Andreev Reflection Research Articles

Interplay between magnetic gap and quasi-particle lifetime in topological insulator ferromagnet/f-wave superconductor junctions

Using the modified Blonder–Tinkham–Klapwijk (BTK) theory, the interplay between the lifetime of quasi particles and the magnetic gap in a topological insulator-based ferromagnet/f-wave superconductor (TI-based FM/f–wave SC) tunnel structure is theoretically studied. Two symmetries of f 1 and f 2 waves are considered for superconducting pairing states. The results indicate that reducing the finite quasi-particle lifetime will induce a transformation of energy-gap peaks into a zero-bias peak in tunneling conductance spectrum, as well as a transformation of energy-gap dips into a zero-bias dip in shot noise spectrum, ultimately resulting in the smoothing of the zero-bias conductance peak and the zero-bias shot noise dip. An increase in magnetic gap will suppress the tunnel conductance and shot noise when the conventional Andreev retro-reflection dominates, but will enhance them when the specular Andreev reflection is dominant. Both specular Andreev reflection and conventional Andreev retro-reflection will be enhanced as the quasi-particle lifetime increases. When Fermi energy equals the magnetic gap, shot noise and tunneling conductance vanish across all energy ranges. These findings not only contribute to a better understanding of specular Andreev reflection in the FM/f–wave SC junction based on TIs but also provide insights for experimentally determining the f-wave pairing symmetry.

Contribution of Andreev Reflection to the Mobility of Surface State Electrons on Superfluid $$^3$$He-B

Contribution of Andreev Reflection to the Mobility of Surface State Electrons on Superfluid $$^3$$He-B

Andreev reflection, Andreev states, and long ballistic SNS junction

The analysis in the present paper is based on the most known concept introduced by the brilliant physicist Alexander Andreev: Andreev bound states in a normal metal sandwiched between two superconductors. The paper presents results of direct calculations of ab initio expressions for the currents in a long ballistic SNS junction. The expressions are expanded in 1/L (L is the thickness of the normal layer). The main contribution ∝1/L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\propto 1/L$$\\end{document} to the current agrees with the results obtained in the past, but the analysis suggests a new physical picture of the charge transport through the junction free from the problem with the charge conservation law. The saw-tooth current-phase relation at T=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=0$$\\end{document} directly follows from the Galilean invariance of the Bogolyubov–de Gennes equations proved in the paper. The proof is valid for any variation of the energy gap in space if the Andreev reflection is the only scattering process. The respective roles of the contributions of bound and continuum states to the current are clarified. They depend on the junction dimensionality.

Superconducting Field-Effect Transistors with PdxTe-Te Intimate Contacts.

Superconducting-based electronic devices have shown great potential for future quantum computing applications. One key building block device is a superconducting field-effect transistor based on a superconductor-semiconductor-superconductor Josephson-junction (JJ) with a gate-tunable semiconducting channel. However, the performance of such devices is highly dependent on the quality of the superconductor to semiconductor interface. In this study, we present an alternative method to obtain a high-quality interface by using intimate contact. We investigate the proximity-induced superconductivity in chiral crystal tellurium (Te) and fabricate a PdxTe-Te-PdxTe JJ with an ambipolar supercurrent that is gate-tunable and exhibits multiple Andreev reflections. The semiconducting two-dimensional Te single crystal is grown hydrothermally and partially converted to superconducting PdxTe by controlled annealing. Our work demonstrates a promising path for realizing controllable superconducting electronic devices with high-quality superconducting interfaces; thus, we can continue to advance the field of quantum computing and other interface-based technologies.

Weak and strong chirality-anomaly-manipulations in a superconducting Weyl semimetal sandwich structure

We investigate the quantum interference of the electron–hole conversions from the two interfaces in a Weyl semimetal (WSM)-based hybrid structure, in which a superconducting WSM is sandwiched in between two normal ones. The quantum interference is characterized by the chirality-anomaly-manipulation (CAM). It is found that only low energy is in favor for s-wave BCS pairing states. The Andreev reflection (AR) chirality blockade can be tuned by the stagger angle α for the relative orientation of paired Weyl points, accompanied by an AR bipolar chirality diode. Thus, a strong CAM is indicated for the electron–hole conversion. However, the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) pairing states have no energy preference, with the weak and strong CAMs being near and far away from the zero energy, respectively. More interestingly, a perfect AR with the normal reflection suppressed thoroughly can be obtained at any α as a result of the FFLO paring with the same chirality. In addition, the conductance or noise power, which incorporates the contributions of the two paired Weyl nodes, not only, in turn, embodies the respective features of their contributions but also can be experimentally measured to discern between the BCS and FFLO paring states.

