Minimal two-band model of the superconducting iron oxypnictides

Following the discovery of the Fe-pnictide superconductors, local-density approximation (LDA) band structure calculations showed that the dominant contributions to the spectral weight near the Fermi energy came from the $\text{Fe}\text{ }3d$ orbitals. The Fermi surface is characterized by two hole surfaces around the $\ensuremath{\Gamma}$ point and two electron surfaces around the $M$ point of the two Fe/cell Brillouin zone. Here, we describe a two-band model that reproduces the topology of the LDA Fermi surface and exhibits both ferromagnetic and $q=(\ensuremath{\pi},0)$ spin-density wave fluctuations. We argue that this minimal model contains the essential low energy physics of these materials.