We consider a two-dimensional electron gas (2DEG) in the Quantum Hall regime in the presence of a Zeeman field, with the Fermi level tuned to filling factor $ν=1$. We show that, in the presence of spin-orbit coupling, contacting the 2DEG to a narrow strip of an s-wave superconductor produces a topological superconducting gap along the contact as a result of crossed Andreev reflection (CAR) processes across the strip. The sign of the topological gap, controlled by the CAR amplitude, depends periodically on the Fermi wavelength and strip width and can be externally tuned. An interface between two halves of a long strip with topological gaps of opposite sign implements a robust $π$-junction, hosting a pair of Majorana zero modes that do not split despite their overlap. We show that such a situation can be exploited to perform protected non-Abelian tunnel-braid operations without any fine tuning.
We propose toy models of crossed Andreev reflection in multiterminal hybrid structures containing out-of-equilibrium conductors. We apply the description to two possible experiments: (i) to a device containing a large quantum dot inserted in a crossed Andreev reflection circuit. (ii) To a device containing an Aharonov-Bohm loop inserted in a crossed Andreev reflection circuit.
We report on the experimental investigation of electronic transport in superconductor-ferromagnet spin-valve structures. Our samples consist of two ferromagnetic iron leads forming planar tunnel contacts to a superconducting aluminum wire. At energies below the superconducting gap, we observe a negative four-probe resistance that can be explained by crossed Andreev reflection.
We study the crossed Andreev effects in two-dimensional conductor/superconductor hybrid systems under a perpendicular magnetic field. Both a graphene/superconductor hybrid system and an electron gas/superconductor one are considered. It is shown that an exclusive crossed Andreev reflection, with other Andreev reflections being completely suppressed, is obtained in a high magnetic field because of the chiral edge states in the quantum Hall regime. Importantly, the exclusive crossed Andreev reflection not only holds for a wide range of system parameters, e.g., the size of system, the width of ce…
We study nonlocal transport in a two-leg Kitaev ladder connected to two normal metals. The coupling between the two legs of the ladder when the legs are maintained at a (large) superconducting phase difference, results in the creation of subgap Andreev states. These states in turn are responsible for the enhancement of crossed Andreev reflection. We find that tuning the different parameters of the system suitably leads to enhancement of crossed Andreev reflection signalled by transconductance acquiring the most negative value possible. Furthermore, subgap states cause oscillations of the trans…
We consider non-local transport in a system with one superconducting and two normal metal terminals. Electron focusing by weak perpendicular magnetic fields is shown to tune the ratio between crossed Andreev reflection (CAR) and electron transfer (ET) in the non-local current response. Additionally, electron focusing facilitates non-local signals between normal metal contacts where the separation is as large as the mean free path rather than being limited by the coherence length of the superconductor. CAR and ET can be selectively enhanced by modulating the magnetic field.
We theoretically investigate the quantum transports in a junction between a superconductor and a silicene nanoribbon, under the effect of a magnetic exchange field. We find that for a narrow nanoribbon of silicene, remarkable crossed Andreev reflection (with a fraction $>50\%$) can be induced in the energy window of the elastic cotunneling, by destroying some symmetries of the system. Since the energy responses of electrons to the exchange field are opposite for opposite spins, these transport channels can be well spin polarized. Moreover, due to the helicity conservation of the topological ed…
We investigate the transport properties of three-terminal graphene devices, where one terminal is superconducting and two are normal metals. The terminals are connected by nanoribbons. Electron transfer (ET) and crossed Andreev reflection (CAR) are identified via the non-local signal between the two normal terminals. Analytical expressions for ET and CAR in symmetric devices are found. We compute ET and CAR numerically for asymmetric devices. ET dominates CAR in symmetric devices, but CAR can dominate ET in asymmetric devices, where only the zero-energy modes of the zigzag nanoribbons contribu…
We investigate the Majorana physics and its effect on the electron transport in the non-topological superconductor(NS)-topological superconductor(TS) double junctions of a ring geometry. We find that, depending on the ratio between the lengths of two topologically different regions and the localization lengths of the Majorana fermions formed between them, two completely different transport mechanisms are working: perfect crossed Andreev reflection (CAR) for the short NS region and perfect normal Andreev reflection for the short TS region. The difference is explained in terms of the topological…
