Coexistence between superconducting and spin density wave states in iron-basedsuperconductors: Ginzburg–Landau analysis

Abstract

We consider the interplay between superconducting (SC) and commensurate spin-density-wave(SDW) orders in iron pnictides by analyzing a multiple-order Ginzburg–Landau free energy.We are particularly interested in whether the doping-induced transition between the twostates is first order or whether the two pure phases are separated by an intermediate phasewith coexisting SC and SDW orders. For perfect nesting, the two orders do not coexist,because SDW order, which comes first, gaps the full Fermi surface leaving nospace for SC to develop. When nesting is not perfect due to either ellipticity ofelectron bands or doping-induced difference in chemical potentials for holes andelectrons, SDW order still leaves modified Fermi surfaces for not too strong SDWmagnetism and the SC order may develop. We show that the two orders coexist onlywhen certain relations between ellipticity and doping are met. In particular, in acompensated metal, ellipticity alone is not sufficient for coexistence of the two orders.