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We consider the interplay between superconducting (SC) and commensuratespin-density-wave (SDW) orders in iron-pnictides by analyzing a multiple orderGinzburg-Landau free energy. We are particularly interested in whether thedoping-induced transition between the two states is first order, or the twopure phases are separated by an intermediate phase with coexisting SC and SDWorders. For perfect nesting, the two orders do not coexist, because SDW order,which comes first, gaps the full Fermi surface leaving no space for SC todevelop. When nesting is not perfect due to either ellipticity of electronbands or doping-induced difference in chemical potentials for holes andelectrons, SDW order still leaves modified Fermi surfaces for not too strongSDW magnetism and the SC order may develop. We show that the two orders coexistonly when certain relations between ellipticity and doping are met. Inparticular, in a compensated metal, ellipticity alone is not sufficient forcoexistence of the two orders.

Coexistence between superconducting and spin density wave states in iron-based superconductors: Ginzburg-Landau analysis