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The key feature of the Fe-based superconductors is their quasi 2D multibandFermi surface. By relating the problem to a negative U Hubbard model and itssuperconducting ground state, we show that the defining instability of such aFermi surface is the valley density-wave (VDW), a combined spin/chargedensity-wave at the wavevector connecting the electron and hole valleys. As thevalley parameters change by doping or pressure, the fictitious superconductorexperiences "Zeeman splitting", eventually going into a non-uniform"Fulde-Ferrell-Larkin-Ovchinikov" (FFLO) state, an itinerant and oftenincommensurate VDW of the real world, characterized by the metallicconductivity from the ungapped remnants of the Fermi surface. When "Zeemansplitting" exceeds the "Chandrasekhar-Clogston" limit, the "FFLO" statedisappears, and the VDW is destabilized. Near this point, the VDW fluctuationsand interband pair repulsion are essential ingredients of high-Tcsuperconductivity in Fe-pnictides.

Valley density-wave and multiband superconductivity in Fe-pnictides