We investigate the process of annihilation between vortices of opposite flux in superconducting thin films in the presence of randomly distributed pinning centers. The number and distribution of pairs of vortex-antivortex that avoid annihilation due to pinning on two pinning centers is estimated analytically and compared with numerical simulations. The situation can be realized, for example, when the system is quenched from high temperature (above or below the Kosterlitz-Thouless temperature) or when the current is reduced abruptly. Qualitatively two different cases can be distinguished. The simpler one is when the pairs are well separated. In this case, the problem under mild assumptions can be solved analytically. When the vortex pairs are not very rare, the situation is much more complicated because a great variety of processes become significant. We isolate the important ones and construct an iterative (real-space renormalization-group) scheme to describe the behavior of the interacting multivortex system. Some dynamical aspects of pinning and vortex motion are discussed.

• Received 17 June 1996

DOI:https://doi.org/10.1103/PhysRevB.55.1162