Geometric edge barrier in the Shubnikov phase of type II superconductors

In type-II superconductors the magnetic response can be irreversible for two different reasons: vortex pinning and barriers to flux penetration. Even without bulk pinning and in the absence of a microscopic Bean–Livingston surface barrier for vortex penetration, superconductors of nonellipsoidal shape can exhibit a large geometric barrier for flux penetration. This edge barrier and the resulting irreversible magnetization loops and flux-density profiles are computed from continuum electrodynamics for superconductor strips and disks of constant thickness, both without and with bulk pinning. Expressions are given for the field of first flux entry Hen and for the reversibility field Hrev above which the pin-free magnetization becomes reversible. Both fields are proportional to the lower critical fieldHc1 but otherwise depend only on the specimen shape. These results for rectangular cross section are compared with the well-known reversible magnetic behavior of ideal ellipsoids.