Vortex state and dynamics of a d-wave superconductor: Finite-element analysis

Abstract

The finite-element method is extended to simulate the d-wave time-dependent Ginzburg-Landau equations. By utilizing this method and in the context of the (s+d)-wave pairing, we discuss the nature of a single vortex, the structure of equilibrium vortex lattices in bulk samples, the nature of vortices in finite-size samples, and most importantly the transport of the vortices. In particular, the low-field free-flux-flow resistivity turns out to obey the law of corresponding states discovered in conventional superconductors, while the high-field resistivity reveals a noticeable effect of the s-wave coupling on lifting the effective upper critical field. The flux flow near and above the depinning current in the presence of a twin boundary or random impurities also assumes a conventional behavior: The current dependence of the flux-flow resistivity can be well described by an overdamped model for a particle subject to driving and pinning forces. However, our results show a noticeable difference between the flux-flow resistivities at large currents in the presence and absence of pinning.