Pinning phenomena and critical currents in disordered long Josephson junctions

The critical current ${\mathit{I}}_{\mathit{c}}$ of a long one-dimensional (1D) Josephson junction in the presence of different types of structural disorder is investigated both analytically and numerically. It is shown that most properties of ${\mathit{I}}_{\mathit{c}}$ can be understood from the behavior of the elementary pinning force (PF) of a single defect, which we calculate exactly as a function of the external magnetic field ${\mathit{H}}_{\mathit{e}}$, pinning-center size, and strength. The following types of disorder are discussed: (i) For a given field, and pinning centers with equal strength, a unique arrangement of pins that maximizes ${\mathit{I}}_{\mathit{c}}$ is found. (ii) In the case of a periodic pinning-center lattice, we reproduce the commensurability peaks in the field dependence of the critical current, ${\mathit{I}}_{\mathit{c}}$(${\mathit{H}}_{\mathit{e}}$), previously reported by Oboznov and Ustinov [Phys. Lett. A 139, 481 (1989)]. In addition, we predict that a peak can be damped or disappear, if its position coincides with a field value at which the elementary PF vanishes. (iii) The most interesting effects appear in the presence of random disorder. Using the exact expression for the elementary PF, we extend the collective pinning analysis of Koshelev and Vinokur (Zh. Eksp. Teor. Fiz. 97, 976 (1990) [Sov. Phys. JETP 70, 547 (1990)]) to arbitrary fields and properties of the disorder, and compare the obtained predictions with the results of numerical simulations.