Numerical study of the phase slip in two-dimensional superconducting strips

Abstract

In this paper, we numerically investigate the phase slips in two-dimensional (2D) superconducting strips using the string method, which has been presented as an efficient tool for the study of thermally activated rare events. In the framework of Ginzburg--Landau (GL) theory, we calculate the most probable transition pathway for thermally activated phase slips that are responsible for spontaneous current dissipation. Along the most probable pathway, the saddle point of the GL free-energy functional can be located, from which the energy barrier is also determined. We find there exists a critical width ${w}_{c}$ for narrow strips. Below ${w}_{c}$, the strip behaves as a one-dimensional superconducting wire for which the phase slips are described by the Langer--Ambegaokar--McCumber--Halperin theory [Phys. Rev. 164, 498 (1967); Phys. Rev. B 1, 1054 (1970)]. Above ${w}_{c}$, however, the 2D character of the strip is recovered, and the phase slips are dominated by vortices crossing the strip. In this 2D regime, our numerical results based on the GL theory are compared to the analytical results of the London theory. While there is good agreement for large strip widths, deviation is noticed for small widths (still $>{w}_{c}$) because of the closeness of vortex core to the strip edges.