Non-quantized penetration of magnetic field in the vortex state of superconductors

Abstract

As first pointed out by Bardeen and Ginzburg in the early sixties^1,2, the amount of magnetic flux carried by vortices in superconducting materials depends on their distance from the sample edge, and can be smaller than one flux quantum, φ₀ = h/2e (where h is Planck's constant and e is the electronic charge). In bulk superconductors, this reduction of flux becomes negligible at sub-micrometre distances from the edge, but in thin films the effect may survive much farther into the material^3,4. But the effect has not been observed experimentally, and it is often assumed that magnetic field enters type II superconductors in units of φ₀. Here we measure the amount of flux introduced by individual vortices in a superconducting film, finding that the flux always differs substantially from φ₀. We have observed vortices that carry as little as 0.001φ₀, as well as ‘negative vortices’, whose penetration leads to the expulsion of magnetic field. We distinguish two phenomena responsible for non-quantized flux penetration: the finite-size effect^1,2,3,4 and a nonlinear screening of the magnetic field due to the presence of a surface barrier. The latter effect has not been considered previously, but is likely to cause non-quantized penetration in most cases.