On the threshold pinning force in type II superconducting films

The maximum pinning force of a two-dimensional vortex lattice in a random potential is calculated. A connection is established between this threshold pinning force and the potential energy discontinuities due to elastic and plastic instabilities of the vortex lattice. Inspired by recent computer simulations, we assume that the fluctuations in the commensurability between the random potential and the vortex potential breaks the vortex system up into a set of flowing channels in between trapped regions. Two instability mechanisms and their contribution to the threshold force are discussed within this channel-flow picture. We find that three different regimes exist depending on, w, the width of the channels;w=∞,a0