We numerically solve the time-dependent Ginzburg–Landau equations for two-gap superconductors using the finiteelement technique. The real-time simulation shows that at low magnetic field, the vortices in small-size samples tend to form clusters or other disorder structures. When the sample size is large, stripes appear in the pattern. These results are in good agreement with the previous experimental observations of the intriguing anomalous vortex pattern, providing a reliable theoretical basis for the future applications of multi-gap superconductors.
We derive the linearized Ginzburg-Landau (GL) equation on a spatially curved surface in the presence of a magnetic field. By introducing a novel transverse order parameter varying very slowly along the surface, we decouple the linearized GL equation into a surface part and a transverse part, and obtain the superconducting geometric potential (GP) under the superconducting/vacuum boundary condition. Further, we numerically study the nucleation of a rectangle thin superconducting film bent around the surface of a cylinder. Our results show that, the geometric curvature can weaken the effect of the magnetic field, and the competition between the applied magnetic field and the superconducting GP will lead to an abnormal Tc(B) dependence in the GP dominant region and a Tc enhancement in the magnetic field dominant region.
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