Superconducting thin rings with finite penetration depth

Details Superconducting thin rings with finite penetration depth Superconducting thin rings with finite penetration depth

2003-12-18

arxiv.org/abs/cond-mat/0312497v1

Physics

Condensed Matter

Superconductivity

with 19 figures, gives 11.5 pages

Scientific paper

10.1103/PhysRevB.69.184509

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.

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