Phase slips in superconducting wires with nonuniform cross section: A numerical evaluation using the string method

We employ the string method to numerically evaluate the thermally activated phase slips in one-dimensional superconducting wires with nonuniform cross section. A defect with reduced cross-sectional area opens up a channel for phase-slip transition, for which the free-energy barrier and the preexponential factor associated with the transition rate are numerically calculated. The contribution of the defect to the total rate of transition is compared to that of the uniform section. We find that even a weak defect can greatly enhance the total rate of transition when the temperature is a bit away from Tc. In particular, for a uniform wire carrying a current that is smaller than but close to its critical current, introducing a defect can greatly lower the free-energy barrier and even destroy the metastability at all. The reduction of the critical current by defect is also discussed.