Josephson junction between anisotropic superconductors

The sin-Gordon equation for Josephson junctions with arbitrary misaligned anisotropic banks is derived. As an application, the problem of Josephson vortices at twin planes of a YBCO-like material is considered. It is shown that for an arbitrary orientation of these vortices relative to the crystal axes of the banks, the junctions should experience a mechanical torque which is evaluated. This torque and its angular dependence may, in principle, be measured in small fields, since the flux penetration into twinned crystals begins with nucleation of Josephson vortices at twin planes.Comment: 6 page

Electromagnetic waves in a Josephson junction in a thin film

We consider a one-dimensional Josephson junction in a superconducting film with the thickness that is much less than the London penetration depth. We treat an electromagnetic wave propagating along this tunnel contact. We show that the electrodynamics of a Josephson junction in a thin film is nonlocal if the wave length is less than the Pearl penetration depth. We find the integro-differential equation determining the phase difference between the two superconductors forming the tunnel contact. We use this equation to calculate the dispersion relation for an electromagnetic wave propagating along the Josephson junction. We find that the frequency of this wave is proportional to the square root of the wave vector if the wave length is less than the Pearl penetration depth.Comment: 12 pages, a figure is included as a uuencodeded postscript file, ReVTe

Semantics and Proof Theory of the Epsilon Calculus

The epsilon operator is a term-forming operator which replaces quantifiers in ordinary predicate logic. The application of this undervalued formalism has been hampered by the absence of well-behaved proof systems on the one hand, and accessible presentations of its theory on the other. One significant early result for the original axiomatic proof system for the epsilon-calculus is the first epsilon theorem, for which a proof is sketched. The system itself is discussed, also relative to possible semantic interpretations. The problems facing the development of proof-theoretically well-behaved systems are outlined.Comment: arXiv admin note: substantial text overlap with arXiv:1411.362

Interference patterns of multifacet 20x(0-pi-) Josephson junctions with ferromagnetic barrier

We have realized multifacet Josephson junctions with periodically alternating critical current density (MJJs) using superconductor-insulator-ferromagnet-superconductor heterostructures. We show that anomalous features of critical current vs. applied magnetic field, observed also for other types of MJJs, are caused by a non-uniform flux density (parallel to the barrier) resulting from screening currents in the electrodes in the presence of a (parasitic) off-plane field component.Comment: submitted to PR

Visualizing supercurrents in ferromagnetic Josephson junctions with various arrangements of 0 and \pi segments

Josephson junctions with ferromagnetic barrier can have positive or negative critical current depending on the thickness $d_F$ of the ferromagnetic layer. Accordingly, the Josephson phase in the ground state is equal to 0 (a conventional or 0 junction) or to $\pi$ ($\pi$ junction). When 0 and $\pi$ segments are joined to form a "0-$\pi$ junction", spontaneous supercurrents around the 0-$\pi$ boundary can appear. Here we report on the visualization of supercurrents in superconductor-insulator-ferromagnet-superconductor (SIFS) junctions by low-temperature scanning electron microscopy (LTSEM). We discuss data for rectangular 0, $\pi$, 0-$\pi$, 0-$\pi$-0 and 20 \times 0-$\pi$ junctions, disk-shaped junctions where the 0-$\pi$ boundary forms a ring, and an annular junction with two 0-$\pi$ boundaries. Within each 0 or $\pi$ segment the critical current density is fairly homogeneous, as indicated both by measurements of the magnetic field dependence of the critical current and by LTSEM. The $\pi$ parts have critical current densities $j_c^\pi$ up to 35\units{A/cm^2} at T = 4.2\units{K}, which is a record value for SIFS junctions with a NiCu F-layer so far. We also demonstrate that SIFS technology is capable to produce Josephson devices with a unique topology of the 0-$\pi$ boundary.Comment: 29 pages, 8 figure

The Epsilon Calculus and Herbrand Complexity

Hilbert's epsilon-calculus is based on an extension of the language of predicate logic by a term-forming operator $\epsilon_{x}$. Two fundamental results about the epsilon-calculus, the first and second epsilon theorem, play a role similar to that which the cut-elimination theorem plays in sequent calculus. In particular, Herbrand's Theorem is a consequence of the epsilon theorems. The paper investigates the epsilon theorems and the complexity of the elimination procedure underlying their proof, as well as the length of Herbrand disjunctions of existential theorems obtained by this elimination procedure.Comment: 23 p

Shapiro steps in Josephson junctions with alternating critical current density

We treat theoretically Shapiro steps in tunnel Josephson junctions with spatially alternating critical current density. Explicit analytical formulas for the width of the first integer (normal) and half-integer (anomalous) Shapiro steps are derived for short junctions. We develop coarse-graining approach, which describes Shapiro steps in the voltage-current curves of the asymmetric grain boundaries in YBCO thin films and different superconductor-ferromagnet-superconductor Josephson-type heterostructures.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev.

Experimental evidence of a {\phi} Josephson junction

We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase \psi=\pm{\phi}. The value of {\phi} can be chosen by design in the interval 0<{\phi}<\pi. The junctions used in our experiments are fabricated as 0-{\pi} Josephson junctions of moderate normalized length with asymmetric 0 and {\pi} regions. We show that (a) these {\phi} Josephson junctions have two critical currents, corresponding to the escape of the phase {\psi} from -{\phi} and +{\phi} states; (b) the phase {\psi} can be set to a particular state by tuning an external magnetic field or (c) by using a proper bias current sweep sequence. The experimental observations are in agreement with previous theoretical predictions

Role of Interfaces in the Proximity Effect in Anisotropic Superconductors

We report measurements of the critical temperature of YBCO-Co doped YBCO Superconductor-Normal bilayer films. Depending on the morphology of the S-N interface, the coupling between S and N layers can be turned on to depress the critical temperature of S by tens of degrees, or turned down so the layers appear almost totally decoupled. This novel effect can be explained by the mechanism of quasiparticle transmission into an anisotropic superconductor.Comment: 13 pages, 3 figure

Suppression of surface barrier in superconductors by columnar defects

We investigate the influence of columnar defects in layered superconductors on the thermally activated penetration of pancake vortices through the surface barrier. Columnar defects, located near the surface, facilitate penetration of vortices through the surface barrier, by creating ``weak spots'', through which pancakes can penetrate into the superconductor. Penetration of a pancake mediated by an isolated column, located near the surface, is a two-stage process involving hopping from the surface to the column and the detachment from the column into the bulk; each stage is controlled by its own activation barrier. The resulting effective energy is equal to the maximum of those two barriers. For a given external field there exists an optimum location of the column for which the barriers for the both processes are equal and the reduction of the effective penetration barrier is maximal. At high fields the effective penetration field is approximately two times smaller than in unirradiated samples. We also estimate the suppression of the effective penetration field by column clusters. This mechanism provides further reduction of the penetration field at low temperatures.Comment: 8 pages, 9 figures, submitted to Phys. Rev.