Monte Carlo calculation of longitudinal and transverse resistivities in a model type-II superconductor

We study the effect of a transport current on the vortex-line lattice in isotropic type-II superconductors in the presence of strong thermal fluctuations by means of driven-diffusion Monte Carlo simulations of a discretized London theory with finite magnetic penetration depth. We calculate the current-voltage (I-V) characteristics for various temperatures, for transverse as well as longitudinal currents $I.$ From these characteristics, we estimate the linear resistivities Rₓₓ=Ryy and Rzz and compare these with equilibrium results for the vortex-lattice structure factor and the helicity moduli. From this comparison a consistent picture arises, in which the melting of the flux-line lattice occurs in two stages for the system size considered. In the first stage of the melting, at a temperature Tₘ, the structure factor drops to zero and Rₓₓ becomes finite. For a higher temperature Tz, the second stage takes place, in which the longitudinal superconducting coherence is lost, and Rzz becomes finite as well. We compare our results with related recent numerical work and experiments on cuprate superconductors.