A scanning SQUID microscope was used to image vortex trapping as a function of the magnetic induction during cooling in thin-film YBCO strips for strip widths W from 2 to 50 um. We found that vortices were excluded from the strips when the induction Ba was below a critical induction Bc. We present a simple model for the vortex exclusion process which takes into account the vortex - antivortex pair production energy as well as the vortex Meissner and self-energies. This model predicts that the real density n of trapped vortices is given by n=(Ba-BK)/Phi0 with BK = 1.65Phi0/W^2 and Phi0 = h/2e the superconducting flux quantum. This prediction is in good agreement with our experiments on YBCO, as well as with previous experiments on thin-film strips of niobium. We also report on the positions of the trapped vortices. We found that at low densities the vortices were trapped in a single row near the centers of the strips, with the relative intervortex spacing distribution width decreasing as the vortex density increased, a sign of longitudinal ordering. The critical induction for two rows forming in the 35 um wide strip was (2.89 + 1.91-0.93)Bc, consistent with a numerical prediction.
@article{arxiv.0801.2283,
title = {Vortex trapping and expulsion in thin-film YBCO strips},
author = {K. H. Kuit and J. R. Kirtley and W. van der Veur and C. G. Molenaar and F. J. G. Roesthuis and A. G. P. Troeman and J. R. Clem and H. Hilgenkamp and H. Rogalla and J. Flokstra},
journal= {arXiv preprint arXiv:0801.2283},
year = {2009}
}