We investigated flux front penetration in a disordered type II superconductor by molecular dynamics (MD) simulations of interacting vortices and found scaling laws for the front position and the density profile. The scaling can be understood performing a coarse graining of the system and writing a disordered non-linear diffusion equation. Integrating numerically the equation, we observed a crossover from flat to fractal front penetration as the system parameters are varied. The value of the fractal dimension indicates that the invasion process is described by gradient percolation.
A new class of artificial atoms, such as synthetic nanocrystals or vortices in superconductors, naturally self-assemble into ordered arrays. This property makes them applicable to the design of novel solids, and devices whose properties often depend on the response of such assemblies to the action of external forces. We study the transport properties of a vortex array in the Corbino disk geometry by numerical simulations. In response to an injected current in the superconductor, the global resistance associated to vortex motion exhibits sharp jumps at two threshold current values. The first corresponds to a tearing transition from rigid rotation to plastic flow, due to the reiterative nucleation around the disk center of neutral dislocation pairs that unbind and glide across the entire disk. After the second jump, we observe a smoother plastic phase proceeding from the coherent glide of a larger number of dislocations arranged into radial grain boundaries.
A vortex polycrystal in type II superconductors is formed from the competition between pinning and elastic forces. We have computed the elastic energy of a deformed grain boundary, that is strongly non-local, and obtained the depinning stress for weak and strong pinning. Our estimates for the grain size dependence on the magnetic field strength are in good agreement with previous experiments on Nb Mo. Finally, we have analyzed the effect of thermal noise on grain growth.