Josephson Penetration Depth Research Articles

Direct imaging of integer and half-integer Josephson vortices in high-Tc grain boundaries.

We have used a high-resolution scanning SQUID microscope to directly image conventional ( $h/2e$) Josephson vortices trapped in grain boundaries, and half-integer ( $h/4e$) Josephson vortices trapped at the tricrystal point, of the high- ${T}_{c}$ superconductor ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ grown on tricrystal substrates of SrTi${\mathrm{O}}_{3}$. Our observation of the half-integer vortex at the tricrystal point is the first direct demonstration of the positive paramagnetic Meissner effect in a polycrystalline high- ${T}_{c}$ film. In addition, our images provide the first direct measurement of the Josephson penetration depth.

Annular Josephson tunnel junctions in an external magnetic field: The statics.

We have investigated the static configurations of the phase inside an annular Josephson tunnel junction in the presence of an externally applied magnetic field. We report here a detailed study of the dependence on the magnetic field of the critical current for different annular geometries. The periodic conditions for the phase difference across the barrier are derived from fluxoid quantization. For rings having a radius less than the Josephson penetration depth analytical results are derived which are in excellent agreement with the experimental data. For longer junctions numerical analysis is carried out after the derivation of the appropriate perturbed sine-Gordon equation. We find that a number of different phase profiles may exist for a given applied field which differ according to the number of fluxon-antifluxon pairs present in the line. Experimental data support the theoretical analysis provided self-field effects are taken into account in real devices. {copyright} {ital 1996 The American Physical Society.}

Tricrystal Determination of the Symmetry of Cuprate Superconductors

Epitaxial thin films of YBa_2Cu_3O_{7 - \delta} (YBCO) grown on substrates designed, for an assumed d-wave symmetry, to have an odd number of sign changes to the component of the order parameter normal to the grain boundaries, show flux quantization in half-integer multiples of \Phi_0 = h/2e at the tricrystal point. We have used a scanning SQUID microscope to directly image the magnetic fields associated with these half-integer flux quanta. Experiments with three different substrate geometries show that this effect results from the symmetry of the superconducting gap, and prove that the gap has sign changes consistent with d-wave symmetry. This effect occurs in rings, disks, and blanket coverage samples. The experiments with blanket samples provide a direct measurement of the Josephson penetration depth, and give a means for making symmetry tests that do not require lithographic patterning. Half-integer flux quantization also occurs for the single-layer, tetragonal cuprate superconductor Tl(2201), indicating that these effects are not due to the unusual properties of YBCO.

Enhancement of the critical current in a Josephson tunnelling junction with defect size in μm

The blocking mechanism of a metallic impurity in a grain boundary in high temperature superconducting wires or tapes was studied by a mechanical simulation. The defect modulated the current distribution tremendously when it sited near by the edge of the junction. A surprising enhancement of the critical current under the field was observed when the defect located at 2 λ J, twice the Josephson penetration depth, to the edge of a junction and had a size larger than 2 λ J(≈ 5 μm) which were much larger than the conventional pinning size: the coherence length ξ (20 Å). This effect could be contributed to a self-field, which was generated by the applied current or by the applied magnetic field, that penetrated smoothly into and was blocked at the area between the defect and the edge of the junction. A repulsive interaction between the penetrated self-field and the external field kept any further flux from penetrating abruptly into the junction from the defected side. The increment in the critical current under applied field was up to 160% of the original defect free one. By producing a large conductive defect spans to 2 λ J to both edges of the junction, the zero field critical current and the critical magnetic field were enhanced up to 220% of a defect free junction. A maximum enhancement of 270% in the zero field critical current can be reached by combining oxide and conductive defects in the junction.

Josephson-vortex Cherenkov radiation.

We predict the Josephson vortex Cherenkov radiation of an electromagnetic wave. We treat a long one--dimensional Josephson junction. We consider the wave length of the radiated electromagnetic wave to be much less than the Josephson penetration depth. We use for calculations the nonlocal Josephson electrodynamics. We find the expression for the radiated power and for the radiation friction force acting on a Josephson vortex and arising due to the Cherenkov radiation. We calculate the relation between the density of the bias current and the Josephson vortex velocity.

