Andreev Reflection Effect Research Articles

Doping Evolution of the Superconducting Order Parameter of Na(Fe, Co)As Alkali-Metal Pnictides

Using incoherent multiple Andreev reflection effect spectroscopy, we have studied the multiple-gap superconducting state of underdoped and overdoped Na(Fe, Co)As single crystals. We directly determined the magnitudes of the microscopic superconducting order parameters, their temperature dependences, and characteristic ratios \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\Delta (0){\ ext{/}}{{k}_{B}}{{T}_{c}}$$\\end{document}. The obtained large data statistics unambiguously proves a significant decrease in the degree of the large superconducting gap possible anisotropy in the overdoped compositions away from the antiferromagnetic and nematic regions of the doping phase diagram.

Enhancement and switch effect of equal-spin Andreev reflection in ferromagnet/insulator/Ising superconductor junctions

We study the property of equal-spin Andreev reflection (ESAR) in the ferromagnet/insulator/Ising superconductor junction where Ising spin–orbit coupling is taken into account in the insulator. It is found that the ESAR exhibits a regular oscillation with the insulating barrier, the amplitude and period of which can be effectively controlled by the chemical potentials. Compared to that in the ferromagnet/Ising superconductor junction, the ESAR is greatly increased due to the resonant mode, suggesting an enhanced spin-triplet pairing. As an application, the proposed junction may work as a switch to turn on and off the ESAR. Furthermore, the insulating barrier does not change the magnetoanisotropic period of ESAR because of the invariant symmetry of the system, however, the magnetoanisotropy is strengthened.

Comparison of the Gap Structure of Underdoped and Overdoped Superconducting Pnictides BaFe2 – xNixAs2

We compare the structure of the superconducting order parameter of overdoped BaFe1.88Ni0.12As2and underdoped BaFe1.92Ni0.08As2pnictides with similarTc≈18.0−18.3K. Using incoherent multiple Andreev reflection effect spectroscopy, we directly determined the magnitudes of the two microscopic superconducting order parameters: the small superconducting gap and probably anisotropic large gap, their characteristic ratios and temperature dependences. We discuss similarity and difference in the gap structure, as well as possible influence of antiferromagnetic phase to superconducting properties.

Upper Critical Field and Tunneling Spectroscopy of Underdoped Na(Fe,Co)As Single Crystals.

A comprehensive study of superconducting properties of underdoped NaFe0.979Co0.021As single crystals by a combination of upper critical field measurements and incoherent multiple Andreev reflection effect (IMARE) spectroscopy is presented. The Hc2(T) temperature dependences are measured at magnetic fields up to 16 T with in-plane and out-of-plane field directions and considered within single-band and two-band models in order to estimate the Hc2(0) value. In IMARE spectroscopy probes, the magnitude, characteristic ratio, and temperature dependence of the superconducting order parameters (ΔL,S(T)) are determined locally and directly. A possible k-space anisotropy of the large superconducting gap is demonstrated. We show that usage of a quadruple of λij0 coupling constants obtained in the IMARE experiment can significantly reduce the number of free parameters required to fit the Hc2(T) dependence within a two-band approach (from six to two).

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.

Andreev reflection and Josephson effect in the α−T3 lattice

We investigate the Andreev reflection and Josephson effect in the $\alpha$-T3 lattice which falls between graphene ($\alpha = 0$) and the dice lattice ($\alpha = 1$) by adjusting the parameter $\alpha$. In the regime of specular Andreev reflection, when the incident energy of electron is small, the probability of Andreev reflection decreases as the parameter $\alpha$ increases. On the contrary, when the incident energy is large, the probability of Andreev reflection increases as the parameter $\alpha$ increases. Interestingly, when the incident energy approaches the superconducting energy-gap function, the Andreev reflection with approximate all-angle perfect transmission happens in the case of $\alpha = 1$. In the regime of Andreev retro-reflection, when the parameter $\alpha$ increases, the probability of Andreev reflection increases regardless of the value of incident energy. When the incident energy approaches the superconducting energy-gap function, the Andreev reflection with approximate all-angle perfect transmission happens regardless of the value of $\alpha$. We also give the differential conductance in these two regimes and find that the differential conductance increases as the parameter $\alpha$ increases generally. In addition, the $\alpha$-T3 lattice-based Josephson current increases as $\alpha$ increases. When the length of junction approaches zero, the critical Josephson currents in the different values of $\alpha$ approach the same value.

Multiple-Band Andreev Transport in Optimally Doped Superconducting Oxypnictides

Using multiple Andreev reflections (MAR) effect spectroscopy of SnS junctions, we directly determine temperature dependences of the superconducting order parameters, excess Andreev current, and zero-bias conductance (ZBC) in polycrystalline samples of superconducting oxypnictides Sm0.7Th0.3OFeAs and NdO0.6H0.36FeA with almost optimal critical temperatures. It is shown that the results obtained are self-consistent and could be described in the framework of a two-band model. We estimate a dominating contribution 70–85% of the bands with the large gap to the total conductance.

