Size effects in the nonlinear resistance in a virtual Berezinskii-Kosterlitz-Thouless state of superconducting films

We show that the size effects strongly affect the nonlinear electric field-current ($E-I$) relation of superconducting films. We calculate $E(J)$ due to thermally-activated hopping of single vortices driven by current $I$ across the film in a magnetic field $H$, taking into account interaction of free vortices with their antivortex images and peaks in the Meissner currents at the film edges. Unbinding of virtual vortex-antivortex pairs not only mimics the transport uniform BKT behavior, it can dominate the observed $E(J)$ and result in the field-dependent ohmic resistance at small $I$. We show that $E(I)$ can be tuned by changing the film geometry and propose experimental tests of this theory.