Unconventional superconductivity originating from disconnected Fermi   surfaces in the iron-based compound
  The iron-based LaFeAsO$_{1-x}$F$_x$ recently discovered by Hosono's group is a fresh theoretical challenge as a new class of high-temperature superconductors. Here we describe the electronic structure of the material and the mechanism of superconductivity. We start with constructing a tight-binding model in terms of the maximally localized Wannier orbitals from a first-principles electronic structure calculation, which has turned out to involve all the five Fe 3d bands. This is used to calculate the spin and charge susceptibilities with the random phase approximation. The spin susceptibility has peaks around ${\Vec k} = (\pi, 0), (0, \pi)$ arising from a nesting across disconnected Fermi surface pockets. We have then plugged the susceptibilities into the linearised Eliashberg equation. For the doping concentration $x = 0.1$, we obtain an unconventional s-wave pairing, which is roughly an extended s in that the gap changes sign between the Fermi pockets, but the gap function is actually a 5$\times$5 matrix. Its experimental implications are also discussed. 
Hideo Aoki