Observation ofd-wave interference pattern:Short junction is crucial

The properties of a one-dimensional 0-π-Josephson junction, consiting of an s-d junction or selected boundaries between three suitably oriented d-wave superconductors, are studied. It is shown that a d-wave type interference pattern can only be observed in the field-modulated critical current if the junction is short compared to the Josephson penetration depth. However, the behavior of a 0-π junction is found to be indistinguishable from that of a 0-junction between s-wave superconductors in the long junction limit, due to the formation of a π-vortex.

Nonlocal response of grain-boundary-type Josephson junctions to local perturbation.

The effect of a focused electron or laser beam on the critical current of Josephson junctions with grain-boundary geometry is analyzed using a numerical iteration method. Beyond a change in the critical current which is proportional to the local critical current density in the irradiated junction region, there is an additional change of the critical current due to a nonlocal modification of the phase difference function. For Josephson junctions larger than the Josephson penetration depth this nonlocal contribution is significant and the total electron beam induced change of the critical current is no longer proportional to the local Josephson current density. Our model calculations are compared to experimental results obtained from the analysis of YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} grain-boundary Josephson junctions (GBJ`s) using low temperature scanning electron microscopy (LTSEM). Comparing the LTSEM measurements to the model calculations gives information on the spatial homogeneity of the critical current density, the influence of the junction geometry on the distribution of the Josephson current density, and the spatial structure of static magnetic flux states.

Magnetic vortices in a distributed Josephson junction with electrodes of finite thickness.

A distributed Josephson junction with electrodes of finite thickness is considered in the case of high critical current density when the Josephson penetration depth ${\ensuremath{\lambda}}_{\mathit{j}}$ is less than the London depth ${\ensuremath{\lambda}}_{\mathit{L}}$. A nonlinear nonlocal equation for steady-state distributions of phase difference cphi across the junction is derived. In the asymptotical case of thin electrodes an exact nonlinear solution for this equation which corresponds to an isolated at-rest Josephson vortex is found. A numerical investigation of the equation derived is carried out and some static and dynamic characteristics of vortices in such a Josephson junction are represented.

Thin-film anisotropic transport measurement on tilted Bi2Sr2CaCu2Ox.

To make a relevant transport measurement between adjacent Cu-O (or double Cu-O) layers, a high-quality single-crystal sample with a rather small area having a restricted number of Cu-O layers is required. To satisfy such requirements, we have prepared a tilted epitaxial ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{CaCu}}_{2}$${\mathrm{O}}_{\mathit{x}}$ film. The c axis of the film makes a nonzero angle with respect to the film normal. In a certain direction, the transport current has to traverse Bi-O layers. Few-micrometer-wide strips containing several tens of Cu-O layers in series were made. The resistivities, critical currents, and I-V characteristics showed marked anisotropies in two transport orientations. The possibility of direct observation of interlayer Josephson coupling was investigated. However, no ac or dc Josephosn effect was observed. The voltage near ${\mathit{I}}_{\mathit{c}}$ seemed to be generated by the dynamics of the Josephson vortices. These observations are consistent with a theoretical analysis based on the Josephson-coupled layered model, which gives a Josephson penetration depth considerably smaller than our smallest sample size, and a transport analysis considering the detailed junction geometry.

Pi -vortex state in a long 0- pi Josephson junction.

We study the static configurations of a one-dimensional 0-{pi} Josephson junction, consisting of an {ital s}-{ital d} junction or selected boundaries between three suitably oriented {ital d}-wave superconductors. We find that a {ital d}-wave-type interference pattern can only be observed in the field-modulated critical current if the junction is short compared to the Josephson penetration depth. However, the behavior of a 0-{pi} junction is found to be indistinguishable from that of a 0 junction between {ital s}-wave superconductors in the long junction limit, due to the formation of a {pi} vortex.

