Vortex trapping and expulsion in thin-film YBa₂Cu₃O_7−δ strips

A scanning superconducting quantum interference device microscope was used to image vortex trapping asa function of the magnetic induction during cooling in thin-film YBa₂Cu₃O_7-δ (YBCO) strips for strip widths W from 2 to 50μm. We found that vortices were excluded from the strips when the induction B_a was below a critical induction B_c. 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 predictsthat the real density n of trapped vortices is given by n=(B_a-B_K) φ₀ with B_K=1.65φ₀ /W² and φ₀=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 35μm wide strip was (2.89+1.91 0.93)B_c, consistent with a numerical prediction.