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 Aplas, 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 Aplas. The vortex lattice is rapidly destroyed as the strength of the pinning centres is increased above Aplas. The cross-over value Aplas depends on the density of the pinning centres and decreases logarithmically with increasing system size. The dynamic response to an external applied force Fdr is investigated using diffusive dynamics. The time averaged centre of mass velocity, < v > versus Fdr (corresponding to the current-voltage characteristics of a type II superconductor) is measured. The response exhibits a strong cross-over at Aplas. There is no significant non-linearity in the < v > − Fdr curves for pinning strengths weaker than Aplas. At Aplas, a non-linear region appears whose size grows rapidly with increasing pinning strength. In the linear sections of the < v > − Fdr curves the vortex system moves coherently as a lattice. The non-linearity is caused by a fluid-like flow of the vortices.