Amplitudes of minima in dynamic conductance spectra of the SNS Andreev contact

Although several theoretical approaches describing multiple Andreev reflection (MAR) effects in the superconductor–normal metal–superconductor (SNS) junction are elaborated, the problem of the comprehensive and adequate description of MAR is highly actual. In particular, a broadening parameter Γ is still unaccounted at all, whereas a ballistic condition (the mean free path for inelastic scattering l to the barrier width d ratio) is considered only in the framework of Kümmel, Gunsenheimer, and Nikolsky (KGN), as well as Gunsenheimer–Zaikin approaches, for an isotropic case and fully transparent constriction. Nonetheless, the influence of the l/d ratio on the dynamic conductance spectrum (dI/dV) features remains disregarded, thus being one of the aims of the current work. Our numerical calculations in the framework of an extended KGN approach develop the l/d variation to determine both the number of the Andreev features and their amplitudes in the dI/dV spectrum. We show, in the spectrum of a diffusive SNS junction (l/d→1), a suppression of the Andreev excess current and a dramatic change in the current voltage I(V)-curve slope at low bias, with only the main harmonic at eV=2Δ bias voltage remaining well-distinguished in the dI/dV-spectrum. Additionally, we attempt to make a first-ever comparison between experimental data for the high-transparency SNS junctions (more than 85%) and theoretical predictions. As a result, we calculate the temperature dependences of amplitudes and areas of Andreev features within the extended KGN approach, which qualitatively agree with our experimental data obtained using a “break-junction” technique.

Characteristics of superconducting subsystems in magnesium diborides and iron oxypnictides from data on spectroscopy of multiple Andreev reflections

Physical parameters of condensates in multiple-gap superconductors are determined by coupling both within and between bands. The simplest description of the physics of the system in case of two superconducting order parameters is offered by the Moskalenko-Suhl two-band model, in which strength of coupling is determined by four constants of electron–boson interaction. The characteristic ratio 2Δ0/kBTc usually exceeds the limit of the BCS theory equal to 3.53, thus requiring renormalization to be introduced for Δ0 or Tc in both BCS integrals. This implies that at least six parameters are to be handled in the Moskalenko–Suhl model to describe a two-gap superconducting system. The quantities observed using various techniques are superposition of contributions from each band and interband interaction, and thus usually cannot be separated in the experiment. Moreover, it is not possible to explore in the experiment individual properties of each of the superconducting subsystems, i.e. to study them in the absence of crossband interaction. In contrast to the Eliashberg model extended for the two-band case, the Moskalenko-Suhl model provides the simplest technique to describe the superconducting state using a minimal set of quantities, a feature that is undoubtedly attractive for experimentalists. The factor that is required for such an estimate to be reliable is direct, simultaneous, and accurate measurement of both order parameters as a function of temperature, a task that is very challenging for the experiment. Multiple Andreev reflection effect (MARE) spectroscopy may be used to determine dependences of order parameters Δ1,2(T) directly without involving additional approximation of experimental spectra of the dynamic conductance of Andreev contacts. We have fitted the experimental dependences Δ1,2(T) obtained within the extended Moskalenko–Suhl model to estimate parameters of superconducting systems such as MgB2 + MgO, Mg1-xAlxB2, and iron-containing oxypnictides ReO1-xFyFeAs (Re = Gd, Sm:Th, La). The intraband coupling was shown to be stronger than the crossband coupling by a factor of 15 for magnesium diborides and 10 for ferrous arsenides with maximal Tc, this ratio decreases together with Tc. The estimated eigen characteristic ratios for “strong” bands are ≈5.5 and 4.6, respectively, are almost independent on chemical composition in the explored range Tc > 20 K. This ratio for “weak” bands is close to the weak-coupling BCS limit 3.5.

Charge Transport Properties of the Majorana Zero Mode Induced Noncollinear Spin Selective Andreev Reflection**Supported by the National Natural Science Foundation of China under Grant Nos 11674028, 61774017, 11734004 and 21421003, and the National Key Research and Development Program of China under Grant No 2017YFA0303300.

We study the charge transport properties of the spin-selective Andreev reflection (SSAR) effect between a spin polarized scanning tunneling microscope (STM) tip and a Majorana zero mode (MZM). Considering both the MZM and the excited states, we calculate the conductance and the shot noise power of the noncollinear SSAR using scattering theory. We find that the excited states give rise to inside peaks. Moreover, we numerically calculate the shot noise power and the Fano factor of the SSAR effect. Our calculation shows that the shot noise power and the Fano factor are related to the angle between the spin polarization direction of the STM tip and that of the MZM, which provide additional characteristics to detect the MZM via SSAR.

