Vortex matter and critical magnetic fields in mesoscopic superconducting strips

As compared with bulk materials, superconducting strips with lateral dimensions limited to the mesoscopic region exhibit non-trivial properties, among which the critical magnetic fields related to both vortex penetration B-p and full vortex expulsion B-m still remain elusive. By using low-temperature scanning Hall probe microscope, the critical magnetic fields are studied experimentally in a series of superconducting Pb strips with different widths. It is found that the penetration magnetic field follows a power law dependence with strip width, and vortices can only penetrate the strips when the energy barrier at the edges is completely suppressed. In the field-cooling process, vortices are fully expelled from the strips below B-m, above which the number of trapped vortices linearly increases with magnetic field. Compared with various theoretical predictions, we have found that the experimentally observed B-m corresponds to the field at which the Gibbs free energy in the strip center is minimized. Our study provides important implications for designing nanostructured devices with superconducting strips.