Multiple Andreev Reflections Research Articles

Over-the-Gap Conductance Oscillations in Superconducting Vanadium Nanocontacts Induced by Hydrogen Impurities.

We have investigated the current-voltage (I-V) characteristics of Josephson junctions made by a low-temperature superconductor of vanadium (V) with a small amount of hydrogen (H) and deuterium (D) impurities using a mechanically controllable break junction (MCBJ) technique. Below the superconducting transition temperature TC, the differential conductance dI/dV spectra show distinct peaks within the superconducting gap, known as the subgap structure, which result from multiple Andreev reflections in pure V nanocontacts. Additionally, the H and D impurities in V nanocontacts induce several new conductance peaks outside the gap, referred to as an over-the-gap structures (OGSs). We found that the OGS peaks exhibit strong temperature dependence until the temperature is close to TC and follow the gap function predicted by BCS theory. When the contact diameter is changed at low temperature using the MCBJ technique, the OGS anomalies change almost linearly with the inverse of the contact diameter. In addition, the gap anomalies are significantly shifted outward by changing the positions of the H atoms through application of a high bias voltage between the contacts. The above features suggest that the OGS peaks are caused by the superconducting quasiparticle interference induced by H or D impurities and/or inhomogeneous structures in the nanocontacts.

Photon-Assisted Tunneling of High-Order Multiple Andreev Reflections in Epitaxial Nanowire Josephson Junctions.

Semiconductor/superconductor hybrids exhibit a range of phenomena that can be exploited for the study of novel physics and the development of new technologies. Understanding the origin of the energy spectrum of such hybrids is therefore a crucial goal. Here, we study Josephson junctions defined by shadow epitaxy on InAsSb/Al nanowires. The devices exhibit gate-tunable supercurrents at low temperatures and multiple Andreev reflections (MARs) at finite voltage bias. Under microwave irradiation, photon-assisted tunneling (PAT) of MARs produces characteristic oscillating sidebands at quantized energies, which depend on MAR order, n, in agreement with a recently suggested modification of the classical Tien-Gordon equation. The scaling of the quantized energy spacings with microwave frequency provides independent confirmation of the effective charge, ne, transferred by the nth-order tunneling process. The measurements suggest PAT as a powerful method for assigning the origin of low-energy spectral features in hybrid Josephson devices.

Phase tuning of multiple Andreev reflections of Dirac fermions and the Josephson supercurrent in Al–MoTe2–Al junctions

When an electron is incident on a superconductor from a metal, it is reflected as a hole in a process called Andreev reflection. If the metal N is sandwiched between two superconductors S in an SNS junction, multiple Andreev reflections (MARs) occur. We have found that, in SNS junctions with high transparency ([Formula: see text]) based on the Dirac semimetal MoTe2, the MAR features are observed with exceptional resolution. By tuning the phase difference [Formula: see text] between the bracketing Al superconductors, we establish that the MARs coexist with a Josephson supercurrent [Formula: see text]. As we vary the junction voltage V, the supercurrent amplitude [Formula: see text] varies in step with the MAR order n, revealing a direct relation between them. Two successive Andreev reflections serve to shuttle a Cooper pair across the junction. If the pair is shuttled coherently, it contributes to [Formula: see text]. The experiment measures the fraction of pairs shuttled coherently vs. V. Surprisingly, superconductivity in MoTe2 does not affect the MAR features.

Multiple Andreev reflections effect spectroscopy of LiFeAs single crystals: three superconducting order parameters and their temperature evolution

The structure of the superconducting order parameter of LiFeAs is studied by incoherent multiple Andreev reflections effect (IMARE) spectroscopy. The high transparent superconductor–thin normal metal–superconductor (SnS) contacts are created by a planar “break-junction” technique. Below T_c approx 17.5 K, the obtained I(V) and dI(V)/dV characteristics of SnS junctions show a presence of at least three bulk superconducting order parameters in LiFeAs. We directly determine the magnitudes, characteristic ratios, and temperature dependences of the superconducting gaps and discuss their symmetry.

