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.
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev reflection and electron transfer between the two normal metal terminals, in addition to the conductance from direct Andreev reflection and quasiparticle tunneling. Dephasing and proximity effect are taken into account.
The charge character of Andreev bound states (ABSs) in a three-terminal semiconductor-superconductor hybrid nanowire was measured using local and nonlocal tunneling spectroscopy. The device is fabricated using an epitaxial InAs/Al two-dimensional heterostructure with several gate-defined side probes. ABSs are found to oscillate around zero as a function of gate voltage, with modifications of their charge consistent with theoretical expectations for the total Bardeen-Cooper- Schrieffer (BCS) charge of ABSs.
Crossed Andreev reflection in multiterminal structures in the diffusive regime is addressed within the quasiclassical Keldysh-Usadel formalism. The elastic cotunneling and crossed Andreev reflection of quasiparticles give nonlocal currents and voltages (depending on the actual biasing of the devices) by virtue of the induced proximity effect in the normal metal electrodes. The magnitude of the nonlocal processes is found to scale with the square of the barrier transparency and to decay exponentially with interface spacing. Nonlocal cotunneling and crossed Andreev conductances are found to cont…
We propose the "Andreev molecule", an artificial quantum system composed of two closely spaced Josephson junctions. The coupling between Josephson junctions in an Andreev molecule occurs through the overlap and hybridization of the junction's "atomic" orbitals, Andreev Bound States. A striking consequence is that the supercurrent flowing through one junction depends on the superconducting phase difference across the other junction. Using the Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local current-phase relation for arbitrary separation. We demonstrate the possibilit…
Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the loc…
Each end of a Kitaev chain in topological phase hosts a Majorana fermion. Zero bias conductance peak is an evidence of Majorana fermion when the two Majorana fermions are decoupled. These two Majorana fermions are separated in space and this nonlocal aspect can be probed when the two are coupled. Crossed Andreev reflection is the evidence of the nonlocality of Majorana fermions. Nonlocality of Majorana fermions has been proposed to be probed by noise measurements since simple conductance measurements cannot probe it due to the almost cancellation of currents from electron tunneling and crossed…
We study Andreev reflection and Josephson currents in topological bilayer exciton condensates (TEC). These systems can create 100% spin entangled nonlocal currents with high amplitudes due to perfect nonlocal Andreev reflection. This Andreev reflection process can be gate tuned from a regime of purely retro reflection to purely specular reflection. We have studied the bound states in TEC-TI-TEC Josephson junctions and find a gapless dispersion for perpendicular incidence. The presence of a sharp transition in the supercurrent-phase relationship when the system is in equilibrium is a signature …
Crossed Andreev reflection in a lateral spin valve geometry device is an aspect of considerable recent interest, particularly with regards to Cooper pair splitting experiments to realize solid state quantum entanglement. In this work, devices are fabricated consisting of two ferromagnetic permalloy (Py) electrodes contacted by a overlaid perpendicular superconducting Ta electrode, of variable lateral in-plane offset within the expected BCS superconducting coherence length $ξ_0$. Experimental electrical transport measurements are presented of local and nonlocal conduction, showing characteristi…
We show experimentally that in nanometer scaled superconductor/normal metal hybrid devices and in a small window of contact resistances, crossed Andreev reflection (CAR) can dominate the nonlocal transport for all energies below the superconducting gap. Besides CAR, elastic cotunneling (EC) and nonlocal charge imbalance (CI) can be identified as competing subgap transport mechanisms in temperature dependent four-terminal nonlocal measurements. We demonstrate a systematic change of the nonlocal resistance vs. bias characteristics with increasing contact resistances, which can be varied in the f…
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 discuss the phase dependent nonlocal thermoelectric effect in a topological Josephson junction in contact with a normal-metal probe. We show that, due to the helical nature of topological edge states, nonlocal thermoelectricity is generated by a purely Andreev interferometric mechanism. This response can be tuned by imposing a Josephson phase difference, through the application of a dissipationless current between the two superconductors, even without the need of applying an external magnetic field. We discuss in detail the origin of this effect and we provide also a realistic estimation of…
We investigate local and nonlocal entanglement of particle pairs induced by direct and crossed Andreev reflections at the interfaces between a superconductor and two normal conductors. It is shown theoretically that both local and nonlocal entanglement can be quantified by concurrence and detected from the violation of a Bell inequality of spin current correlators, which are determined only by normal reflection and Andreev reflection eigenvalues. There exists a one-to-one correspondence between the concurrence and the maximal Bell-CHSH parameter in the tunneling limit.
