Nonlocal Josephson electrodynamics and pinning in superconductors

Local Josephson electrodynamics based on the sine-Gordon equation is generalized to the nonlocal case of high critical current density ${\mathit{j}}_{\mathit{s}}$ across a contact for which the Josephson penetration depth is smaller than the London magnetic penetration depth. Magnetic flux is shown to penetrate the contact in the form of Abrikosov vortices having highly anisotropic cores much larger than the coherence length. An exact solution describing such a vortex is found; the lower critical field, vortex mass, and flux-flow resistivity are calculated. It is argued that vortices localized on planar crystalline defects are weakly pinned, therefore any weak links with ${\mathit{j}}_{\mathit{s}}$ smaller than the depairing current density form a dissipative network which essentially reduces the critical current and facilitates a possibility of quantum flux creep.