Band structure of the one-dimensional tetrameric Kitaev chain induced by imaginary potentials

We investigate the one-dimensional tetramerised Kitaev chain induced by imaginary potentials {iγ,−iγ,−iγ,iγ} applied to the dimerised Kitaev chain. It is found that the imaginary potentials cause a variety of topological phase transitions. When the chemical potential μ is tuned to the energy zero point, they lead to the appearance of the mixed phase of the system consisting of two purely real Kitaev-like modes and four purely imaginary energy SSH-like zero-energy modes, which appear as the transition of the Kitaev-like-mixed-SSH-like phase. In addition, the Kitaev-like phase can be broadened by imaginary potentials, manifested as the widening of the quantised Andreev reflection plateau. When μ≠0, the same topological phase transition occurs, from the topologically-trivial phase to the Kitaev-like phase. One can believe that this work provides theoretical support for probing the generation of Majorana zero modes in new topological superconducting systems.

Andreev Conductance in Disordered SF Junctions with Spin-Orbit Scattering

We calculate the conductance of a junction between a disordered superconductor and a very strong half-metallic ferromagnet admitting electrons with only one spin projection. A usual mechanism of Andreev reflection is strongly suppressed in this case since Cooper pairs are composed of electrons with opposite spins. However, this obstacle can be overcome if we take into account spin-orbit scattering inside the superconductor. Spin-orbit scattering induces a fluctuational (zero on average) spin-triplet component of the superconducting condensate, which is enough to establish Andreev transport into a strong ferromagnet. This remarkably simple mechanism is quite versatile and can explain long-range triplet proximity effect in a number of experimental setups. One particular application of the suggested effect is to measure the spin-orbit scattering time τSO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{\ ext {SO}}$$\\end{document} in disordered superconducting materials. The value of Andreev conductance strongly depends on the parameter ΔτSO\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta \ au _\ ext {SO}$$\\end{document} and can be noticeable even in very disordered but relatively light metals like granular aluminum.

Electrically controlled crossed Andreev reflection in altermagnet/superconductor/altermagnet junctions

Altermagnets are a novel class of magnetic materials with a significant non-relativistic spin splitting band structure but zero net macroscopic magnetization. We here investigate the interplay between altermagnetism and superconductivity and how the band structures of the altermagnet affect nonlocal transport across altermagnet/superconductor/altermagnet junctions. The two types of spin-momentum coupling: anisotropic and valley-dependent spin-momentum couplings are considered. The pure crossed Andreev reflection (CAR) can be observed by tuning the chemical potential and a switch effect between pure CAR and pure electron elastic cotunneling (EC) can be realized by reversing the Néel vector of the right altermagnet. For the anisotropic spin-momentum coupling, increasing the altermagnetism strength decreases the amplitude of EC while increases that of CAR. Furthermore, a switch between pure EC and pure CAR is predicted for the Néel vectors of the altermagnets in the parallel configuration for the valley-dependent spin-momentum coupling by tuning the on-site energy.

Crossed Andreev reflection in normal-superconductor-normal junction based on Kekulé-Y patterned graphene

We theoretically study the crossed Andreev reflection (CAR) of the normal metal-superconductor-normal metal (NSN) heterojunction based on Kekulé-Y patterned graphene with two doping types, i.e. nSn and nSp configurations. It is found that the enhanced CAR is more likely to occur in the nSp junction rather than the nSn junction. To be concrete, the almost perfect CAR occurs in a large range of incident angle in the single Dirac cone phase when the incident energy is inside the gap of the nonlinear band. Furthermore, the roles of the length of superconductor and pseudospin-valley coupling on conductance are also evaluated.