Multiband superconductivity in SrFe2−xNixAs2

In this paper, we present a detailed study of the upper critical field and the energy gap structure of SrFe2−xNixAs2 single crystals with different nickel doping levels. Superconducting transitions were measured resistively in longitudinal and transverse magnetic fields up to 16T. The anisotropy of the upper critical field Hc2||ab/Hc2||c decreases monotonically to 1.4 with decreasing temperature for all measured samples. The WHH model was not able to fit measured Hc2(T) temperature dependences well, but the effective two-band model is in good agreement with the data and anisotropy behavior. Values and temperature dependences of superconducting gaps were determined directly by multiple Andreev reflection spectroscopy on symmetrical SnS junctions. Andreev reflections study revealed two superconducting gaps; our data are in line with the experimental results on most iron-based superconductors.Article highlightsWe obtained values and temperature dependencies of two distinct energy gaps in SrFe2−xNixAs2 (Sr-122) superconductor. This is important addition to multiband superconductivity studies in Sr-122 system. Upper critical field temperature dependencies in H||c and H||ab orientations are analyzed in terms of two band model.

Direct transport between superconducting subgap states in a double quantum dot

We demonstrate direct transport between two opposing sets of Yu-Shiba-Rusinov (YSR) subgap states realized in a double quantum dot. This sub-gap transport relies on intrinsic quasiparticle relaxation, but the tunability of the device allows us to explore also an additional relaxation mechanism based on charge transferring Andreev reflections. The transition between these two relaxation regimes is identified in the experiment as a marked gate-induced stepwise change in conductance. We present a transport calculation, including YSR bound states and multiple Andreev reflections alongside with quasiparticle relaxation, due to a weak tunnel coupling to a nearby normal metal, and obtain excellent agreement with the data.

Extracting transport channel transmissions in scanning tunneling microscopy using superconducting excess current

Transport through quantum coherent conductors, such as atomic junctions, is described by conduction channels. Information about the number of channels and their transmissions can be extracted from various sources, such as multiple Andreev reflections, dynamical Coulomb blockade, or shot noise. We complement this set of methods by introducing the superconducting excess current as a new tool to continuously extract the transport channel transmissions of an atomic scale junction in a scanning tunneling microscope. In conjunction with ab initio simulations, we employ this technique in atomic aluminum junctions to determine the influence of the structure adjacent to the contact atoms on the transport properties.

Hydrogen-impurity-induced conductance peaks in constriction type Josephson junctions

We studied hydrogen (H) and deuterium (D) impurity effects of superconducting Josephson current flowing through the superconductor-constriction-superconductor Josephson junctions (ScS-JJ). When H or D impurities are adsorbed on the surface of the ScS-JJ prepared by niobium or lead, many spike-like peaks with almost the same spacing appear inside the superconducting gap in addition to anomalies owing to the multiple Andreev reflection in the differential conductance spectra. The spacing between the adjacent peaks is independent of the temperature variation. These indicate that H or D impurities adsorbed on the JJ are sources of noise for the Josephson current.

Multiple andreev reflections in topological insulator nanoribbons

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 Bi2Se3 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 conductance due to multiple Andreev reflections. The interface transparency of the TI NR JJs estimated based on the excess current reaches τ = 0.83, which is among the highest values reported for TI JJs. The temperature dependence of critical current is consistent with the short and ballistic junction model confirming the formation of highly transparent superconducting contacts on the TI NR. Our observations would be useful for exploring topological Josephson effects in TI NRs.

Superconducting order parameters in overdoped BaFe1.86Ni0.14As2 revealed by multiple Andreev reflection spectroscopy of planar break junctions

Using multiple Andreev reflection (MAR) spectroscopy, we studied superconductor - normal metal - superconductor (SnS) semiballistic contacts with incoherent transport in overdoped pnictide superconductors BaFe$_{1.86}$Ni$_{0.14}$As$_2$ with critical temperature $T_c \approx 12$ K. We directly determined an anisotropic large gap with the characteristic ratios $2\Delta_L^{\rm out}(0)/k_BT_c \approx 6$ and $2\Delta_L^{\rm in}(0)/k_BT_c \approx 4$, almost isotropic small gap with $2\Delta_S(0)/k_BT_c \approx 2$, and the temperature dependence of the resolved superconducting order parameters. Above the large gap position $2\Delta_L$, a fine dI(V)/dV structure fully vanishing at $T_c$ and possibly caused by a resonant coupling with a bosonic mode was observed.