At the domain wall between two regions with the opposite Chern number, there should be the one-dimensional chiral states, which are called as the kink states. The kink states are robust for the lattice deformations. We design a multi-terminal device with the kink states to study the local Andreev reflection and the crossed Andreev reflection. The coefficient of the crossed Andreev reflection can reach 1 in the four-terminal device. Besides adjusting the phase difference between superconductors, the local Andreev reflection and the crossed Andreev reflection can be controlled by changing the on…
Using a generalized wave matching method we solve the full scattering problem for quantum spin Hall insulator (QSHI) - superconductor (SC) - QSHI junctions. We find that for systems narrow enough so that the bulk states in the SC part couple both edges, the crossed Andreev reflection (CAR) is significant and the electron cotunneling (T) and CAR become spatially separated. We study the effectiveness of this separation as a function of the system geometry and the level of doping in the SC. Moreover, we show that the spatial separation of both effects allows for an all-electrical measurement of C…
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 theoretically study the crossed Andreev reflection in a hybrid nanostructure which comprises a d-wave superconductor and two normal-metal quantum wires. When the superconductor of the (110) oriented surface is in contact with the wires parallel and placed close to each other, the Andreev bound state is formed by the crossed Andreev reflection. When the contact barrier potential is sufficiently large, two sharp peaks appear in the conductance well below the gap structure, which originate from the bonding and antibonding Andreev bound states. We propose that these Andreev bound states form a …
The crossed Andreev reflection in a hybrid nanostructure consisting of a d-wave superconductor and two quantum wires is theoretically studied. When the (110) oriented surface of the superconductor is in contact with the wires parallel and placed close to each other, the Andreev bound state is formed by the crossed Andreev reflection. The conductance has two resonance peaks well below the gap structure in the case of tunnel contacts. These peaks originate from the bonding and antibonding Andreev bound states of hole wave functions.
We study electron transport through a normal lead-quantum dot-topological superconductor-quantum dot-normal lead (N-QD-TS-QD-N) junction. Due to the non-local nature of Majorana fermions (MFs) in the topological superconductor, there are two types of single electron transport processes in the junction: crossed Andreev reflection (CAR) and electron teleportation (ET). When the coupling energy of MFs is much larger than the coupling between MFs and QDs, electron can tunnel through topological superconductor either via CAR or ET depending on the energy levels of QDs. For instance, when both energ…
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 calculate the full transport counting statistics in a three-terminal tunnel device with one superconducting source and two normal-metal or ferromagnet drains. We obtain the transport probability distribution from direct Andreev reflection, crossed Andreev reflection, and electron transfer which reveals how these processes' statistics are determined by the device conductances. The cross-correlation noise is a result of competing contributions from crossed Andreev reflection and electron transfer, as well as antibunching due to the Pauli exclusion principle. For spin-active tunnel barriers th…
Crossed Andreev reflection (CAR) is an intriguing effect that occurs in a normal-superconductor-normal junction. In CAR, an incoming electron from one terminal is coherently scattered as an outgoing hole into the other terminal. Here, we reveal that there exists a transverse spatial shift in CAR, i.e., the plane of CAR for the outgoing hole may have a sizable transverse shift from the plane of incidence for the incoming electron. We explicitly demonstrate the effect in a model system based on Weyl semimetals. We further show that the effect is quite general and exists when the terminals have s…
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.
A theory of crossed Andreev reflection in structures consisting of a superconductor with two ferromagnetic leads is presented. The electric current due to the crossed Andreev reflection strongly depends on the relative orientation of the magnetization of two ferromagnetic leads. It is shown that the dependence of the electric current and the magnetoresistance on the distance between two ferromagnetic leads is understood by considering the interference between the wave functions in ferromagnets. The current and the magnetoresistance are calculated as functions of the exchange field and the heig…
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.
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…
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 analyze the non-local transport properties of a d-wave superconductor coupled to metallic electrodes at nanoscale distances. We show that the non-local conductance exhibits an algebraical decay with distance rather than the exponential behavior which is found in conventional superconductors. Crossed Andreev processes, associated with electronic entanglement, are favored for certain orientations of the symmetry axes of the superconductor with respect to the leads. These properties would allow its experimental detection using present technologies.