Enhancement of critical current and magnetic field in a defected Josephson tunneling junction

A Josephson junction with a length of 10 times the Josephson penetration depth ( λ J) and a defect size of 0.5 λ J to 2 λ J in different positions has been studied by a mechanical simulation. It was found that the defect modulated the current distribution tremendously when it was near the edge of the junction. A surprising enhancement of the critical current under the field was observed when the defect was located at 0.5 λ J and had a size from 0.5 λ J to 2 λ J, which was much larger than the conventional pinning size: the coherent length ξ. This effect could be attributed to a self-field, which was either generated by the current itself or by the applied magnetic field, penetrating into the defect smoothly and being pinned at the defect. A repulsive interaction between the self-field and the external field kept any further flux from abruptly penetrating into the junction. The increment in the critical current under the applied field was up to 125% of the original defect-free one. By fitting two defects of the same size of 2 λ J and positioning them at 0.5 λ J to both edges of the junction, the zero field critical current and the critical magnetic field were enhanced up to 150% of a defect-free junction.

Commensurability effects in large Josephson junctions.

Two types of commensurability effects are possible in a large Josephson junction patterned with columnar defects. The first occurs for a periodic array of pins when the mean fluxon spacing (tuned by the magnitude of the applied in-plane magnetic field) is a rational fraction of the defect spacing. We show that this effect leads, under fairly general conditions, to a mapping of the behavior of the Josephson junction near the commensurate field values to that of a zero field junction with an effective Josephson penetration depth. The second occurs for more general arrangements of pinning sites, when the orientation of the Josephson vortex lattice (tuned by the direction of the applied field) nearly matches the orientation of the defects. We investigate this tilt response in the limit of a single Josephson vortex. The results are compared, where possible, to recent experiments. As an aside from our main analysis, we prove that, contrary to recent claims in the literature, the critical current density vanishes in the thermodynamic limit, even in the presence of (nonpathologically distributed) pinning disorder.

Periodic microwave absorption in superconducting whiskers

The microwave absorption and structural studies of BiSrCaCuO (2212) whiskers have been performed. The low-angle boundaries in the (a, b) and (a, c) planes have been observed. The periodic microwave absorption signal indicated the flux quantization in a system of weak links and superconducting loops formed on the boundaries. Regular character of this signal suggests possible applications in SQUID magnetometry. Lower Josephson critical fieldHclJ=1.6 Oe and the critical temperatureTc=89 K have been determined. The Josephson penetration depth was estimated from the Ginzgurg-Landau, and Clem models.

Equilibrium magnetization of Josephson junction arrays

The equilibrium magnetization of an array consisting of infinite rows containing 2 N + 1 uniform Josephson junctions each is calculated from the dc Josephson equations with gauge-invariant phase differences. The calculated magnetization curves oscillate with modulated amplitudes. When the parameter α (=2 Na 0/ λ J , where λ J is the Josephson penetration depth and a 0 the lattice constant), is sufficently large, sweeping the external field up and down results in hysteresis loops. The differences from the conventional equilibrium curves for type-II superconductors are discussed.

Evidence for Josephson vortices in (BEDT-TTF)2Cu(NCS)2.

We present evidence for and study the properties of coreless Josephson vortices (parallel to the superconducting layers) in the organic superconductor (BEDT-TTF${)}_{2}$Cu(NCS${)}_{2}$, using ac susceptibility measurements in the mixed state. We observe (1) extremely weak-pinning restoring forces for flux motion parallel to the layers, due to the absence of the vortex normal core; (2) single vortex (noncollective) pinning, due to weak interactions between Josephson vortices; (3) the ``lock-in'' of the vortices parallel to the layers when the dc field is applied at an arbitrary angle; and (4) highly nonlinear response to the ac field h in the lock-in state, above a threshold of h\ensuremath{\sim}0.5 G. The behavior of tilted flux lines is dominated by the much stronger pinning and collective interactions of two-dimensional Abrikosov ``pancake'' vortices, and linear response is largely restored when the flux lines unlock from the layers. We measure the Josephson penetration depth to be ${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\perp}}}$(T=5 K)\ensuremath{\sim}200 \ensuremath{\mu}m, yielding a penetration depth anisotropy of \ensuremath{\gamma}=${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\perp}}}$/${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\sim}160-350.