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 demonstr…
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 consider transport in a three terminal device attached to one superconducting and two normal metal terminals, using the circuit theory of mesoscopic superconductivity. We compute the nonlocal conductance of the current out of the first normal metal terminal in response to a bias voltage between the second normal metal terminal and the superconducting terminal. The nonlocal conductance is given by competing contributions from crossed Andreev reflection and electron cotunneling, and we determine the contribution from each process. The nonlocal conductance vanishes when there is no resistance …
In this PhD thesis, quantum devices based on molecular-beam epitaxy grown InAs semiconductor with an in-situ grown epitaxial Al film were investigated. Novel device geometries were realized that allow for the study of bound states that emerge at low temperatures in semiconducting nanowires due to the presence of spin-orbit coupling, Zeeman effect, and superconducting proximity effect. Experiments utilizing either gate-defined nanowires in two-dimensional heterostructures or vapor-liquid-solid grown nanowires with a full-shell of Al are presented. Devices and experimental methods were developed…
The proximity effect in hybrid superconductor-semiconductor structures, crucial for realizing Majorana edge modes, is complicated to control due to its dependence on many unknown microscopic parameters. In addition, defects can spoil the induced superconductivity locally in the proximitised system which complicates measuring global properties with a local probe. We show how to use the nonlocal conductance between two spatially separated leads to probe three global properties of a proximitised system: the bulk superconducting gap, the induced gap, and the induced coherence length. Unlike local …
Using a wavefunction Dirac Bogoliubov-de Gennes method, we demonstrate that the tunable Fermi level of a graphene layer in the presence of Rashba spin orbit coupling (RSOC) allows for producing an anomalous nonlocal Andreev reflection and equal spin superconducting triplet pairing. We consider a graphene junction of a ferromagnet-RSOC-superconductor-ferromagnet configuration and study scattering processes, the appearance of spin triplet correlations, and charge conductance in this structure. We show that the anomalous crossed Andreev reflection is linked to the equal spin triplet pairing. More…
Unlike the more common local conductance spectroscopy, nonlocal conductance can differentiate between nontopological zero-energy modes localized around inhomogeneities, and true Majorana edge modes in the topological phase. In particular, negative nonlocal conductance is dominated by the crossed Andreev reflection. In graphene, the Andreev reflection and the inter-band Klein tunneling couple electron-like and hole-like states through the action of either a superconducting (SC) pair potential or an electrostatic potential. We are here probing quantum phenomena in modified graphitic samples. Fou…
A pure spin current injector is proposed based on adiabatic pumping and crossed normal/Andreev reflection. The device consists of a three-terminal ferromagnet-superconductor-semiconductor system in which the injection of a pure spin current is into the semiconductor which is coupled to the superconductor within a coherence length away from the ferromagnet enabling the phenomena of crossed normal /Andreev reflection to operate. Quantum pumping is induced by adiabatically modulating two independent parameters of the ferromagnetic lead, namely the magnetization strength and the strength of coupli…
We report on a novel exchange mechanism, mediating the Kondo screening, in a correlated double quantum dot structure in the proximity of superconductor, stemming from nonlocal Andreev reflection processes. We estimate its strength perturbatively and corroborate analytical predictions with accurate numerical renormalization group calculations using an effective model for the superconductor-proximized nanostructure. We demonstrate that superconductor-induced exchange leads to a two-stage Kondo screening. We determine the dependence of the Kondo temperature on the coupling to superconductor and p…
We study Andreev processes and nonlocal transport in a three-terminal graphene-superconductor hybrid system under a quantizing perpendicular magnetic field [G.-H. Lee et al., Nature Phys. 13, 693 (2017)]. We find that the amplitude of the crossed Andreev reflection (CAR) processes crucially depends on the orientation of the lattice. By employing Landauer-Büttiker scattering theory, we find that CAR is generally very small for a zigzag edge, while for an armchair edge it can be larger than the normal transmission, thereby resulting in a negative nonlocal resistance. In the case of an armchair e…
