This review provides a theoretical basis for understanding the current-phase relation (CPhiR) for the stationary (dc) Josephson effect in various types of superconducting junctions The authors summarize recent theoretical developments with an emphasis on the fundamental physical mechanisms of the deviations of the CPhiR from the standard sinusoidal form A new experimental tool for measuring the CPhiR is described and its practical applications are discussed The method allows one to measure the electrical currents in Josephson junctions with a small coupling energy as compared to the thermal energy A number of examples illustrate the importance of the CPhiR measurements for both fundamental physics and applications

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The current-phase relation in Josephson junctions

Recent studies on high-Tc superconductors have aroused new interest in tunnelling effects in unconventional superconductors. Unlike in conventional s-wave superconductors, the d-wave pairing state in these materials has an internal phase of the pair potential. The internal phase as a function of the wavevector of the Cooper pairs has a large influence on the electric properties of tunnelling junctions. Important effects of the internal phase on the Josephson current were first predicted theoretically. The idea has been established through several experiments using high-Tc Josephson junctions, which detect ?-phase shift between the a- and b-axis directions and fractional flux quanta. These results give convincing evidence for d-wave symmetry in high-Tc superconductors. In addition, the existence of new interference effects in the quasiparticle states near surfaces and boundaries has been suggested through theoretical predictions. Experimentally, a large number of tunnelling spectroscopy data showed zero-bias conductance peaks (ZBCPs), the origin of which cannot be explained in terms of the classical concept that a tunnelling conductance spectrum is a phase-insensitive probe of the electronic states. It is clarified theoretically that the observed ZBCPs reflect the formation of zero-energy states on the surface due to the ?-phase shift of internal phase in the d-wave pairing symmetry. The formulation developed for tunnelling spectroscopy suggests that tunnelling spectroscopy is essentially phase sensitive. In addition, the formation of the bound states has been shown to have a serious influence on the electrical properties of Josephson junctions. Several anomalous properties including strong enhancement of the Josephson current in the low-temperature region have been predicted theoretically. In this report, recent developments in tunnelling effects on surface bound states in unconventional superconductors are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/63/10/202/pdf

Tunnelling effects on surface bound states in unconventional superconductors

In the past few years magneto-optical flux imaging (MOI) has come to take an increasing role in the investigation and understanding of critical current densities in high-Tc superconductors (HTS). This has been related to the significant progress in quantitative high-resolution magneto-optical imaging of flux distributions together with the model-independent determination of the corresponding current distributions. We review in this article the magneto-optical imaging technique and experiments on thin films, single crystals, polycrystalline bulk ceramics, tapes and melt-textured HTS materials and analyse systematically the properties determining the spatial distribution and the magnitude of the supercurrents. First of all, the current distribution is determined by the sample geometry. Due to the boundary conditions at the sample borders, the current distribution in samples of arbitrary shape splits up into domains of nearly uniform parallel current flow which are separated by current domain boundaries, where the current streamlines are sharply bent. Qualitatively, the current pattern is described by the Bean model; however, changes due to a spatially dependent electric field distribution which is induced by flux creep or flux flow have to be taken into account. For small magnetic fields, the Meissner phase coexists with pinned vortex phases and the geometry-dependent Meissner screening currents contribute to the observed current patterns. The influence of additional factors on the current domain patterns are systematically analysed: local magnetic field dependence of jc(B), current anisotropy, inhomogeneities and local transport properties of grain boundaries. We then continue to an overview of the current distribution and current-limiting factors of materials, relevant to technical applications like melt-textured samples, coated conductors and tapes. Finally, a selection of magneto-optical experiments which give direct insight into vortex pinning and depinning mechanisms are reviewed.

https://iopscience.iop.org/article/10.1088/0034-4885/65/5/202/pdf

Magneto-optical studies of current distributions in high-Tc superconductors

The past 2 years have seen the uniquely rapid emergence of a new class of solar cell based on mixed organic-inorganic halide perovskite. Grain boundaries are present in polycrystalline thin film solar cell, and they play an important role that could be benign or detrimental to solar-cell performance. Here we present efficient charge separation and collection at the grain boundaries measured by KPFM and c-AFM in CH3NH3PbI3 film in a CH3NH3PbI3/TiO2/FTO/glass heterojunction structure. We observe the presence of a potential barrier along the grain boundaries under dark conditions and higher photovoltage along the grain boundaries compare to grain interior under the illumination. Also, c-AFM measurement presents higher short-circuit current collection near grain boundaries, confirming the beneficial roles grain boundaries play in collecting carriers efficiently.

Benefit of Grain Boundaries in Organic–Inorganic Halide Planar Perovskite Solar Cells

High-quality pinhole-free perovskite film with optimal crystalline morphology is critical for achieving high-efficiency and high-stability perovskite solar cells (PSCs). In this study, a p-type π-conjugated polymer poly[(2,6-(4,8-bis(5-(2-ethylhexyl) thiophen-2-yl)-benzo[1,2-b:4,5-b'] dithiophene))-alt-(5,5-(1',3'-di-2-thienyl-5',7'-bis(2-ethylhexyl) benzo[1',2'-c:4',5'-c'] dithiophene-4,8-dione))] (PBDB-T) is introduced into chlorobenzene to form a facile and effective template-agent during the anti-solvent process of perovskite film formation. The π-conjugated polymer PBDB-T is found to trigger a heterogeneous nucleation over the perovskite precursor film and passivate the trap states of the mixed perovskite film through the formation of Lewis adducts between lead and oxygen atom in PBDB-T. The p-type semiconducting and hydrophobic PBDB-T polymer fills in the perovskite grain boundaries to improve charge transfer for better conductivity and prevent moisture invasion into the perovskite active layers. Consequently, the PSCs with PBDB-T modified anti-solvent processing leads to a high-efficiency close to 20%, and the devices show excellent stability, retaining about 90% of the initial power conversion efficiency after 150 d storage in dry air.