Josephson junctions via anodization of epitaxial Al on an InAs heterostructure

We combine electron beam lithography and masked anodization of epitaxial aluminum to define tunnel junctions via selective oxidation, alleviating the need for wet-etch processing or direct deposition of dielectric materials. Applying this technique to define Josephson junctions in proximity-induced superconducting Al-InAs heterostructures, we observe multiple Andreev reflections in transport experiments, indicative of a high quality junction. We further compare the mobility and density of Hall-bars defined via wet etching and anodization. These results may find utility in uncovering better fabrication approaches to junction-based qubit platforms.

Electrical Properties of Selective-Area-Grown Superconductor-Semiconductor Hybrid Structures on Silicon

We present a superconductor-semiconductor material system that is both scalable and monolithically integrated on a silicon substrate. It uses selective area growth of Al-InAs hybrid structures on a planar III-V buffer layer, grown directly on a high resistivity silicon substrate. We characterized the electrical properties of this material system at millikelvin temperatures and observed a high average field-effect mobility of $\mu \approx 3200\,\mathrm{cm^2/Vs}$ for the InAs channel, and a hard induced superconducting gap. Josephson junctions exhibited a high interface transmission, $\mathcal{T} \approx 0.75 $, gate voltage tunable switching current with a product of critical current and normal state resistance, $I_{\mathrm{C}}R_{\mathrm{N}} \approx 83\,\mathrm{\mu V}$, and signatures of multiple Andreev reflections. These results pave the way for scalable and high coherent gate voltage tunable transmon devices and other superconductor-semiconductor hybrids fabricated directly on silicon.

Shadow-wall lithography of ballistic superconductor\u2013semiconductor quantum devices

The realization of hybrid superconductor–semiconductor quantum devices, in particular a topological qubit, calls for advanced techniques to readily and reproducibly engineer induced superconductivity in semiconductor nanowires. Here, we introduce an on-chip fabrication paradigm based on shadow walls that offers substantial advances in device quality and reproducibility. It allows for the implementation of hybrid quantum devices and ultimately topological qubits while eliminating fabrication steps such as lithography and etching. This is critical to preserve the integrity and homogeneity of the fragile hybrid interfaces. The approach simplifies the reproducible fabrication of devices with a hard induced superconducting gap and ballistic normal-/superconductor junctions. Large gate-tunable supercurrents and high-order multiple Andreev reflections manifest the exceptional coherence of the resulting nanowire Josephson junctions. Our approach enables the realization of 3-terminal devices, where zero-bias conductance peaks emerge in a magnetic field concurrently at both boundaries of the one-dimensional hybrids.

A Perfect Andreev Reflection Induced by Anderson Disorder in a Normal–Superconductor Junction

The electronic transport properties of a 2D normal metal superconductor are studied by a nonequilibrium Green's function method. The normal metal is the non‐inverted HgTe/CdTe quantum well doped by electrons. It is found that Andreev reflection (AR) is enhanced in the weak disorder regime while weakened in the strong disorder regime. However, the AR coefficient can be perfect () with vanished fluctuations in the moderate disorder regime, whereas other scattering processes are forbidden. The mechanism goes that Anderson disorder leads to a topological Anderson insulator with bulk states localized while edge states still extensive. Multiple ARs and spin‐momentum locking cooperate to vanish the normal reflection and leave AR only. A detailed numerical study shows that fixing the Fermi surface in conduction band, a large enough junction width, and a strong coupling between the normal and superconducting leads are necessary for perfect AR.

