Numerical study of the phase slips in ultrathin doubly connected superconducting cylinders

In the framework of Ginzburg-Landau theory, we numerically investigate the thermally activated phase slips which are responsible for the current dissipation in ultrathin doubly connected superconducting cylinders in the presence of transport current and external magnetic field along the cylinder axis. A hollow cylinder of radius $R$ is mathematically transformed into a two-dimensional (2D) superconducting strip of width $w=2\pi R$ with periodic boundary condition. The phase slips may occur via free-energy saddle points of two distinct kinds. The saddle points of the first kind exhibit a one-dimensional (1D) variation of order parameter described by the (extended) Langer-Ambegaokar-McCumber-Halperin (LAMH) theory [Phys. Rev. 164, 498 (1967); Phys. Rev. B 1, 1054 (1970)]. The saddle points of the second kind exhibit a 2D variation of order parameter, showing that each phase slip is realized through a thermally activated process of vortex-antivortex pair creation and annihilation. In particular, there exists a critical radius $R_c$ separating the 1D LAMH behavior (below $R_c$) and the 2D vortex-antivortex behavior (above $R_c$). The effects of external magnetic field on these saddle points are presented. The critical radius $R_c$ is found to decrease with increasing field strength, and hence applying a magnetic field may induce a transition in the phase-slip characteristics.