Valley controlled Andreev reflection and valley-switch effect in graphene-based superconducting hybrid structures

The presence of the valley degree of freedom in two-dimensional materials leads to the valleytronics, in which information is encoded by the valley quantum number of the electron. For graphene-based superconducting hybrid structures, with the incoming electron and the Andreev reflected hole belonging to two opposite valleys, the Andreev reflection (AR) can be controlled by the valley degree of freedom. Here, we investigate theoretically the AR in graphene-based normal/supercondcutor junctions. Due to the interplay of the staggered potentials and the off-resonant circularly polarized light, the conductances demonstrate rich features. In particular, when the Fermi level of the normal lead is smaller than the superconducting gap, the retro AR and specular AR are well separated in energy, so we can easily distinguish them by studying the conductance spectra. More importantly, for normal/supercondcutor/normal junctions, the local AR is forbidden due to the vanishing density of states in one valley, and one may observe a valley-switch effect between perfect elastic cotunneling and perfect crossed AR, by reversing the handedness of the circularly polarized light.

Enhanced thermoelectric properties of graphene-based ferromagnetic-superconductor junctions, Andreev reflection effect

We have theoretically studied ballistic graphene-based Ferromagnetic/Superconductor (FG/SG) junction operated as thermoelectric generators. Ferromagnetism and superconductivity in graphene are assumed to be induced by superconducting and ferromagnetic electrodes placed on the top of the graphene sheet. We calculate the normal and Andreev reflection probabilities using the Blonder-Tinkham-Klapwijk (BTK) formalism to solve a four-dimensional version of the Dirac-Bogoliubov-de Gennes equation. By a special choice of system parameters it is possible to achieve a condition in which thermal conductance declines significantly while electrical conductance increases. We also calculate output power and thermoelectric power-conversion efficiency at low temperature based on such a structure and show that the power generation efficiency is close to the Carnot limit.

What can Andreev bound states tell us about superconductors?

Zero-energy Andreev bound states, which manifest themselves in the tunnelling spectra as zero-bias conductance peaks (ZBCPs), are abundant at interfaces between superconductors and other materials and on the nodal surface of high-temperature superconductors. In this review, we focus on the information such excitations can provide on the properties of superconductor systems. First, a general introduction to the physics of Andreev bound states in superconductor/normal metal interfaces is given with a particular emphasis on why they appear at zero energy in d-wave superconductors. Then, specific spectroscopic tunnelling studies of thin films, bilayers and junctions are described, focusing on the corresponding ZBCP features. Scanning tunnelling spectroscopy (STS) studies show that the ZBCPs on the c-axis YBa2Cu3O7-δ (YBCO) films are correlated with the surface morphology and appear only in proximity to (110) facets. STS on c-axis La1.88Sr0.12CuO4 (LSCO) films exhibiting the 1/8 anomaly shows spatially modulated peaks near zero bias associated with the anti-phase ordering of the d-wave order parameter predicted at this doping level. ZBCPs were also found in micrometre-size edge junctions of YBCO/SrRuO3/YBCO, where SrRuO3 is ferromagnetic. Here, the results are consistent with a crossed Andreev reflection effect (CARE) at the narrow domain walls of the SrRuO3 ZBCPs measured in STS studies of manganite/cuprate bilayers could not be attributed to CARE because the manganite's domain wall is much larger than the coherence length in YBCO, and instead are attributed to proximity-induced triplet-pairing superconductivity with non-conventional symmetry. And finally, ZBCPs found in junctions of non-intentionally doped topological insulator films of Bi2Se3 and the s-wave superconductor NbN are attributed to proximity-induced px + ipy triplet order parameter in the topological material.This article is part of the theme issue 'Andreev bound states'.

Structure and Anisotropy of the Superconducting Order Parameter in Ba0.65K0.35Fe2As2 Probed by Andreev Spectroscopy

The superconducting order parameters in optimally doped Ba0.65K0.35Fe2As2 single crystals have been directly measured using multiple Andreev reflection effect spectroscopy of superconductor–normal metal–superconductor break-junctions. We determine two superconducting gaps, which are nodeless in the k x k y -plane of the momentum space, and resolve a substantial in-plane anisotropy of the large gap. The temperature dependences of the gaps indicate a strong coupling within the bands where ΔL develops, a weak coupling in the condensate with the small gap ΔS, and a moderate interband interaction between the two condensates. The own critical temperatures of both condensates have been estimated (under the hypotherical assumption of zero interband interaction).

