Vortex pinning by natural linear defects in thin films of (formula presented)

The behavior of the superconducting current density (formula presented) and the dynamical relaxation rate (formula presented) of (formula presented) thin films exhibits a number of features typical for strong pinning of vortices by growth induced linear defects. At low magnetic fields (formula presented) and (formula presented) are constant up to a characteristic field (formula presented) that is directly proportional to the linear defect density (formula presented) The pinning energy (formula presented) can be explained by half-loop excitations determining the thermal activation of vortices at low magnetic fields. Extending the Bose glass theory [D. R. Nelson and V. M. Vinokur, Phys. Rev. B 48, 13 060 (1993)], we derive a different expression for the vortex pinning potential (formula presented) which is valid for all defect sizes and describes its renormalization due to thermal fluctuations. With this expression we explain the temperature dependence of the true critical current density (formula presented) and of the pinning energy (formula presented) at low magnetic fields. At high magnetic fields (formula presented) the current density experiences a power law behavior (formula presented) with (formula presented) for films with low (formula presented) and (formula presented) to -1.1 for films with high (formula presented) The pinning energy in this regime, (formula presented) is independent of magnetic field, but depends on the dislocation density. This implies that vortex pinning is still largely determined by the linear defects, even when the vortex density is much larger than the linear defect density. Our results show that natural linear defects in thin films form an analogous system to columnar tracks in irradiated samples. There are, however, three essential differences: (i) typical matching fields are at least one order of magnitude smaller, (ii) linear defects are smaller than columnar tracks, and (iii) the distribution of natural linear defects is nonrandom, whereas columnar tracks are randomly distributed. Nevertheless the Bose glass theory, that has successfully described many properties of pinning by columnar tracks, can be applied also to thin films. A better understanding of pinning in thin films is thus useful to put the properties of irradiated samples in a broader perspective.