Energy cost associated with vortex crossing in superconductors

Starting from the Ginzburg-Landau free energy of a type-II superconductor in a magnetic field we estimate the energy associated with two vortices crossing. The calculations are performed by assuming that we are in a part of the phase diagram where the lowest-Landau-level approximation is valid. We consider only two vortices but with two markedly different sets of boundary conditions: on a sphere and on a plane with quasiperiodic boundary conditions. We find that the answers are very similar suggesting that the energy is localized to the crossing point. The crossing energy is found to be field and temperature dependent with a value at the experimentally measured melting line of U(x) congruent-to 7.5kT(m) congruent-to 1.161c(L)2, where c(L) is the Lindemann-melting-criterion parameter. The crossing energy is then used with an extension of the Marchetti, Nelson, and Cates hydrodynamic theory to suggest an explanation of the recent transport experiments of Safar et al.