Multiple Andreev Reflections Research Articles

Ballistic supercurrent discretization and micrometer-long Josephson coupling in germanium

We fabricate Josephson field-effect-transistors in germanium quantum wells contacted by superconducting aluminum and demonstrate supercurrents carried by holes that extend over junction lengths of several micrometers. In superconducting quantum point contacts we observe discretization of supercurrent, as well as Fabry-Perot resonances, demonstrating ballistic transport. The magnetic field dependence of the supercurrent follows a clear Fraunhofer-like pattern and Shapiro steps appear upon microwave irradiation. Multiple Andreev reflections give rise to conductance enhancement and evidence a transparent interface, confirmed by analyzing the excess current. These demonstrations of ballistic superconducting transport are promising for hybrid quantum technology in germanium.

Supercurrent carried by nonequilibrium quasiparticles in a multiterminal Josephson junction

We theoretically study coherent multiple Andreev reflections in a biased three-terminal Josephson junction. We demonstrate that the direct current flowing through the junction consists of supercurrent components when the bias voltages are commensurate. This dissipationless current depends on the phase in the superconducting leads and stems from the Cooper pair transfer processes induced by non-local Andreev reflections of the quasiparticles originating from the superconducting leads. We identify supercurrent-enhanced lines in the current and conductance maps of the recent measurement [Y. Cohen, et al., PNAS 115, 6991 (2018)] on a nanowire Josephson junction and show that the magnitude of the phase-dependent current components is proportional to the junction transparency with the power corresponding to the component order.

Andreev reflections and magnetotransport in 2D Josephson junctions

In this paper, the subharmonic energy gap structures (SGS) and induced superconductivity, due to multiple Andreev reflections, in indium gallium arsenide (In0.75Ga0.25As) two-dimensional electron gas (2DEG) are discussed at different temperatures and magnetic fields. Strong suppression of both SGS and induced gap are observed as a function of temperature and magnetic field. The differential conductance of the Josephson junctions (JJs) as a function of external in-plane magnetic fields shows an asymmetric response to positive and negative magnetic field sweeps with a conductance maximum at close to zero. Our approach to quantum transport studies of the ballistic 2D JJs may open a new road towards scalable and integrated quantum processing and help pave the way for the development of topological circuits for the realization of the next generation of quantum processors.

Supercurrent and Multiple Andreev Reflections in InSb Nanosheet SNS Junctions

In this study, the realization of mesoscopic Josephson junctions based on free‐standing InSb nanosheet grown by molecular‐beam epitaxy is reported. Below the critical temperature of superconducting aluminium electrodes (≈1.1 K), the high transparency of the contacts gives rise to proximity‐induced superconductivity. A dissipationless supercurrent which can be modulated by a gate voltage acting on the electron density in the nanosheet flows through the superconducting weak links. At finite bias voltage, subharmonic energy‐gap structures (SGS) originating from multiple Andreev reflections (MARs) are observed, indicating a highly transparent InSb nanosheet–superconductor interface. At last, a superconducting hybrid device with niobium electrodes is shown, suitable for further higher temperature and magnetic field transport measurements.

Short ballistic Josephson coupling in micrometer-long tantalum/graphene/tantalum junction

Enhancing the Josephson coupling strength inside superconductor-normal-superconductor junctions facilitates the versatile applications of Josephson devices. We adopted DC magnetron sputtered tantalum film for the superconducting contact of graphene Josephson junction which resulted in reinforcing the superconducting correlation. The transport properties of the micrometer scale graphene Josephson junctions both in normal and superconducting states are investigated. The strong Josephson coupling is manifested by two transport characteristics of Josephson junction. First, the ICRN product in scale of superconducting gap energy approaches to 2, which is close to the theoretical prediction for the Josephson junction in short and ballistic regime. Second, the temperature dependence of critical current shows a good agreement with the short Josephson junction characteristics suggested by Kulik and Omel'yanchek. This strong Josephson coupling over significantly long channel length of greater than micrometer scale can be attributed to the small superconducting gap energy that leads to long superconducting correlation length in graphene. Clear features of multiple Andreev reflections up to the third order also support that Josephson coupling persists over micrometer scale.

Full Counting Statistics of Superconductor-Quantum Dot-Superconductor Contacts in the Presence of Interactions

In this paper, we discuss the full counting statistics of superconducting quantum dot contacts. We discuss the effects both of phonon and onsite electronic interaction focusing on the experimentally most relevant case of strong onsite electronic interactions. We find that in general, the Josephson effect and multiple Andreev reflections in these systems are strongly suppressed due to the onsite interaction. However, in case resonant phonons are found, the effect of the onsite interaction can be overcome.

