Quantum Interference in Superconducting Wire Networks and Josephson Junction Arrays: Analytical Approach based on Multiple-Loop Aharonov-Bohm Feynman Path-Integrals

We investigate analytically and numerically the mean-field superconducting-normal phase boundaries of two-dimensional superconducting wire networks and Josephson junction arrays immersed in a transverse magnetic field. The geometries we consider include square, honeycomb, triangular, and kagome' lattices. Our approach is based on an analytical study of multiple-loop Aharonov-Bohm effects: the quantum interference between different electron closed paths where each one of them encloses a net magnetic flux. Specifically, we compute exactly the sums of magnetic phase factors, i.e., the lattice path integrals, on all closed lattice paths of different lengths. A very large number, e.g., up to $10^{81}$ for the square lattice, exact lattice path integrals are obtained. Analytic results of these lattice path integrals then enable us to obtain the resistive transition temperature as a continuous function of the field. In particular, we can analyze measurable effects on the superconducting transition temperature, $T_c(B)$, as a function of the magnetic filed $B$, originating from electron trajectories over loops of various lengths. In addition to systematically deriving previously observed features, and understanding the physical origin of the dips in $T_c(B)$ as a result of multiple-loop quantum interference effects, we also find novel results. In particular, we explicitly derive the self-similarity in the phase diagram of square networks. Our approach allows us to analyze the complex structure present in the phase boundaries from the viewpoint of quantum interference effects due to the electron motion on the underlying lattices.Comment: 18 PRB-type pages, plus 8 large figure

AC Josephson effect in Nb3Sn thin-film bridges

The AC Josephson effect has been observed in Nb3Sn variable thickness bridges, at liquid hydrogen temperatures. The microwave radiation power dependence of the critical current and the current steps height have been studied. The results are in agreement with a theory based on vortex motion in the superconducting thin-film bridges. We consider these results as indicating good prospects for the use of high temperature superconducting alloys in cryogenic electronics.On présente les résultats d'observations de l'effet Josephson non stationnaire dans des microponts à épaisseur variable de Nb3Sn à la température de l'hydrogène liquide. Le courant critique et l'amplitude des premiers paliers induits sont étudiés en fonction de la puissance hyperfréquence. Les résultats obtenus correspondent à la théorie des tourbillons en mouvement dans les ponts supraconducteurs, ils mettent en évidence les avantages de l'utilisation d'alliages à haute température supraconductrice dans le domaine de la cryoélectronique

Calculation of the Parameters for a Superconducting Thin Plate within Ginzburg-landau Theory

AbstractThe behavior of a superconducting plate with transport current in a magnetic field parallel to its surface was studied by using numerical solution of Ginzburg-Landau (GL) equations. Boundary conditions for the order parameter in their general form have been used. The boundary conditions allow to consider the influence of the plate's boundaries on the superconducting state inside it. According to the calculations some features of the dependences of critical current and critical magnetic field in the parallel to the plate's surface direction as a function of the plate thickness have been detected. Such dependences are not explained by standard formulas for thin plates. On the basis of the calculations, an approach to estimate the coherence length ξ has been proposed. The results of the calculations are consistent with experimental data and qualitative analysis of the calculations within GL theory