Stable and Efficient Organo-Metal Halide Hybrid Perovskite Solar Cells via π-Conjugated Lewis Base Polymer Induced Trap Passivation and Charge Extraction.

Grain boundaries in high-${T}_{c}$ superconductors have attracted wide interest for their potential in a variety of applications and in fundamental studies of high-${T}_{c}$ superconductivity. Two recent experimental results provide a basis for a better understanding of the grain boundary properties, the mechanisms of which, despite their widespread use, are not yet completely understood. First, it is now well established that the order parameter in many high-${T}_{c}$ cuprates has a predominant ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Second, microscopy studies have revealed that practical grain boundaries are comprised of facets having various orientations and typical dimensions of the order of 10- 100 nm. We analyze the combined effects of faceting and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry on the transport properties of high-${T}_{c}$ grain boundaries. It is found that these effects can partially account for the experimentally observed reduction of the critical current density ${J}_{c}$ with increasing grain boundary angle $\ensuremath{\alpha}$. The angular dependence of ${J}_{c}$ for individual grain boundary facets may deviate considerably from the ${J}_{c}(\ensuremath{\alpha})$ dependence observed in standard measurements that employ macroscopic grain boundaries. This also holds for the product of ${J}_{c}$ and the normal state resistivity ${\ensuremath{\rho}}_{n}$. The ${J}_{c}{\ensuremath{\rho}}_{n}$ product measured for standard grain boundary junctions is therefore not a direct measure of the intrinsic barrier properties. The faceting and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry lead to an inhomogeneous current distribution in the grain boundary which is different for the superconducting and the normal states.

Implications of dx2-y2 symmetry and faceting for the transport properties of grain boundaries in high-Tc superconductors.

Using scanning SQUID microscopy, we have directly imaged spontaneously generated delocalized magnetic flux in 45{degree} [001] tilt grain boundaries in YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} films. Implications for the transport properties of the grain boundaries are discussed. A model based on a {ital d}{sub {ital x}{sup 2}{minus}{ital y}{sup 2}}-wave symmetry component of the superconducting order parameter and on grain-boundary faceting is consistent with the results of our experiments. {copyright} {ital 1996 The American Physical Society.}

Generation of Magnetic Flux by Single Grain Boundaries of YBa 2 Cu 3 O 7 − x

Direct observations of the half-integer flux quantum effect in rings, disks, and blanket films of the high-Tc cuprate superconductorsY Ba
 2
 Cu
 3O
 7−δ
 (YBCO),GdBa
 2
 Cu
 3O
 7−δ
 (GdBCO),Tl
 2
 Ba
 2
 CuO
 6+δ
 (Tl2201), andBi
 2
 Sr
 2
 CaCu
 2O
 8+δ
 (BSCCO) with three tricrystal substrate geometries show that their gaps have sign changes consistent with d-wave symmetry. The blanket geometry gives the Josephson penetration depth directly, and provides a means for symmetry tests without patterning. Tl2201 is a tetragonal, single-layer, cuprate without chains. When combined with photoemission results, our BSCCO results imply that the gap followsd
 x
 2−y2 symmetry closely. Asymmetric 45 degree bicrystal grain boundary samples show spontaneous magnetization, as expected for d-wave superconductors with interface roughness.

Scanning SQUID microscope tests of the symmetry of the high-T c gap

Grain boundaries are extensively used as high-quality Josephson junctions in high-T c superconductors. Their superconducting characteristics can generally be well described by conventional models of strongly coupled Josephson junctions. Here, we report on highly anomalous critical current vs. magnetic field dependencies of grain boundaries in YBa 2 Cu 3 O 7-x . Direct imaging with scanning SQUID microscopy provides evidence of magnetic flux generated by single grain boundaries. Conventional Josephson junction models cannot explain these effects if a superconducting order parameter with a pure s-wave symmetry is assumed. The results have significant implications for our understanding of the properties of grain boundaries in high-T c superconductors and for their applications.

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Basic Aspects of High-Tc Grain Boundary Devices

AbstFact-Grain boundary junctions in high-?; thin films generally consist of facets with typical dimensions below 100 nm. In combination with a ~,Z-~Z symmetry component of the order parameter, this faceting gives rise to an inhomogeneous critical current density J, along the grain boundary. The inhomogeneity is most prominent for asymmetric 45’ [OOI] tilt grain boundaries. For a large fraction of the facets in these boundaries the order parameter orientation gives rise to an additional 7r phase difference, and therefore to a ‘negative’ critical current density. This leads to highly anomalous magnetic field dependences of the critical current. Direct imaging with scanning SQUID microscopy provides evidence that magnetic flux is generated spontaneously in these boundaries. These observations have several significant implications, both for understanding the properties of grain boundaries in high-T, superconductors and for their applications. In recent years, it has been debated extensively whether the symmetry of the order parameter in high-T, superconductors is best described by an s or a ~,Z-~Z function [l], [2]. This symmetry is of interest to identify the underlying mechanisms of high-T, superconductivity, but is also important for device applications. Enhanced knowledge of the order parameter symmetry can help provide better control over the properties of devices such as Josephson junctions.

B. Mayer

Papers

Implications of dx2-y2 symmetry and faceting for the transport properties of grain boundaries in high-Tc superconductors.

Generation of Magnetic Flux by Single Grain Boundaries of YBa 2 Cu 3 O 7 − x

Scanning SQUID microscope tests of the symmetry of the high-T c gap

Basic Aspects of High-Tc Grain Boundary Devices

ence of d,24 Symmetry on Device Applications igh-Tc Grain Boundary Junctions