The Ginzburg–Landau theory and the surface energy of a colour superconductor Original Research Article

We apply the Ginzburg–Landau theory to the colour superconducting phase of a lump of dense quark matter. We calculate the surface energy of a domain wall separating the normal phase from the super phase with the bulk equilibrium maintained by a critical external magnetic field. Because of the symmetry of the problem, we are able to simplify the Ginzburg–Landau equations and express them in terms of two components of the di-quark condensate and one component of the gauge potential. The equations also contain two dimensionless parameters: the Ginzburg–Landau parameter κ and ρ. The main result of this paper is a set of inequalities obeyed by the critical value of the Ginzburg–Landau parameter—the value of κ for which the surface energy changes sign—and its derivative with respect to ρ. In addition we prove a number of inequalities of the functional dependence of the surface energy on the parameters of the problem and obtain a numerical solution of the Ginzburg–Landau equations. Finally a criterion for the types of colour superconductivity (type I or type II) is established in the weak coupling approximation.