In-plane fluxon in layered superconductors with arbitrary number of layers

TL;DR

This paper derives an approximate analytical solution for in-plane fluxons in layered superconductors with any number of layers, validated by numerical simulations, revealing phase/magnetic field decoupling and a Josephson core feature.

Contribution

It provides a new approximate analytical solution for in-plane fluxons in layered superconductors with arbitrary layers, supported by extensive numerical validation.

Findings

Phase/current and magnetic field are decoupled in large N layered systems.

Magnetic field decays at the effective London penetration depth, $\\lambda_c$, larger than the Josephson length.

Fluxons exhibit a Josephson core with a sharp magnetic induction peak.

Abstract

I derive an approximate analytic solution for the in-plane vortex (fluxon) in layered superconductors and stacked Josephson junctions (SJJ's) with arbitrary number of layers. The validity of the solution is verified by numerical simulation. It is shown that in SJJ's with large number of thin layers, phase/current and magnetic field of the fluxon are decoupled from each other. The variation of phase/current is confined within the Josephson penetration depth, $\lambda_J$, along the layers, while magnetic field decays at the effective London penetration depth, $\lambda_c \gg \lambda_J$. For comparison with real high-$T_c$ superconducting samples, large scale numerical simulations with up to 600 SJJ's and with in-plane length up to 4000 $\lambda_J$%, are presented. It is shown, that the most striking feature of the fluxon is a Josephson core, manifesting itself as a sharp peak in magnetic induction at the fluxon center.