Andreev reflections in deformed semi-Dirac material superconducting junctions

Besides the strong anisotropy, another unique feature of the semi-Dirac materials (SDMs) is the evolution of its dispersion with gap parameter from a merging semi-Dirac point to two Dirac points. In this study, we study the superconducting coherent transport at the SDM superconducting junction and focus on the influence of evolution of the SDM dispersion on the Andreev reflection. We found that the coexistence of peculiar quadruple reflections, including double specular normal reflection and double retro Andreev reflection, can occur within a wide range of parameters. We in detail discuss the dependence of reflection probabilities on the incident angle, incident energy, and gap parameter. By modulating these parameters, we also observe rich double reflection scenarios. These results enrich our understanding of the superconducting coherent transport and facilitate the probing of the intrinsic gap parameter in SDMs experimentally.

Andreev reflections in black phosphorus based normal-superconducting junctions modulated by linearly polarized light

Andreev reflections in black phosphorus based normal-superconducting junctions modulated by linearly polarized light

Selective-Area-Grown PbTe-Pb Planar Josephson Junctions for Quantum Devices.

Planar Josephson junctions are predicted to host Majorana zero modes. The material platforms in previous studies are two-dimensional electron gases (InAs, InSb, InAsSb, and HgTe) coupled to a superconductor such as Al or Nb. Here, we introduce a new material platform for planar JJs, the PbTe-Pb hybrid. The semiconductor, PbTe, was grown as a thin film via selective area epitaxy. The Josephson junction was defined by a shadow wall during the deposition of superconductor Pb. Scanning transmission electron microscopy reveals a sharp semiconductor-superconductor interface. Gate-tunable supercurrents and multiple Andreev reflections are observed. A perpendicular magnetic field causes interference patterns of the switching current, exhibiting Fraunhofer-like and SQUID-like behaviors. We further demonstrate a prototype device for Majorana detection wherein phase bias and tunneling spectroscopy are applicable.

Anisotropic s-Wave Gap in the Vicinity of a Quantum Critical Point in Superconducting BaFe2(As1–x P x )2 Single Crystals: A Study of Point-Contact Spectroscopy

We report on soft c-axis point-contact Andreev reflection (PCAR) spectroscopy combining with resistivity measurements on BaFe2(As0.7P0.3)2, to elucidate the superconducting gap structure in the vicinity of the quantum critical point. A double peak at the gap edge plus a dip feature at zero-bias has been observed on the PCAR spectra, indicative of the presence of a nodeless gap in BaFe2(As0.7P0.3)2. Detailed analysis within a sophisticated theoretical model reveals an anisotropic gap with deep gap minima. The PCARs also feature additional structures related to the electron–bosonic coupling mode. Using the extracted superconducting energy gap value, a characteristic bosonic energy Ω b and its temperature dependence are obtained, comparable with the spin-resonance energy observed in neutron scattering experiment. These results indicate a magnetism-driven quantum critical point in the BaFe2(As1−x P x )2 system.

Levitons in correlated nano-scale systems.

In this short review (written to celebrate David Campbell's 80th birthday), we provide a theoretical description of quantum transport in nanoscale systems in the presence of single-electron excitations generated by Lorentzian voltage drives, termed Levitons. These excitations allow us to realize the analog of quantum optics experiments using electrons instead of photons. Importantly, electrons in condensed matter systems are strongly affected by the presence of different types of non-trivial correlations, with no counterpart in the domain of photonic quantum optics. After providing a short introduction about Levitons in non-interacting systems, we focus on how they operate in the presence of two types of strong electronic correlations in nanoscale systems, such as those arising in the fractional quantum Hall effect or in superconducting systems. Specifically, we consider Levitons in a quantum Hall bar of the fractional quantum Hall effect, pinched by a quantum point contact, where anyons with fractional charge and statistics tunnel between opposite edges. In this case, a Leviton-Leviton interaction can be induced by the strongly correlated background. Concerning the effect of superconducting correlations on Levitons, we show that, in a normal metal system coupled to BCS superconductors, half-integer Levitons minimize the excess noise in the Andreev regime. Interestingly, energy-entangled electron states can be realized on-demand in this type of hybrid setup by exploiting crossed Andreev reflection. The results exposed in this review have potential applications in the context of quantum information and computation with single-electron flying qubits.

