Superconductivity and spin-density waves in multiband metals

We present a detailed description of two-band quasi-two-dimensional metals with s-wave superconducting (SC) and antiferromagnetic spin-density-wave (SDW) correlations. We present a general approach and use it to investigate the influence of the difference between the shapes and the areas of the two Fermi surfaces on the phase diagram. In particular, we determine the conditions for the coexistence of SC and SDW orders at different temperatures and dopings. We argue that a conventional s-wave SC order coexists with SDW order only at very low T and in a very tiny range of parameters. An extended s-wave superconductivity, for which SC gap changes sign between the two bands, coexists with antiferromagnetic SDW over a much wider range of parameters and temperatures but even for this SC order the regions of SDW and SC can still be separated by a first-order transition. We show that the coexistence range becomes larger if SDW order is incommensurate. We apply our results to iron-based pnictide materials, in some of which coexistence of SDW and SC orders has been detected.