Anomalous Andreev reflection on a torus-shaped Fermi surface

Andreev reflection (AR) refers to the electron-hole conversion at the normal metal-superconductor interface. In a three-dimensional metal with spherical Fermi surface, retro (specular) AR can occur with the sign reversal of all three (a single) components of particle velocity. Here, we predict a novel type of AR with the inversion of two velocity components, dubbed "anomalous-trajectory Andreev reflection" (AAR), which can be realized in a class of materials with torus-shaped Fermi surface, such as doped nodal line semimetals. For its toroidal circle perpendicular to the interface, the Fermi torus doubles the AR channels and generates multiple AR processes. In particular, the AAR and retro AR are found to dominate electron transport in the light and heavy doping regimes, respectively. We show that the AAR visibly manifests as a ridge structure in the spatially resolved nonlocal conductance, in contrast to the peak structure for the retro AR. Our work opens a new avenue for the AR spectroscopy and offers a clear transport signature of torus-shaped Fermi surface.

Tunneling processes between Yu-Shiba-Rusinov bound states

Very recent experiments have reported the tunneling between Yu-Shiba-Rusinov (YSR) bound states at the atomic scale. These experiments have been realized with the help of a scanning tunneling microscope where a superconducting tip is functionalized with a magnetic impurity and is used to probe another magnetic impurity deposited on a superconducting substrate. In this way it has become possible to study for the first time the spin-dependent transport between individual superconducting bound states. Motivated by these experiments, we present here a comprehensive theoretical study of the tunneling processes between YSR bound states in a system in which two magnetic impurities are coupled to superconducting leads. Our theory is based on a combination of an Anderson model with broken spin degeneracy to describe the impurities and nonequilibrium Green's function techniques to compute the current-voltage characteristics. This combination allows us to describe the spin-dependent transport for an arbitrary strength of the tunnel coupling between the impurities. We first focus on the tunnel regime and show that our theory naturally explains the experimental observations of the appearance of current peaks in the subgap region due to both the direct and thermal tunneling between the YSR states in both impurities. Then, we study in detail the case of junctions with increasing transparency, which has not been experimentally explored yet, and predict the occurrence of a large variety of (multiple) Andreev reflections mediated by YSR states that give rise to a very rich structure in the subgap current. In particular, we predict the occurrence of multiple Andreev reflections that involve YSR states in different impurities. These processes have no analogue in single-impurity junctions and they are manifested as current peaks with negative differential conductance for subgap voltages.

Zero-Bias Conductance Peaks Effectively Tuned by Gating-Controlled Rashba Spin-Orbit Coupling.

Zero-bias conductance peaks (ZBCPs) can manifest a number of notable physical phenomena and thus provide critical characteristics to the underlying electronic systems. Here, we report observations of pronounced ZBCPs in hybrid junctions composed of an oxide heterostructure LaAlO_{3}/SrTiO_{3} and an elemental superconductor Nb, where the two-dimensional electron system (2DES) at the LaAlO_{3}/SrTiO_{3} interface is known to accommodate gate-tunable Rashba spin-orbit coupling (SOC). Remarkably, the ZBCPs exhibit a domelike dependence on the gate voltage, which correlates strongly with the nonmonotonic gate dependence of the Rashba SOC in the 2DES. The origin of the observed ZBCPs can be attributed to the reflectionless tunneling effect of electrons that undergo phase-coherent multiple Andreev reflection, and their gate dependence can be explained by the enhanced quantum coherence time of electrons in the 2DES with increased momentum separation due to SOC. We further demonstrate theoretically that, in the presence of a substantial proximity effect, the Rashba SOC can directly enhance the overall Andreev conductance in the 2DES-barrier-superconductor junctions. These findings not only highlight nontrivial interplay between electron spin and superconductivity revealed by ZBCPs, but also set forward the study of superconducting hybrid structures by means of controllable SOC, which has significant implications in various research fronts from superconducting spintronics to topological superconductivity.

Tkwant: a software package for time-dependent quantum transport

Tkwant is a Python package for the simulation of quantum nanoelectronics devices to which external time-dependent perturbations are applied. Tkwant is an extension of the kwant package (https://kwant-project.org/) and can handle the same types of systems: discrete tight-binding-like models that consist of an arbitrary central region connected to semi-infinite electrodes. The problem is genuinely many-body even in the absence of interactions and is treated within the non-equilibrium Keldysh formalism. Examples of Tkwant applications include the propagation of plasmons generated by voltage pulses, propagation of excitations in the quantum Hall regime, spectroscopy of Majorana fermions in semiconducting nanowires, current-induced skyrmion motion in spintronic devices, multiple Andreev reflection, Floquet topological insulators, thermoelectric effects, and more. The code has been designed to be easy to use and modular. Tkwant is free software distributed under a BSD license and can be found at https://tkwant.kwant-project.org/.