Indium Arsenide (InAs) near surface quantum wells (QWs) are promising for the fabrication of semiconductor-superconductor heterostructures given that they allow for a strong hybridization between the two-dimensional states in the quantum well and the ones in the superconductor. In this work we present results for InAs QWs in the quantum Hall regime placed in proximity of superconducting NbTiN. We observe a negative downstream resistance with a corresponding reduction of Hall (upstream) resistance, consistent with a very high Andreev conversion. We analyze the experimental data using the Landau…
We study the interband transport in a superconducting device composed of graphene with EuO-induced exchange interaction. We show that pure crossed Andreev reflection can be generated exclusively without the parasitic local Andreev reflection and elastic cotunnelling over a wide range of bias and Fermi levels in an EuO-graphene/superconductor/EuO-graphene device. The pure non-local conductance exhibits rapid on/off switching and oscillatory behavior when the Fermi levels in the normal and the superconducting leads are varied. The oscillation reflects the quasiparticle propagation in the superco…
We present an experimental study of inverted InAs/GaSb composite quantum wells in the hybridization regime and contacted by superconducting electrodes. A front gate is used to vary the Fermi level into the mini-gap, where recent experiments indicate existence of helical edge modes [arXiv:1105.0137]. Zero bias dips in differential resistance are observed across the mini-gap, suggesting transport dominated by Andreev reflection processes. Evolution of the mini-gap differential resistance with applied bias as well as measured mini-gap excess current of 150 nA are in good agreement with the predic…
We consider a hybrid quantum Hall-superconductor system, where a superconducting finger with oblique profile is wedged into a two-dimensional electron gas in the presence of a perpendicular magnetic field, as considered by Lee et al., Nat. Phys. 13, 693 (2017). The electron gas is in the quantum Hall regime at filling factor $ν=1$. Due to the Meissner effect, the perpendicular magnetic field close to the quantum Hall-superconductor boundary is distorted and gives rise to an in-plane component of the magnetic field. This component enables nonlocal crossed Andreev reflection between the spin-pol…
Perfect Cooper pair splitting is proposed, based on crossed Andreev reflection (CAR) in a p-type semiconductor - superconductor - n-type semiconductor (pSn) junction. The ideal splitting is caused by the energy filtering that is enforced by the bandstructure of the electrodes. The pSn junction is modeled by the Bogoliubov-de Gennes equations and an extension of the Blonder-Tinkham-Klapwijk theory beyond the Andreev approximation. Despite a large momentum mismatch, the CAR current is predicted to be large. The proposed straightforward experimental design and the 100% degree of pureness of the n…
We theoretically investigate the subgapped transport phenomena through a normal-superconductor-normal (NSN) junction made up of ultra thin topological insulator with proximity induced superconductivity. The dimensional crossover from three dimensional ($3$D) topological insulator (TI) to thin two-dimensional ($2$D) TI introduces a new degree of freedom, the so-called hybridization or coupling between the two surface states. We explore the role of hybridization in transport properties of the NSN junction, especially how it affects the crossed Andreev reflection (CAR). We observe that a rib-like…
The recent proposals of devices with overlapping Andreev bound states (ABS) open up the opportunities to control and fine-tune their spectrum, that can be used in various applications. In this Article, we study the ABS in a device consisting of a semiconducting nanowire covered with three superconducting leads. The ABS are formed at two junctions where the wire is not covered. They overlap in the wire where the electron propagation is 1D, and in one of the leads where the propagation is 3D. We identify a number of regimes where these two overlaps either dominate or compete, depending on the ju…
