Using a perturbative approach to the infinitely degenerate Bogomolnyi vortex state for a superconductor with $\kappa =1/\sqrt{2},\overrightarrow{T}{T}_c,$ we calculate the interaction of vortices in a superconductor with $\kappa$ close to $1/\sqrt{2}.$ We find, numerically and analytically, that depending on the material the interaction potential between the vortices varies with decreasing $\kappa$ from purely repulsive (as in a type-II superconductor) to purely attractive (as in a type-I superconductor) in two different ways: either vortices form a bound state and the distance between them changes gradually from infinity to zero or this transition occurs in a discontinuous way as a result of a competition between minima at infinity and zero. We study the discontinuous transition between the vortex and Meissner states caused by the nonmonotonous vortex interaction and calculate the corresponding magnetization jump.

• Received 8 February 2002

DOI:https://doi.org/10.1103/PhysRevB.65.224504