We report on electronic transport properties of mesoscopic superconductor-ferromagnet spin-valve structures. Two ferromagnetic iron leads form planar tunnel contacts to a superconducting aluminum wire, where the distance of the two contacts is of the order of the coherence length of the aluminum. We observe a negative non-local resistance which can be explained by crossed Andreev reflection, a process where an electron incident from one of the leads gets reflected as a hole into the other, thereby creating a pair of spatially separated, entangled particles.
We propose a scheme to detect the Majorana-zero-mode-induced crossed Andreev reflection by measuring tunneling current directly. In this scheme a metallic ring structure is utilized to separate electron and hole signals. Since tunneling electrons and holes have different propagating wave vectors, the conditions for them to be constructively coherent in the ring differ. We find that when the magnetic flux threading the ring varies, it is possible to observe adjacent positive and negative current peaks of almost equal amplitudes.
Perfect crossed Andreev reflection (CAR) is striking for high-efficiency Cooper pair splitting which bears promising applications in quantum communication. Recent experimental advances have disclosed the way to explore CAR in Dirac fermion systems under ultra-strong magnetic fields. We develop a scattering approach to study quantum Hall-superconductor-quantum Hall (QH-S-QH) junctions formed by a two-dimensional (2D) time-reversal symmetric Dirac semimetal. We propose two different setups of the hybrid junction in the quantum limit where only zeroth Landau levels are involved in transport to ex…
We show that very large negative magnetoresistance can be obtained in magnetic trilayers in a current-in-plane geometry owing to the existence of crossed Andreev reflection. This spin-valve consists of a thin superconducting film sandwiched between two ferromagnetic layers whose magnetization is allowed to be either parallelly or antiparallelly aligned. For a suitable choice of structure parameters and nearly fully spin-polarized ferromagnets the magnetoresistance can exceed -80%. Our results are relevant for the design and implementation of spintronic devices exploiting ferromagnet-supercondu…
We propose a novel method for the generation of the transverse valley currents, which is based on the pure crossed Andreev reflection (pCAR) in the superconducting hybrid junctions composed of the gapped $α-\mathcal{T}_3$ lattices with ferromagnet-induced exchange interaction. The angle-resolved pCAR probability is asymmetric for a given valley, resulting in the transverse valley currents with zero net charge. This pCAR assisted charge-valley conversion is highly efficient with the valley Hall angle reaching an order of unity, suggesting potential applications for valleytronic devices.
We provide a new analytical tool to calculate the energies of Andreev bound states (ABS) in long imperfect SNS junctions, at present these can only be described by numerical tools. We model an NS junction as a delta-function "Andreev" impurity, i.e., a localized potential which scatters an electron into a hole with opposite spin. We show using the scattering matrix formalism that, quite surprisingly, an "Andreev" impurity is equivalent to an NS junction characterized by both Andreev reflection and a finite amount of normal scattering. The ABS energies are then calculated using the T-matrix for…
The coexistence of superconductivity and ferromagnetism has brought about the phenomena of ferromagnetic superconductors. The theory needed to understand the compatibility of such antagonistic phenomena cannot be built until the pairing symmetry of such superconductors is correctly identified. The proper and unambiguous identification of the pairing symmetry of such superconductors is the subject of this paper. This work shows that crossed Andreev reflection can be a very effective tool in order to identify the pairing symmetry of these superconductors.
