Growth of a Vortex Polycrystal in Type II Superconductors

We discuss the formation of a vortex polycrystal in type II superconductors from the competition between pinning and elastic forces. We compute the elastic energy of a deformed grain boundary, which is strongly nonlocal, and obtain 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 NbMo. Finally, we discuss the effect of thermal noise on grain growth.

Figure 1

Grain boundary structure from a simulation of interacting vortices after a sudden field cooling from a disordered vortex state. The colored nonsixfold coordinated vortices indicate dislocations, mostly arranged into grain boundaries.

Figure 2

The grain size of a vortex polycrystal experimentally obtained from Bitter decoration of a NbMo sample as a function of the applied magnetic field (Ref. 12) is compared with the theoretical predictions. The calculation based on Friedel statistics with nonlocal elasticity compares favorably with the data. For comparison, we report as well the result obtained using Friedel theory with local elasticity and the earlier estimate from Ref. 12, formally equivalent to our weak pinning result.