Enhanced Shot Noise of Multiple Andreev Reflections in a Carbon Nanotube Quantum Dot in SU(2) and SU(4) Kondo regimes.

The sensitivity of shot noise to the interplay between Kondo correlations and superconductivity is investigated in a carbon nanotube quantum dot connected to superconducting electrodes. Depending on the gate voltage, the SU(2) and SU(4) Kondo unitary regimes can be clearly identified. We observe enhancement of the shot noise via the Fano factor in the superconducting state. Its divergence at low bias voltage, which is more pronounced in the SU(4) regime than in the SU(2) one, is larger than what is expected from proliferation of multiple Andreev reflections predicted by the existing theories. Our result suggests that the Kondo effect is responsible for this strong enhancement.

Andreev Reflection at the Interface with an Oxide in the Quantum Hall Regime

Quantum Hall/superconductor junctions have been an attractive topic as the two macroscopically quantum states join at the interface. Despite longstanding efforts, however, experimental understanding of this system has not been settled yet. One of the reasons is that most semiconductors hosting high-mobility two-dimensional electron systems (2DES) usually form Schottky barriers at the metal contacts, preventing efficient proximity between the quantum Hall edge states and Cooper pairs. Only recently have relatively transparent 2DES/superconductor junctions been investigated in graphene. In this study, we propose another material system for investigating 2DES/superconductor junctions, that is ZnO-based heterostrcuture. Due to the ionic nature of ZnO, a Schottky barrier is not effectively formed at the contact with a superconductor MoGe, as evidenced by the appearance of Andreev reflection at low temperatures. With applying magnetic field, while clear quantum Hall effect is observed for ZnO 2DES, conductance across the junction oscillates with the filling factor of the quantum Hall states. We find that Andreev reflection is suppressed in the well developed quantum Hall regimes, which we interpret as a result of equal probabilities of normal and Andreev reflections as a result of multiple Andreev reflection at the 2DES/superconductor interface.

Controlled transport between Fermi superfluids through a quantum point contact

Recent advances in experimental techniques allow one to create a quantum point contact between two Fermi superfluids in cold atomic gases with a tunable transmission coefficient. In this Letter we propose that three distinct behaviors of charge transports between two Fermi superfluids can be realized in this single setup, which are the multiple Andreev reflection, the self-trapping and the Josephson oscillation. We investigate the dynamics of atom number difference between two reservoirs for different initial conditions and different transmission coefficients, and present a coherent picture of how the crossover between different regimes takes place. Our results can now be directly verified in current experimental system.

Spin-Orbit Interaction and Induced Superconductivity in a One-Dimensional Hole Gas.

Low dimensional semiconducting structures with strong spin–orbit interaction (SOI) and induced superconductivity attracted great interest in the search for topological superconductors. Both the strong SOI and hard superconducting gap are directly related to the topological protection of the predicted Majorana bound states. Here we explore the one-dimensional hole gas in germanium silicon (Ge–Si) core–shell nanowires (NWs) as a new material candidate for creating a topological superconductor. Fitting multiple Andreev reflection measurements shows that the NW has two transport channels only, underlining its one-dimensionality. Furthermore, we find anisotropy of the Landé g-factor that, combined with band structure calculations, provides us qualitative evidence for the direct Rashba SOI and a strong orbital effect of the magnetic field. Finally, a hard superconducting gap is found in the tunneling regime and the open regime, where we use the Kondo peak as a new tool to gauge the quality of the superconducting gap.

Single interface effects dominate in exciton-condensate/normal-barrier/exciton-condensate (EC/N/EC) structures of long-barrier

We study theoretically the exciton-condensate/normal-barrier/exciton-condensate (EC/N/EC) structures in bilayers with a tunable relative phase ϕ0 between the two exciton condensates (ECs). It is a setup inspired initially by the superconducting Josephson junction but with a special ingredient added for bilayer systems, namely, the interlayer tunneling. Our results shows that in a EC/N/EC structure of long-barrier, the single Andreev reflection at one EC/N interface dominates—as opposed to the same structure of short-barrier, in which multiple Andreev reflections can be accommodated (similar to the superconducting Josephson junctions). The single interface effect turns the other EC inert and the system can no longer be understood as a Josephson junction. The supercurrent, however, still occurs at the N/EC interface since the current conservation is still fulfilled with the assistance of the interlayer tunneling in barriers. This exotic mechanism gives rise to only a half portion from a fractional soliton of a doubled topological charge 2Q = ϕ0/π (for the same relative phase ϕ0), as opposed to a full portion fraction soliton of charge Q = ϕ0/2π in the structures of short-barriers. We predict the current phase relation for the EC/N/EC structures of long-barriers which can be tested experimentally.

