The Ginzburg-Landau Theory and the Surface Energy of a Colour Superconductor

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 ${\kappa}$ and ${\rho}$. The main result of this paper is a set of inequalities obeyed by the critical value of the Ginzburg-Landau parameter--the value of ${\kappa}$ for which the surface energy changes sign--and its derivative with respect to ${\rho}$. 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.