Superconducting thin rings with finite penetration depth
Ernst Helmut Brandt, John R. Clem
DOI 10.1103/PhysRevB.69.184509 · Physical Review B
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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 Λ=λ2/d (λ is the London depth and d<λ/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 Ba and the quantum number N defining the size of the fluxoid Nφ0 trapped in the hole.
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