  The key feature of the Fe-based superconductors is their quasi 2D multiband
Fermi surface. By relating the problem to a negative U Hubbard model and its
superconducting ground state, we show that the defining instability of such a
Fermi surface is the valley density-wave (VDW), a combined spin/charge
density-wave at the wavevector connecting the electron and hole valleys. As the
valley parameters change by doping or pressure, the fictitious superconductor
experiences "Zeeman splitting", eventually going into a non-uniform
"Fulde-Ferrell-Larkin-Ovchinikov" (FFLO) state, an itinerant and often
incommensurate VDW of the real world, characterized by the metallic
conductivity from the ungapped remnants of the Fermi surface. When "Zeeman
splitting" exceeds the "Chandrasekhar-Clogston" limit, the "FFLO" state
disappears, and the VDW is destabilized. Near this point, the VDW fluctuations
and interband pair repulsion are essential ingredients of high-Tc
superconductivity in Fe-pnictides.
