Computer simulations of flux pinning and flux flow in two dimensions

The deformations of a two-dimensional vortex lattice pinned by a random configuration of pinning centres are studied by a molecular dynamics annealing method. The pinning centres collectively induce a softening of the vortex lattice. The shear modulus decreases with increasing strength of the random potential. At a certain strength A_plas, the pinning centres start to induce plastic deformations in the vortex lattice. The lattice is distorted elastically only when the strength of the random potential is below A_plas. The vortex lattice is rapidly destroyed as the strength of the pinning centres is increased above A_plas. The cross-over value A_plas depends on the density of the pinning centres and decreases logarithmically with increasing system size. The dynamic response to an external applied force F_dr is investigated using diffusive dynamics. The time averaged centre of mass velocity, < v > versus F_dr (corresponding to the current-voltage characteristics of a type II superconductor) is measured. The response exhibits a strong cross-over at A_plas. There is no significant non-linearity in the < v > - F_dr curves for pinning strengths weaker than A_plas. At A_plas, a non-linear region appears whose size grows rapidly with increasing pinning strength. In the linear sections of the < v > - F_dr curves the vortex system moves coherently as a lattice. The non-linearity is caused by a fluid-like flow of the vortices.