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…
Despite extensive search for about a decade, specular Andreev reflection is only recently realized in bilayer graphene-superconductor interface. However, the evolution from the typical retro type Andreev reflection to the unique specular Andreev reflection in single layer graphene has not yet been observed. We investigate this transition by measuring the differential conductance at the van der Walls interface of single layer graphene and NbSe2 superconductor. We find that the normalized conductance becomes suppressed as we pass through the Dirac cone via tuning the Fermi level and bias energy,…
We study the quantum transport behavior of a normal-superconductor-normal junction based on type-II Weyl semimetal, which is arranged in the tilting direction of the Weyl semimetal. We find that both the crossed Andreev reflection and normal reflection are forbidden, while there will be double Andreev reflections and double electron transmissions for the incident electron from the semimetal side. Andreev reflections and transmissions occur both in the retro and specular directions simultaneously, symmetric about the normal of the interface but with different amplitudes, depending on the angle …
We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore, it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model sys…
Crossed Andreev reflections and cotunneling occur between two neighbouring superconductor- normal metal or superconducting-ferromagnet interfaces. Previous works assumed a clean BCS superconductor. Here the calculation of the corresponding crossed conductance terms is generalized to a dirty superconductor. The range of the effect is shown to be the coherence length $\tildeξ = \sqrt{\hbar D/Δ}$, instead of the BCS coherence length $ξ_0$. Moreover, in three dimensions, the algebraic prefactor scales as $1/r$ instead of $1/r^2$. The calculation involves the virtual diffusion probability of quasip…
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 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 …
We investigate several factors controlling the physics of hybrid structures involving ferromagnetic domain walls (DWs) and superconducting (S) metals. We discuss the role of non collinear magnetizations in S/DW junctions in a spin $\otimes$ Nambu $\otimes$ Keldysh formalism. We discuss transport in S/DW/N and S/DW/S junctions in the presence of inelastic scattering in the domain wall. In this case transport properties are similar for the S/DW/S and S/DW/N junctions and are controlled by sequential tunneling of spatially separated Cooper pairs across the domain wall. In the absence of inelastic…
We present a theory for the full distribution of current fluctuations in incoherent diffusive superconducting junctions, subjected to a voltage bias. This theory of full counting statistics of incoherent multiple Andreev reflections is valid for arbitrary applied voltage. We present a detailed discussion of the properties of the first four cumulants as well as the low and high voltage regimes of the full counting statistics. The work is an extension of the results of Pilgram and the author, Phys. Rev. Lett. 94, 086806 (2005).
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 construct a nonequilibrium theory for the charge transfer through a diffusive array of alternating normal (N) and superconducting (S) islands comprising an SNSNS junction, with the size of the central S-island being smaller than the energy relaxation length. We demonstrate that in the nonequilibrium regime the central island acts as Andreev retransmitter with the Andreev conversions at both NS interfaces of the central island correlated via over-the-gap transmission and Andreev reflection. This results in a synchronized transmission at certain resonant voltages which can be experimentally o…
Inspired by recent experiments, we study a short superconducting junction of length $L\ll ξ$ (coherence length) inserted in a dc-SQUID containing an ancillary Josephson tunnel junction. We evaluate the nonequilibrium occupation of the Andreev bound states (ABS) for the case of a conventional junction and a topological junction, with the latter case of ABS corresponding to a Majorana mode. We take into account small phase fluctuations of the Josephson tunnel junction, acting as a damped LC resonator, and analyze the role of the distribution of the quasiparticles of the continuum assuming that t…
We study superconducting quantum interference in InSb flake Josephson junctions. An even-odd effect in the amplitude and periodicity of the superconducting quantum interference pattern is found. Interestingly, the occurrence of this pattern coincides with enhanced conduction at both edges of the flake, as is deduced from measuring a SQUID pattern at reduced gate voltages. We identify the specific crystal facet of the edge with enhanced conduction, and confirm this by measuring multiple devices. Furthermore, we argue the even-odd effect is due to crossed Andreev reflection, a process where a Co…
We report on the measurement of multiple Andreev resonances at atomic size point contacts between two superconducting nanostructures of Pb under magnetic fields higher than the bulk critical field, where superconductivity is restricted to a mesoscopic region near the contact. The small number of conduction channels in this type of contacts permits a quantitative comparison with theory through the whole field range. We discuss in detail the physical properties of our structure, in which the normal bulk electrodes induce a proximity effect into the mesoscopic superconducting part.
We have measured the non-local resistance of aluminum-iron spin-valve structures fabricated by e-beam lithography and shadow evaporation. The sample geometry consists of an aluminum bar with two or more ferromagnetic wires forming point contacts to the aluminum at varying distances from each other. In the normal state of aluminum, we observe a spin-valve signal which allows us to control the relative orientation of the magnetizations of the ferromagnetic contacts. In the superconducting state, at low temperatures and excitation voltages well below the gap, we observe a spin-dependent non-local…
We study transport in a voltage biased superconductor-normal-superconductor (SNS) junction made of semiconducting nanowires with strong spin-orbit coupling, as it transitions into a topological superconducting phase for increasing Zeeman field. Despite the absence of a fractional steady-state ac Josephson current in the topological phase, the dissipative multiple Andreev reflection (MAR) current I_dc at different junction transparencies is particularly revealing. It exhibits unique features related to topology, such as the gap inversion, the formation of Majorana bound states, and fermion-pari…
