Molecular response for nematic superconducting media in a hollow cylinder: a numerical approach

Abstract

In the context of the Ginzburg Landau formalism proposed by Barci et al. in 2016 for nematic superconductivity, and by performing a numerical treatment based on the Shooting method, we analyze the behaviour of the radial distribution of the nematic order parameter when the superconducting order parameter reaches the typical non trivial saddle point. We consider the cases of a hollow cylindrical domain, with a disk or an annular domain as its cross section, whether the order parameter is subjected to Newmann or Dirichlet boundary conditions. We conclude that depending on the corresponding situation a non trivial solution holds if certain relations between the radii are satisfied. Moreover, we observe a saturation effect on each instances that constitutes a purely geometrical consequence on the relation between the typical sizes and shapes of the samples. These conclusions can be useful for further experimental realizations and extensions to the interaction of the nematic (superconducting) order parameters with electromagnetic fields.