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

摘要

We consider the appearance of vortices in a two-dimensional (2D) superconducting film exposed to a nonuniform magnetic field B_a produced by a nearby coil. The film has "infinite" radius R_f 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 B_0 at the origin, exceeds the external critical field B_(c1)~0 = 42~(1/2)Λ/R Φ_0/4πΛ~2,whereΦ_0/4πΛ~2ln(Λ/ξ) =B_(c1)~(2D) is the intrinsic critical field in 2D, Λ = 2λ~2/t is the 2D penetration depth introduced by Pearl, and λ is the bulk penetration depth. The prefactor 4~(1/2)Λ/R is calculated in the strong-screening regime A/R ＜＜1. R is the radial distance at which the applied perpendicular field B_(a,z)(ρ) changes sign. In the lab, the onset of vortex effects generally occurs at a field much higher than B_(c1)~0, indicating that vortices are inhibited by the vortex-antivortex unbinding barrier, or by pinning.