Anomalous Fraunhofer Patterns in Gated Josephson Junctions Based on the Bulk-Insulating Topological Insulator BiSbTeSe2.

One-dimensional Majorana modes are predicated to form in Josephson junctions based on three-dimensional topological insulators (TIs). While observations of supercurrents in Josephson junctions made on bulk-insulating TI samples have been reported recently, the Fraunhofer patters observed in such TI-based Josephson junctions, which sometimes present anomalous features, are still not well-understood. Here, we report our study of highly gate-tunable TI-based Josephson junctions made of one of the most bulk-insulating TI materials, BiSbTeSe2, and Al. The Fermi level can be tuned by gating across the Dirac point, and the high transparency of the Al-BiSbTeSe2 interface is evinced by a high characteristic voltage and multiple Andreev reflections, with peak indices reaching 12. Anomalous Fraunhofer patterns with missing lobes were observed in the entire range of gate voltage. We found that, by employing an advanced fitting procedure to use the maximum entropy method in a Monte Carlo algorithm, the anomalous Fraunhofer patterns are explained as a result of inhomogeneous supercurrent distributions on the TI surface in the junction. Besides establishing a highly promising fabrication technology, this work clarifies one of the important open issues regarding TI-based Josephson junctions.

Planar graphene Josephson coupling via van der Waals superconducting contacts

We report on the fabrication and transport characteristics of van der Waals (vdW)-contacted planar Josephson junctions. In a device, two pieces of cleaved 2H-NbSe2 superconducting flakes and a monolayer graphene sheet serve as the superconducting electrodes and the normal-conducting spacer, respectively. A stack of NbSe2−graphene−hexagonal-boron-nitride (hBN) heterostructure with clean and flat interfaces was prepared by a dry transfer technique. The outermost hBN layer protected the NbSe2−graphene−NbSe2 Josephson junction from chemical contamination during the fabrication processes. The Josephson coupling was confirmed by a periodic modulation of the junction critical current Ic in a perpendicular magnetic field. The temperature dependence of Ic showed long and diffusive Josephson coupling characteristics. The temperature dependence of the superconducting gap, obtained from the multiple Andreev reflection features, followed the Bardeen−Cooper−Schrieffer (BCS) prediction.

Andreev bound states and their signatures.

Many of the properties of superconductors related to quantum coherence are revealed when the superconducting state is forced to vary in space in response to an external magnetic field, a proximity contact, an interface to a ferromagnet or to impurities embedded in the superconductor. Among the earliest examples is Andreev reflection of an electron into a retro-reflected hole at a normal-superconducting interface. In regions of strong inhomogeneity, multiple Andreev reflection leads to the formation of sub-gap states, Andreev bound states, with excitation energies below the superconducting gap. These states play a central role in our understanding of inhomogeneous superconductors. The discoveries of unconventional superconductivity in many classes of materials, advances in fabrication of superconducting/ferromagnetic hybrids and nanostructures for confining superfluid 3 He, combined with theoretical developments in topological quantum matter have dramatically expanded the significance of branch conversion scattering and Andreev bound state formation. This collection of articles highlights developments in inhomogeneous superconductivity, unconventional superconductivity and topological phases of superfluid 3 He, in which Andreev scattering and bound states underpin much of the physics of these systems. This article provides an introduction to the basic physics of Andreev scattering, bound-state formation and their signatures. The goal is both an introduction for interested readers who are not already experts in the field, and to highlight examples in which branch conversion scattering and Andreev bound states provide unique signatures in the transport properties of superconductors.This article is part of the theme issue 'Andreev bound states'.

