Molecular response for nematic superconducting media in a hollow cylinder: a numerical approach
INMABB (CONICET), Depto. Matemática, Universidad Nacional del Sur, Bahía Blanca, Argentina
2 Aix-Marseille Université, CNRS, CINaM, Marseille, France
3 ICIFI (CONICET), Centro de Matemática Aplicada, Universidad de San Martín, Buenos Aires, Argentina
Accepted: 16 December 2021
Published online: 29 December 2021
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 Neumann 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 instance 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.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021