrum and Andreev conductance for the double quantum dot vertically coupled between a metallic and superconducting lead. For the monochromatic phonon reservoir we obtain replicas of the interferometric Fano-type structures appearing simultaneously in the particle and hole channels. We furthermore confront the induced on-dot pairing with the electron correlations and investigate how the phonon modes affect the zero-bias signature of the Kondo effect in Andreev conductance.
We investigate the Josephson radiation emitted by a junction made of a quantum dot coupled to two conventional superconductors. Close to resonance, the particle-hole symmetric Andreev states that form in the junction are detached from the continuum above the superconducting gap in the leads, while a gap between them opens near the Fermi level. Under voltage bias, we formulate a stochastic model that accounts for non-adiabatic processes, which change the occupations of the Andreev states. This model allows calculating the current noise spectrum and determining the Fano factor. Analyzing the fin…
A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction $(S_a,S_b,S_c)$ biased with voltages $(V,-V,0)$ is considered, but the conclusions hold more generally for resonant semi-conducting quantum wire set-ups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for $V=0$) evolve into nonequilibrium Floquet-Wann…
We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to re…
We theoretically investigate the behavior of Andreev levels in a single-orbital interacting quantum dot in contact to superconducting leads, focusing on the effect of electrostatic gating and applied magnetic field, as relevant for recent experimental spectroscopic studies. In order to account reliably for spin-polarization effects in presence of correlations, we extend here two simple and complementary approaches that are tailored to capture effective Andreev levels: the static functional renormalization group (fRG) and the self-consistent Andreev bound states (SCABS) theory. We provide bench…
We study charge transport through a metallic dot coupled to a superconducting and a ferromagnetic lead with a precessing magnetization due to ferromagnetic resonance. Using the quasiclassical theory, we find that the magnetization precession induces a dc current in the subgap regime even in the absence of a bias voltage. This effect is due to the rectification of the ac spin currents at the interface with the ferromagnet; it exists in the absence of spin current in the superconductor. When the dot is strongly coupled to the superconductor, we find a strong enhancement in a wide range of parame…
With the aid of the Keldysh technique we develop a microscopic theory of non-local electron transport in three-terminal NSN structures consisting of a chaotic superconducting quantum dot attached to one superconducting and two normal electrodes. Our theory fully accounts for non-equilibrium effects and disorder in a superconducting terminal. We go beyond perturbation theory in tunneling and derive a general expression for the system conductance matrix which remains valid in both weak and strong tunneling limits. We demonstrate that the proximity effect yields a decrease of crossed Andreev refl…
We study subgap transport from a superconductor through a double quantum dot with large on-site Coulomb repulsion to two normal leads. Non-local superconducting correlations in the double dot are induced by the proximity to the superconducting lead, detectable in non-local Andreev transport that splits Cooper pairs in locally separated, spin-entangled electrons. We find that the $I$--$V$ characteristics are strongly asymmetric: for a large bias voltage of certain polarity, transport is blocked by populating the double dot with states whose spin symmetry is incompatible with the superconductor.…
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…
The transport properties of a quantum dot coupled to superconducting leads are analyzed. It is shown that the quasiparticle current in the Kondo regime is determined by the non-equilibrium dynamics of subgap states (Andreev states) under an applied voltage. The current at low bias is suppressed exponentially for decreasing Kondo temperature in agreement with recent experiments. We also predict novel interference effects due to multiple Landau-Zener transitions between Andreev states.
We discuss several scenarios for the creation of nonlocal spin-entangled electrons which provide a source of electronic Einstein-Podolsky-Rosen (EPR) pairs. The central idea is to exploit the spin correlations naturally present in superconductors in form of Cooper pairs. We show that nonlocal spin-entanglement in form of an effective Heisenberg spin interaction is induced between electron spins residing on two quantum dots with no direct coupling between them but each of them being tunnel-coupled to the same superconductor. We then discuss a nonequilibrium setup where mobile and nonlocal spin-…
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…
