Theory of the lower critical magnetic field for a two-dimensional superconducting film in a nonuniform field

Abstract

We consider the appearance of vortices in a two-dimensional (2D) superconducting film exposed to a nonuniform magnetic field Ba produced by a nearby coil. The film has “infinite” radius Rf and thickness t about equal to the coherence length ξ. The coil is approximated as a point dipole. We find that the first vortex-bearing state to appear has both a vortex and an antivortex. The Gibbs free energy of this state is lower than the vortex-free state when the maximum applied perpendicular field, i.e., the applied field B0 at the origin, exceeds the external critical field Bc10=42ΛRΦ04πΛ2ln(Λξ), where Φ04πΛ2ln(Λξ)≡Bc12D is the intrinsic critical field in 2D, Λ≡2λ2/t is the 2D penetration depth introduced by Pearl, and λ is the bulk penetration depth. The prefactor 42Λ/R is calculated in the strong-screening regime Λ/R≪1. R is the radial distance at which the applied perpendicular field Ba,z(ρ) changes sign. In the lab, the onset of vortex effects generally occurs at a field much higher than Bc10, indicating that vortices are inhibited by the vortex-antivortex unbinding barrier, or by pinning.

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