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-$T_c$ superconductivity in Fe pnictides.

Figure 1

(Color online) Phase diagram of Fe pnictides, depicting the evolution of our fictitious superconductor from the fully gapped VDW insulator to the “FFLO superconductor”—a partially gapped metallic VDW—to the real SC under the influence of the Zeeman splitting $\delta \mu$ (doping or pressure). The red dot on the vertical axis symbolizes the parent compounds and the regime below it might be physically inaccessible. Insets: FS of (a) the normal state in the folded $\left(\Gamma \leftrightarrow M\right)$ BZ (Ref. 18), (b) the VDW metal (computed with the interband interaction set to unity)—this is the $C_4$ version of (c) the continuum FFLO state (Ref. 21). The remaining states are fully gapped.

Figure 2

(Color online) (a) Inter/intraband ${\zeta }_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\left(e/h\right)}$ of Eq. (5) (in $k_F⪡M$ limit) for the inner and outer hole bands, and the electron bands as $\mathbf{k}$ and ${\mathbf{k}}^{\prime }$ go around respective FSs. (b) Mixed ${\gamma }_{\mathbf{k},{\mathbf{k}}^{\prime }}^{\left(e,h\right)}$ Eq. (5) are clearly smaller than $\zeta$’s.