Superconducting thin rings with finite penetration depth

TL;DR

This paper extends the analysis of superconducting thin-film rings to include finite magnetic penetration depth, providing analytical and numerical results for various physical properties and energy states.

Contribution

It generalizes previous ideal Meissner state results to rings with arbitrary penetration depth using a matrix inversion method.

Findings

Analytical expressions for magnetic-field and current profiles with finite penetration depth.

Numerical results for self-inductance and magnetic flux focusing.

Energy calculations of superconducting rings as a function of applied field and fluxoid quantum number.

Abstract

Recently Babaei Brojeny and Clem [Phys. Rev. B 68, 174514 (2003)] considered superconducting thin-film rings in perpendicular magnetic fields in the ideal Meissner state with negligibly small magnetic penetration depth and presented useful analytical limiting expressions and numerical results for the magnetic-field and sheet-current profiles, trapped magnetic flux, self-inductance, magnetic moment, and focusing of magnetic flux into the hole when no net current flows in the ring. The present paper generalizes all these results to rings with arbitrary values of the two-dimensional effective penetration depth \Lambda = \lambda^2 /d (\lambda is the London depth and d < \lambda/2 the film thickness) using a straightforward matrix inversion method. We also present results for the energy of a superconducting ring as a function of the applied magnetic induction B_a and the quantum number N defining the size of the fluxoid N \phi_0 trapped in the hole.