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 contribute to the transport.
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 report on the observation of gate-tunable proximity-induced superconductivity and multiple Andreev reflections (MAR) in a bulk-insulating BiSbTeSe$_2$ topological insulator nanoribbon (TINR) Josephson junction (JJ) with superconducting Nb contacts. We observe a gate-tunable critical current ($I_C$) for gate voltages ($V_g$) above the charge neutrality point ($V_{CNP}$), with $I_C$ as large as 430 nA. We also observe MAR peaks in the differential conductance ($dI/dV$) versus DC voltage ($V_{dc}$) across the junction corresponding to sub-harmonic peaks (at $V_{dc} = V_n = 2Δ_{Nb}/en$, where $…
Junctions composed of two crossed graphene nanoribbons (GNRs) have been theoretically proposed as electron beam splitters where incoming electron waves in one GNR can be split coherently into propagating waves in \emph{two} outgoing terminals with nearly equal amplitude and zero back-scattering. Here we scrutinize this effect for devices composed of narrow zigzag GNRs taking explicitly into account the role of Coulomb repulsion that leads to spin-polarized edge states within mean-field theory. We show that the beam-splitting effect survives the opening of the well-known correlation gap and, mo…
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 report the investigation of electron transport through a four-terminal graphene-superconductor hybrid system. Due to the quantum interference of the reflected holes from two graphene-superconductor interfaces with phase difference $θ$, it is found that the specular Andreev reflection vanishes at $θ=0$ while the Andreev retroreflection disappears at $θ=π$. This means that the retroreflection and specular reflection can be easily controlled and separated in this device. In addition, due to the diffraction effect in the narrow graphene nanoribbon, the reflected hole can exit from both graphene…
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 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…
Graphene nanoribbons (GNRs) are promising components in future nanoelectronics due to the large mobility of graphene electrons and their tunable electronic band gap in combination with recent experimental developments of on-surface chemistry strategies for their growth. Here we explore a prototype 4-terminal semiconducting device formed by two crossed armchair GNRs (AGNRs) using state-of-the-art first-principles transport methods. We analyze in detail the roles of intersection angle, stacking order, inter-GNR separation, and finite voltages on the transport characteristics. Interestingly, when…
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 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 tw…
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…
Ballistic point contact (BPC) with zigzag edges in graphene is a main candidate of a valley filter, in which the polarization of the valley degree of freedom can be selected by using a local gate voltage. Here, we propose to detect the valley filtering effect by Andreev reflection. Because electrons in the lowest conduction band and the highest valence band of the BPC possess opposite chirality, the inter-band Andreev reflection is strongly suppressed, after multiple scattering and interference. We draw this conclusion by both the scattering matrix analysis and the numerical simulation. The An…
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 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.
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.
Superconducting proximity junctions made of topological insulator (TI) nanoribbons (NRs) provide a useful platform for studying topological superconductivity. We report on the fabrication and measurement of Josephson junctions (JJs) using Sb doped Bi$_2$Se$_3$ NRs in contact with Al electrodes. Aharonov$-$Bohm and Altshuler$-$Aronov$-$Spivak oscillations of the axial magneto-conductance of TI NR were observed, indicating the existence of metallic surface states along the circumference of the TI NR. We observed the supercurrent in the TI NR JJ and subharmonic gap structures of the differential …
We analyze theoretically 4-terminal electronic devices composed of two crossed graphene nanoribbons (GNRs) and show that they can function as beam splitters or mirrors. These features are identified for electrons in the low-energy region where a single valence or conduction band is present. Our modeling is based on $p_z$ orbital tight-binding with Slater--Koster type matrix elements fitted to accurately reproduce the low-energy bands from density functional theory calculations. We analyze systematically all devices that can be constructed with either zigzag or armchair GNRs in AA and AB stacki…
We study the electron transport through a graphene nanoribbon-superconductor junction. Both zigzag and armchair edge graphene nanoribbons are considered, and the effects of the magnetic field and disorder on the transport property are investigated. By using the tight-binding model and the non-equilibrium Green's function method, the expressions of the current, conductance, normal tunneling coefficient, and Andreev reflection coefficient are obtained. For a clean system and at zero magnetic field, the linear conductance increases approximatively in a linear fashion with the on-site energy. In t…
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 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…
We report anomalous enhancement of the critical current at low temperatures in gate-tunable Josephson junctions made from topological insulator BiSbTeSe$_2$ nanoribbons with superconducting Nb electrodes. In contrast to conventional junctions, as a function of the decreasing temperature $T$, the increasing critical current $I_c$ exhibits a sharp upturn at a temperature $T_*$ around 20$\%$ of the junction critical temperatures for several different samples and various gate voltages. The $I_c$ vs. $T$ demonstrates a short junction behavior for $T>T_*$, but crosses over to a long junction behavio…
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 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 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…
Crossed Andreev reflection (cAR) is a scattering process that happens in a quantum transport set-up consisting of two normal metals (NM) attached to a superconductor (SC), where an electron incident from one NM results in a hole emerging in the other. Typically, an electron tunnelling through the superconductor from one NM to the other (ET) competes with cAR and masks the signature of cAR in the conductance spectrum. We propose a novel scheme to enhance cAR, in which SC part of the NM-SC-NM is side-coupled to another SC having a different SC phase to form a Josephson junction in the transverse…
We develop a theory of the non-local transport of two counter-propagating $ν= 1$ quantum Hall edges coupled via a narrow disordered superconductor. The system is self-tuned to the critical point between trivial and topological phases by the competition between tunneling processes with or without particle-hole conversion. The critical conductance is a random, sample-specific quantity with a zero average and unusual bias dependence. The negative values of conductance are relatively stable against variations of the carrier density, which may make the critical state to appear as a topological one.
Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions
Osipyan Institute of Solid State Physics, Russian Academy of Sciences（俄罗斯科学院奥西皮扬固体物理研究所）；Condensed-Matter Physics Laboratory, HSE University（国立高等经济学院凝聚态物理实验室）；National Research University Higher School of Economics（国立高等经济大学）