Superconducting gap symmetry in the superconductor BaFe1.9Ni0.1As2

We report on the Andreev spectroscopy and specific heat of high-quality single crystals BaFe$_{1.9}$Ni$_{0.1}$As$_{2}$. The intrinsic multiple Andreev reflection spectroscopy reveals two anisotropic superconducting gaps $\Delta_L \approx 3.2 \textendash 4.5$\,meV, $\Delta_S \approx 1.2 \textendash 1.6$\,meV (the ranges correspond to the minimum and maximum value of the coupling energy in the $k_xk_y$-plane). The $25 \textendash 30 \%$ anisotropy shows the absence of nodes in the superconducting gaps. Using a two-band model with s-wave-like gaps $\Delta_L \approx 3.2$\,meV and $\Delta_S \approx 1.6$\,meV, the temperature dependence of the electronic specific heat can be well described. A linear magnetic field dependence of the low-temperature specific heat offers a further support of s-wave type of the order parameter. We find that a d-wave or single-gap BCS theory under the weak-coupling approach cannot describe our experiments.

Current noises in a topological Josephson junction

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor Josephson junction both in the absence and in the presence of a DC bias voltage. As the system is predicted to host Majorana fermions at its interfaces, the Andreev bond states are supposed to exhibit a distinct $4\pi$ periodicity in the superconducting phase difference, namely the fractional Josephson effect. Using the non-equilibrium Greens function method, we calculate the current and the related current noise based on a tight-binding Hamiltonian. Our direct results show that the fractional Josephson effect can not be seen in equilibrium junctions. While in non-equilibrium junctions, this effect can be confirmed by the multiple Andreev reflections induced peaks of the non-equilibrium noise, which appear at discrete frequencies $\omega=neV$ with $n$ being an integer number.

Electron and Cooper-pair transport across a single magnetic molecule explored with a scanning tunneling microscope

The interplay of magnetism and superconductivity gives rise to the emergence of various interesting phenomena in condensed matter physics, such as the Yu-Shiba-Rusinov in-gap modes created by local magnetic moments in superconducting hosts. Using normal-metal and superconducting tips the authors have formed contacts to an individual magnetic molecule adsorbed on a conventional superconductor. Spectroscopy of the differential conductance with tunable junction transparency has unveiled the crossover from quasiparticle tunneling, which probes the Bardeen-Cooper-Schrieffer energy gap as well as the Yu-Shiba-Rusinov levels, to the contact range where multiple Andreev reflection takes over.

Thermoelectric Efficiency of a Topological Nano-Junction.

We studied the non-equilibrium current, transport coefficients and thermoelectric performance of a nano-junction, composed by a quantum dot connected to a normal superconductor and a topological superconductor leads, respectively. We considered a one-dimensional topological superconductor, which hosts two Majorana fermion states at its edges. Our results show that the electric and thermal currents across the junction are highly mediated by multiple Andreev reflections between the quantum dot and the leads, thus leading to a strong nonlinear dependence of the current on the applied bias voltage. Remarkably, we find that our system reaches a sharp maximum of its thermoelectric efficiency at a finite bias, when an external magnetic field is imposed upon the junction. We propose that this feature can be used for accurate temperature sensing at the nanoscale.

Gate-tunable supercurrent and multiple Andreev reflections in a superconductor-topological insulator nanoribbon-superconductor hybrid device

We report on the observation of gate-tunable proximity-induced superconductivity and multiple Andreev reflections (MARs) in a bulk-insulating BiSbTeSe2 topological insulator nanoribbon (TINR) Josephson junction with superconducting Nb contacts. We observe a gate-tunable critical current (IC) for gate voltages (Vg) above the charge neutrality point (VCNP), with IC as large as 430 nA. We also observe MAR peaks in the differential conductance (dI/dV) versus DC voltage (Vdc) across the junction corresponding to sub-harmonic peaks (at Vdc = Vn = 2ΔNb/en, where ΔNb is the superconducting gap of the Nb contacts and n is the sub-harmonic order). The sub-harmonic order, n, exhibits a Vg-dependence and reaches n = 13 for Vg = 40 V, indicating the high transparency of the Nb contacts to TINR. Our observations pave the way toward exploring the possibilities of using TINR in topologically protected devices that may host exotic physics such as Majorana fermions.

Doubled Shapiro steps in a topological Josephson junction

We study the transport properties of a superconductor-quantum spin Hall insulator-superconductor (S-QSHI-S) hybrid system in the presence of a microwave radiation. Instead of adiabatic analysis or using the resistively shunted junction model, we start from the microscopic Hamiltonian and calculate the DC current directly with the help of the non-equilibrium Green's Functions method. The numerical results show that (i) the I-V curves of background current due to multiple Andreev reflections (MAR) exhibit a different structure with that in the conventional junctions, (ii) all Shapiro steps are visible and appear one by one at high frequency, while at low frequency, the steps evolve exactly as the Bessel functions and the odd steps are completely suppressed, implying a fractional Josephson effect.