Superconducting Abrikosov transition in the large-N limit

Abstract

Abstract The continuous transition from a normal metal to a mixed superconducting state, the Abrikosov flux lattice, is known to be driven by fluctuations to a first-order transition immediately below six dimensions. We consider here a fictitious U( N ) internal symmetry for the order parameter and analyze the large- N limit. It leads to a classical theory which differs from the Landau-Ginzburg one by a non-local potential due to fluctuations. The analysis of the non-linear equations and of the full phase diagram is difficult, but we can prove that while the Abrikosov solution remains valid above six dimensions for some range of the parameters, in all dimensions lower or equal to six the transition becomes discontinuous. A separate analysis is needed for the cases 4 d ⩽ 6 and 2 ⩽ 4, but the conclusions are the same.