Competing magnetism and superconductivity in two-band metals

Recently discovered FeAs-based superconductors have a distinct multiple band structure - the hallmark feature of these materials. We consider a simple two-band model for these metals, with one electronic and one hole bands. Within this model, we treat on equal footing magnetic spin density wave (SDW) and superconducting (SC) orders. We find that at low doping, magnetism wins, but at higher dopings superconducting instability comes first. We discuss the type of a transition between the two states, incommensurate SDW order at finite dopings, and co-existence of SDW and SC orders at $T=0$ and finite temperatures. Our results reasonably well explain the phase diagram of LaO$_{1-x}$F$_{x}$FeAs compounds.