Visualization and Exploration of the Dynamics of Phase Slip Centers in Superconducting Wires
The dynamics of phase slip centers in a 1D model of superconducting wire was created based on the set of time-dependent Ginzburg-Landau equations (TDGL). The General Form PDE interface of COMSOL Multiphysics® simulation software was used. TDGL has successfully applied to this problem decades ago and most recently, the visibility of solutions has been enhanced by engaging the power of COMSOL Multiphysics®. The feature which distinguishes the current report here is that, for the first time, the set of TDGL equations for superconductors with finite gap was used in full. The terms relevant to the presence of finite gap were included not only into the equation for the wave function of the condensate, but also into the equation for the current in the form of interference terms.
The performed thorough study of the solutions of these non-linear equations required extensive searches for multiple solutions at certain values of given parameters. We found it extremely helpful using the built-in capability of COMSOL Multiphysics® which could be operated in tandem with MATLAB®. By developing the MATLAB® code, we were able to automate findings of the relevant solutions. We obtained "branching" and "anti-branching" of these solutions at certain parameters of the problem. These properties are directly relevant to experimental results obtained with these objects.
Evolution of phase-slip centers takes place in picosecond time-scale, which can be very hard to visualize in practice. The ability of COMSOL Multiphysics® to generate animation provides unique opportunities to trace details of the microscopic evolution of various observables (such as the Cooper-pair density, superfluid and normal velocities, etc.). The most interesting cases and the most characteristic features will be demonstrated at the presentation as movies. We are grateful to G. Melkonyan for helpful discussions, and J. Tollaksen for encouraging our TDGL modeling. This work was supported in part by ONR Grants N00014-16-1-2269, N00014-17-1-2972, N00014-18-1-2636, and N00014-1901-2265.