Theory of superconductor with kappa close to 1/sqrt{2}

As was firstly shown by E. Bogomolny, the critical Ginzburg-Landay (GL) parameter kappa =1/sqrt{2} at which a superconductor changes its behavior from type-I to type-II, is the special highly degenerate point where Abrikosov vortices do not interact and therefore all vortex states have the same energy. Developing a secular perturbation theory we studied how this degeneracy is lifted when kappa is slightly different from 1\sqrt{2} or when the GL theory is extended to the higher in T-Tc terms. We constructed a simple secular functional, that depends only on few experimentally measurable phenomenological parameters and therefore is quite efficient to study the vortex state of superconductor in this transitional region of kappa. Basing on this, we calculated such vortex state properties as: critical fields, energy of the normal-superconductor interface, energy of the vortex lattice, vortex interaction energy etc. and compared them with previous results that were based on bulky solutions of GL equations.