Josephson critical currents in annular superconductors with Pearl vortices

Abstract

We investigate the influence of Pearl vortices in the vicinity of an edge-type Josephson junction for a superconducting thin-film loop in the form of an annulus, under uniform magnetic field. Specifically, we obtain the exact analytic formulation that allows to describe the circulating current density and the gauge invariant phase increment ∆φ across the junction. The main properties of ∆φ and their influence on the critical current pattern Ic(B) are described quantitatively in terms of the loop's width to radius ratio W/R and of the vortex position within the loop rv. It is shown that narrow loops (W/R < 0.3) may be well described by the straight geometry limit. However, such approximation fails to predict a number of distinctive features captured by our formulation, as the node lifting effect of the Ic(B) pattern in wide loops or the actual influence of a vortex pinned at different positions.

Polyanalytic Reproducing Kernels on the Quantized Annulus

“…For more details on this phenomenon, we refer the reader to ( [42], p.154) where a magnetic flux quantization is also discussed. The annulus appeared as well in relation to the problem of a Josephson junction in a superconducting loop subject to a uniform magnetic field (see [3] and references therein). In a nutshell, the occurrence of the annular geometry becomes has increased in both theoretical and experimental physics.…”

Polyanalytic reproducing Kernels on the quantized annulus

“…For more details on this phenomenon, we refer the reader to (p 154) where a magnetic flux quantization is also discussed. The annulus appeared as well in relation to the problem of a Josephson junction in a superconducting loop subject to a uniform magnetic field (see [3] and references therein). In a nutshell, the occurrence of the annular geometry has increased in both theoretical and experimental physics.…”