Nonequilibrium edge transport in quantum Hall based Josephson junctions

We study the transport properties of a voltage-biased Josephson junction where the BCS superconducting leads are coupled via the edges of a quantum Hall sample. In this scenario, an out of equilibrium Josephson current develops, which is numerically studied within the Floquet-Keldysh Green's function formalism. We particularly focus on the time-averaged current as a function of both the bias voltage and the magnetic flux threading the sample and analyze the resonant multiple Andreev reflection processes that lead to an enhancement of the quasiparticle transmission. We find that a full tomography of the dc current in the voltage-flux plane allows for a complete spectroscopy of the one-way edge modes and could be used as a hallmark of chiral edge mediated transport in these hybrid devices.

Characterization of structure and superconducting properties of low-temperature phase of Pb-Bi alloy films

Lead-bismuth (Pb-Bi) alloys, as a superconducting material, have been widely studied at their superconducting transition temperatures and the critical magnetic fields for different composition ratios. Most of experimental studies focused on the stable ε phase formed at high temperatures, but less on the Pb-Bi alloys grown at low temperatures. So far, the structural and superconducting properties of the low-temperature Pb-Bi phases are far from good understanding. Here, we report our investigation of structural and superconducting properties of a low-temperature phase of Pb-Bi alloy. The Pb-Bi alloy films with a nominal thickness of about 6 nm are prepared by co-depositing Bi and Pb on Bi(111)/Si(111)-(7 × 7) substrates at a low temperature of 100 K followed by annealing at a treatment of 200 K for 2 h. The structural and superconducting properties of the Pb-Bi alloy films are characterized in situ by using low-temperature scanning tunneling microscopy/spectroscopy (STM/STS). It is observed that the spatially separated phases of nearly pure Bi(111) domains and Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> alloy domains are formed in the films, where these phases can be identified by their distinct differences in the atomic structure and the distributions of step heights in the atomically resolved STM images, as well as by their distinguished STS spectra. The Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> alloy phase presents the structure of Pb(111), in which about <i>x</i> ≈ 0.1 Bi is substituted for Pb. The STS spectra show that the Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> alloy phase is superconducting, with a transition temperature <i>T</i><sub>c</sub> = 7.77 K derived from the variable-temperature measurements. This transition temperature is higher than that in pure Pb film (6.0–6.5 K), which can be well explained by the Mattias rules, with considering the fact that the average number of valance electrons increases after Bi atoms with five valance-electrons have been substituted for Pb atoms with four valance-electrons. The analysis shows that the ratio <inline-formula><tex-math id="M1">\begin{document}$ 2\Delta (0)/{k_{\rm{B}}}{T_{\rm{C}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210482_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210482_M1.png"/></alternatives></inline-formula> is about 4.94 with the superconducting gap <inline-formula><tex-math id="M2">\begin{document}$ \varDelta (0) = 1.66$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210482_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210482_M2.png"/></alternatives></inline-formula> meV at 0 K, indicating that the Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> alloy is a strongly-coupled superconductor. The non-superconducting Bi(111) and the superconducting Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> alloy domains form an in-plane superconductor-normal metal-superconductor (S-N-S) Josephson junction. The proximity effect in the Bi(111) domains is measured at different N-S junctions, which suggests that the lateral superconducting penetration length in Bi(111) might be affected by the area of the quasi-two-dimensional interface. The superconducting gap in the Bi(111) region with a narrow width of 23 nm in an S-N-S Josephson junction is found to be greatly enhanced due to the existence of multiple Andreev reflections. Since Bi can host potential topological properties, the lateral Bi(111)-Pb<sub>1–<i>x</i></sub>Bi<i><sub>x</sub></i> heterostructures, because of the existing proximity effect, could have potential applications in exploring the novel topological and superconducting phenomena.