We study the low-energy transport properties of a hybrid device composed by a native quantum dot coupled to both ends of a topological superconducting nanowire section hosting Majorana zero-modes. The account of the coupling between the dot and the farthest Majorana zero-mode allows to introduce the topological quality factor, characterizing the level of topological protection in the system. We demonstrate that Coulomb interaction between the dot and the topological superconducting section leads to the onset of the additional overlap of the wavefunctions describing the Majorana zero-modes, lea…
In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An approximate method, coined as "partially resummed perturbation theory in the number of nonlocal Green's functions", is presented that can be operational on a standard computer and demonstrates compatibility with results existing in the literature. In a linear structure made of two neighboring interfaces (with intermediate transparency) connected by a central …
Confinement at the helical edge of a topological insulator is possible in the presence of proximity-induced magnetic (F) or superconducting (S) order. The interplay of both phenomena leads to the formation of localized Majorana bound states (MBS) or likewise (under certain resonance conditions) the formation of ordinary Andreev bound states (ABS). We investigate the properties of bound states in junctions composed of alternating regions of F or S barriers. Interestingly, the direction of magnetization in F regions and the relative superconducting phase between S regions can be exploited to hyb…
We discuss a quantum thermal machine that generates power from a thermally driven double quantum dot coupled to normal and superconducting reservoirs. Energy exchange between the dots is mediated by electron-electron interactions. We can distinguish three main mechanisms within the device operation modes. In the Andreev tunneling regime, energy flows in the presence of coherent superposition of zero- and two-particle states. Despite the intrinsic electron-hole symmetry of Andreev processes, we find that the heat engine efficiency increases with increasing coupling to the superconducting reserv…
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…
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…
The Josephson current flowing in a junction between two superconductors is a striking manifestation of macroscopic quantum coherence, with applications in metrology and quantum information. This equilibrium current is related with the formation of Andreev states localized in the junction, whose energy depends periodically on the superconducting phase difference. Topology emerged as a guide for predicting exotic properties of Andreev states. In particular, topological superconductors host Majorana modes at their ends. Then, in a junction with such leads, the hybridization of two Majorana modes …
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）
Hybrid system composed by a semiconducting nanowire with proximity-induced superconductivity and a quantum dot at the end working as spectrometer was recently used to quantify the so-called degree of Majorana nonlocality [Deng et al., Phys.Rev.B, 98, 085125 (2018)]. Here we demonstrate that spin-resolved density of states of the dot responsible for zero-bias conductance peak strongly depends on the separation between the Majorana bound states (MBSs) and their relative couplings with the dot and investigate how the charging energy affects the spectrum of the system in the distinct scenarios of …
Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. We show such braiding can be well performed in a parallel semiconductor-superconductor nanowire structure. Considering the fact that the low-energy Andreev bound states (ABSs) usually mix with the MZMs in the present set-up, we further investigate the braiding properties of MZMs when an ABS is presented. Our numerical simulation suggests that ABS can be regarded as a pair of weakly coupled MZMs. The dynamical hybridization of MZMs plus the non-Abelian braiding of MZMs would induce an arbitrary rota…
Majorana bound states (MBS) and Andreev bound states (ABS) in realistic Majorana nanowires setups have similar experimental signatures which make them hard to distinguishing one from the other. Here, we characterize the continuous Majorana/Andreev crossover interpolating between fully-separated, partially-separated, and fully-overlapping Majorana modes, in terms of global and local topological invariants, fermion parity, quasiparticle densities, Majorana pseudospin and spin polarizations, density overlaps and transition probabilities between opposite Majorana components. We found that in inhom…
