  Moving vortex matter, driven by transport currents independent of time, in
which vortices and anti-vortices coexist is investigated theoretically in thin
superconducting films with nanostructured defects. A simple London model is
proposed for the vortex dynamics in films with periodic arrays of nanomagnets
or cylindrical holes (antidots). Common to these films is that vortex
anti-vortex pairs may be created in the vicinity of the defects by relatively
small transport currents, because it adds to the current generated by the
defects - the nanomagnets screening current, or the antidots backflow current -
and may exceed locally the critical value for vortex anti-vortex pair creation.
The model assumes that vortex matter dynamics is governed by Langevin
equations, modified to account for creation and annihilation of vortex
anti-vortex pairs. For pair creation, it is assumed that whenever the total
current at some location exceeds a critical value, equal to that needed to
separate a vortex from an anti-vortex by a vortex core diameter, a pair is
created instantaneously around this location. Pair annihilation occurs by
vortex anti-vortex collisions. The model is applied to films at zero external
magnetic field and low temperatures. It is found that several moving vortex
matter steady-states with equal numbers of vortices and anti-vortices are
possible.