Realization of high Tc DC SQUIDS. Characterization on a broad range of temperature

The analysis of different types of Josephson junctions allows us to depict temperature dependences of the critical current I C (T), the Josephson penetration depth λ J (T) and main SQUID parameters. We show that a DC SQUID can operate on a broad range of temperature, with a current modulation equal to O 0 /L in the limit β1. The analysis is given within the RSJ model. For this purpose, the usual DC SQUID current biasing circuit is replaced by a voltage controlled system which detects current modulation. This voltage biasing is compatible with modulation technique usually applied to reduce the 1/f noise level of the junctions

Current transfer in grain-boundary junctions of Bi(Pb)SrCaCuO thick films

This paper is devoted to the experimental study of the mechanism of energy dissipation caused by DC transport currents in superconducting Bi(Pb)SrCaCuO screen-printed films. Current-voltage characteristics were measured by the standard four-probe method, and their magnetic field and temperature dependence for different film widths was systematically investigated. The magnetic field and temperature ranged from 0 to 10 mT and from 4.5 to 120 K. Some peculiarities of the current-voltage characteristics were observed. Josephson-type vortex-antivortex pairs were generated at the edges of the film and they slip into the inner part of the film resulting in energy dissipation. This phenomenon appeared in the current-voltage characteristics as a linear part. The evaluation of the film width dependence of the critical current made it possible to calculate the Josephson penetration depth with the numerical result: λ j ∼50μm. At higher currents the voltage increased much faster than in the linear part and the characteristics became strongly nonlinear. A clear distinction could be made between the critical-current limitation caused by flux motion and that, at which the curve started to be nonlinear. The difference between these two dissipation mechanisms was demonstrated by quantum interference patterns observed in the nonlinear section of the current-voltage curves.

Reversible and irreversible magnetization in long Josephson junctions

The magnetization curves, M J ( H), of long Josephson junction are computed from the dc Josephson equation with gauge-invariant phase. They are found to be reversible if α≡ L λ J <4 , where L and λ j are the junction length and the Josephson penetration depth, respectively. Irreversibility starts from α=4, and when α⪢4, the M J ( H) curve is similar to that of type-II superconductors with a surface barrier. The corresponding fields for first vortex entry and last vortex exit are H 1 J =2 Jmaxλ J , where J max is the maximum local written current density, and H 2 J , which has a small positive value.

Nonlinear viscous motion of vortices in Josephson contacts

Nonlinear dynamics of vortices in current-carrying long Josephson contacts is considered for the cases of weak (${\ensuremath{\lambda}}_{\mathit{J}}$\ensuremath{\gg}\ensuremath{\lambda}) and strong (${\ensuremath{\lambda}}_{\mathit{J}}$\ensuremath{\ll}\ensuremath{\lambda}) couplings, where ${\ensuremath{\lambda}}_{\mathit{J}}$ and \ensuremath{\lambda} are the Josephson and London penetration depths, respectively. The first case concerns the Josephson vortices described by the sine-Gordon equation, whereas the case ${\ensuremath{\lambda}}_{\mathit{J}}$\ensuremath{\ll}\ensuremath{\lambda} corresponds to Abrikosov-like vortices with highly anisotropic Josephson cores which are described by an integral equation for the phase difference cphi within the framework of a nonlocal Josephson electrodynamics. At ${\ensuremath{\lambda}}_{\mathit{J}}$\ensuremath{\ll}\ensuremath{\lambda}, an exact solution for the moving vortex in the overdamped regime is obtained, the fluxon velocity v(j) and the voltage-current characteristic V(j) are calculated. It is shown that the lack of the Lorentz invariance of the integral equation for cphi in the nonlocal regime leads to specific features of the vortex dynamics as compared to the Josephson vortices. The results obtained are employed for the description of nonlinear viscous motion of magnetic flux along planar crystalline defects in superconductors. It is shown that any percolating network of planar defects can considerably reduce the critical current, change the field dependence of the flux-flow resistivity, and result in a nonlinear V(j) in the flux-flow regime.

A model for rubidium diffusion in RbxC60 fullerites

Superconducting fullerite Rb[sub 3]C[sub 60] synthesized using alkali-metal azides as a source of the alkali metal shows time-dependent development of the superconducting phase based on electron spin resonance and low-field microwave absorption data. Time dependences of both signals observed for several hours after the synthesis are described by the Avrami diffusion model assuming the diffusion process Rb + C[sub 60] [yields] Rb[sub 3]C[sub 60]. The model permits calculation of the Josephson penetration depth as [lambda][sub J] [approximately] 1500 Angstroms, which is in agreement with other measurements. 18 refs., 2 figs.