Theoretical valley-polarized subgap transport and intravalley pairing states in a silicene-based antiferromagnet–superconductor junction

We theoretically study the valley-polarized subgap transport and intravalley pairing states in silicene-based antiferromagnet/superconductor (AF/SC) junctions. It is found that in the absence of an electric field, the antiferromagnetic order induced in silicene can give rise to valley-polarized states that strongly affect the subgap conductance. With the increasing antiferromagnetic exchange field, the gap-edge Andreev-resonant peak is replaced by broadened features for the homo-SC model whereas by a sharp conductance dip for the bulk-SC one. This significant difference arises from the intravalley Andreev reflection caused by the valley-mixing scattering in the bulk-SC model, which can be enhanced by the antiferromagnetic order. Particularly, this intravalley pairing process can be switched on or off by adjusting the spin polarization through the electric field applied in the AF region. Our findings not only pave a new road to employ antiferromagnetic materials in valleytronics, but also facilitate the verification and detection of potential intravalley pairing state and valley polarization in silicene.

Andreev reflection in hybrid [formula omitted] lattices junction

We explore local Andreev reflection and crossed Andreev reflection in a normal metal (N)–superconductor (S)–normal metal (N) hybrid junction based on the α−T3 lattice. Initially, both the left and right sections feature dice lattice structures (α=1). We compute probabilities for electron reflection, local Andreev reflection, electron transmission, and crossed Andreev reflection, as well as local conductance, electron transmission conductance, and crossed Andreev reflection conductance. Subsequently, we analyze structures with the left side featuring dice lattice and the right side graphene (α=0), as well as the reverse configuration. Our findings reveal that crossed Andreev reflections are more prevalent in the graphene–superconductor–dice lattice (GSD) junction, particularly with moderate superconducting region lengths, larger electron incidence angles, and lower electron incidence energy.

Majorana bound state in the continuum and Fano effect formed by the coupling of two Andreev-reflection channels

Majorana-induced Andreev reflection (AR) is theoretically investigated by considering the interplay between two AR channels, each of which is formed by the lead and its coupled topological-superconducting nanowire with Majorana bound states. By means of the Scattering matrix and nonequilibirum Green’s function technique, relevant observables are analyzed, including the differential conductance, the density of states, and shot-noise Fano factors. It is found that Majorana bound states in the continuum (MBIC) can be constructed, under the condition of two uniform nanowires and inter-channel couplings. Otherwise, the Fano effect is allowed to occur, which is manifested as the appearance of additional conductance dips. In particular, the Fano antiresonance can be induced by constructing the identical inter-channel couplings. All these results can be helpful in understanding the MBIC contributed by the Majorana-assisted ARs.

Interplay of Andreev Reflection and Coulomb Blockade in Hybrid Superconducting Single-Electron Transistors.

We study the interplay between Coulomb blockade and superconductivity in a tunable superconductor-superconductor-normal-metal single-electron transistor. The device is realized by connecting the superconducting island via an oxide barrier to the normal-metal lead and with a break junction to the superconducting lead. The latter enables Cooper pair transport and (multiple) Andreev reflection. We show that these processes are relevant also far above the superconducting gap and that signatures of Coulomb blockade may reoccur at high bias while they are absent for small bias in the strong-coupling regime. Our experimental findings agree with simulations using a rate equation approach in combination with the full counting statistics of multiple Andreev reflection.

Crossed Andreev Reflection and Elastic Cotunneling in Three Quantum Dots Coupled by Superconductors.

The formation of a topological superconducting phase in a quantum-dot-based Kitaev chain requires nearest neighbor crossed Andreev reflection and elastic cotunneling. Here, we report on a hybrid InSb nanowire in a three-site Kitaev chain geometry-the smallest system with well-defined bulk and edge-where two superconductor-semiconductor hybrids separate three quantum dots. We demonstrate pairwise crossed Andreev reflection and elastic cotunneling between both pairs of neighboring dots and show sequential tunneling processes involving all three quantum dots. These results are the next step toward the realization of topological superconductivity in long Kitaev chain devices with many coupled quantum dots.

Andreev reflection in Euler materials

Many previous studies of Andreev reflection have demonstrated that unusual effects can occur in media which have a nontrivial bulk topology. Following this line of investigation, we study Andreev reflection by analysing a simple model of a bulk node with a generic winding number n > 0, where the even cases directly relate to topological Euler materials. We find that the magnitudes of the resultant reflection coefficients depend strongly on whether the winding is even or odd. Moreover this parity dependence is reflected in the differential conductance curves, which are highly suppressed for n even but not n odd. This gives a possible route through which the recently discovered Euler topology could be probed experimentally.