Dynamic Vortex Phases in Superconductors with Correlated Disorder

The nature of driven motion of a vortex solid in the presence of a planar pinning defect is investigated by large-scale simulations based on the time-dependent Ginzburg-Landau equations. Three dynamic phases are identiied and characterized by their relative positional and velocity correlations. Vortices in superconductors are a well-deened system of elastic lines or points interacting by electromagnetic and hydrodynamic forces, which can be driven through a eld of pinning sites by an applied current. The dynamic response of the vortices controls most transport properties of superconductors and displays remarkable variety, including nonlinear eeects, steady-state and avalanche dynamics, and thresholds for the onset of motion. A basic understanding of these dynamics is of fundamental interest and is an essential step in controlling vortex motion in technical applications. Vortex motion may be classiied generally as elastic or plastic. In elastic motion, each vortex keeps the same neighbors, while in plastic motion the neighbors change. Plastic vortex ow has been identiied in molecular dynamics simulations 1] and in pioneering transport experiments on NbSe 2 2]. Plastic-to-elastic dynamic transitions have been predicted analytically 3] and explored in neutron scattering experiments 4,5] and transport measurements 6,7]. In this paper, we use large-scale simulations of the time-dependent Ginzburg-Landau equations to investigate the internal structure of elastic and plastic motion, following the individual motions of hundreds of vortices in the presence of a controlled driving force and a planar pinning defect. We nd two distinct plastic phases and an elastic phase, each with diierent internal symmetry. We identify and compare the characteristic features of each dynamic phase and the physical conditions favoring each. The simulations are based on the time-dependent Ginzburg-Landau equations 8,9], h 2 2m s D @ @t = L ; c 2 @A @t = L A 1 4 r r A; L = ajj 2 + b 2 jj 4 + 1 2m s h i r e s c A 2 ; where is the complex order parameter, A the vector potential, and L the Helmholtz free-energy density; the other symbols have their usual meaning. Computational details have been described in 10]. The simulated sample was a rectangular cylinder, in-nitely long and homogeneous in the eld direction. The sample had two parallel free surfaces deened by the boundary condition J s n = 0 (J s is the supercurrent density). A transport current was induced by a eld differential between the free …