Magnetic, superconducting and electron-boson properties of GdO(F)FeAs oxypnictides

We performed comprehensive studies of nearly optimal fluorine-substituted GdO1−xFx FeAs oxypnictide superconductors with TC=48−53K. Specific heat measurements revealed a sharp peak at T=3.5K that shifts to lower temperatures with magnetic field increase. This peak corresponds to an antiferromagnetic ordering in Gd3+ ion sublattice and may indicate coexistence between superconducting and magnetic orderings. Andreev transport through artificially made constriction demonstrated two channels for the carriers from the band(s) with the large superconducting gap as well as from those with the small gap. As expected, the presence of a transport channel with the bands mixing (ΔL+ΔS) was not detected. Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we determined two superconducting gaps, ΔS≈2.7meV, and ΔL≈11.6meV. The reproducible fine structure in the dI(V)/dV spectra of the Andreev contacts (satellites of the main subharmonic gap structure for ΔL) was interpreted as caused by a resonant emission of bosons with the energy ε0=12−15meV≈ΔL+ΔS during the process of multiple Andreev reflections (MAR) for normal carriers in ΔL-band(s) transport channel.

Observation of bosonic resonances in GdO1−x F x FeAs by intrinsic multiple Andreev reflection effect spectroscopy

The current–voltage characteristics and dynamic conductance spectra of Andreev arrays in nearly optimal GdO1 − x F x FeAs superconductors with the critical temperature T c = 46–50 K have been studied. A reproducible fine structure that accompanies large gap features and caused by boson emission during the process of multiple Andreev reflections has been observed. At T = 4.2 K, the bosonic mode energy e0 = (12 ± 2) meV has been obtained.

Anisotropic Andreev reflection and Josephson effect in ballistic phosphorene

We study Andreev reflection and the Josephson effect in a ballistic monolayer of black phosphorous, known as phosphorene. Due to the anisotropic band structure of this system, the supercurrent changes with an order of magnitude when comparing tunneling along two perpendicular directions in the monolayer. We show that the main reason for this effect is a large difference in the number of transverse modes in Andreev bound states. The oscillatory behavior of the supercurrent as a function of the length and chemical potential of the junction also differs substantially depending on the orientation of the superconducting electrodes deposited on the phosphorene sheet. For Andreev reflection, we show that a gate voltage controls the probability of this process and that the anisotropic behavior found in the supercurrent case is also present for conductance spectra.

Evolution of superconducting gaps in Th-substituted Sm1−xThxOFeAs studied by multiple Andreev reflection spectroscopy

Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we studied SnS contacts in the layered oxypnictide superconductors Sm$_{1-x}$Th$_x$OFeAs with various thorium doping and critical temperatures $T_C = 21-54$ K. We observe a scaling between both superconducting gaps and $T_C$. The determined BCS-ratio for the large gap $2\Delta_L/k_BT_C = 5.0-5.7$ and its eigen BCS-ratio (in a hypothetical case of zero interband coupling) $2\Delta_L/k_BT_C^L = 4.1-4.6$ both exceeding the weak-coupling limit 3.52, and for the small gap $2\Delta_S/k_BT_C = 1.2-1.6$ remain nearly constant within all the $T_C$ range studied. The temperature dependences $\Delta_{L,S}(T)$ agree well with a two-band BCS-like Moskalenko and Suhl model. We prove intraband coupling to be stronger than interband coupling, whereas and Coulomb repulsion constants $\mu^{\ast}$ are finite in Sm-based oxypnictides.

Direct evidence of two superconducting gaps in FeSe0.5Te0.5: SnS-Andreev spectroscopy and the lower critical field

We present direct measurements of the superconducting order parameter in nearly optimal FeSe$_{0.5}$Te$_{0.5}$ single crystals with critical temperature $T_C \approx 14$ K. Using intrinsic multiple Andreev reflection effect (IMARE) spectroscopy and measurements of lower critical field, we directly determined two superconducting gaps, $\Delta_L \approx 3.3 - 3.4$ meV and $\Delta_S \approx 1$ meV, and their temperature dependences. We show that a two-band model fits well the experimental data. The estimated electron-boson coupling constants indicate a strong intraband and a moderate interband interaction.

Vortex Structure and Anisotropic Superconducting Gaps in Ba[Fe(Ni)]2As2

We studied nearly optimally Ni-substituted BaFe$_{2-x}$Ni$_x$As$_2$ (BFNA) single crystals with $T_C \approx 18.5$\,K. In irreversible magnetization measurements, we determined the field dependence of the critical-current density and discuss the nature of observed strong bulk pinning. Using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy, we directly determine two distinct superconducting gaps and resolve their moderate anisotropy in the momentum space. The BCS-ratio for the large gap $2\Delta_L/k_BT_C > 4.1$ evidences for a strong coupling in the $\Delta_L$-bands.