Extended object tunneling: Current-carrying states of Abrikosov vortices in a superconductor with artificial nanobarriers

We consider the structure and dynamics of two-dimensional fluxons created by a magnetic field in a type-II superconductor film with critical temperature ${T}_{1}$ in the presence of nanostripes of material with a higher critical temperature ${T}_{2}.$ The width of the stripes is of the order of the coherence length $\ensuremath{\xi}$. Such a stripe plays the role of a potential barrier for vortices. When subjected to the current $J$ parallel to the stripe, vortices move toward the barrier. Below the critical current ${J}_{c}$, the flux flow is effectively halted by the barrier, while above ${J}_{c}$, flux penetrates the stripe and passes the barrier. The mechanism of the barrier penetration (``soliton tunneling'' occurs even at zero temperature) is rather unusual: the vortices adjust their shape, and upon passing the barrier, they shrink their cores. The critical current and the I-V curves are calculated numerically and analytically using variational approach.