Valley density-wave and multiband superconductivity in iron-based pnictide superconductors

The key feature of the Fe-based superconductors is their quasi-two-dimensional 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 wave vector 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 nonuniform ``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.