S^+- Superconductivity in Electron-Doped Iron Selenide by Exchange of Hidden Spin Fluctuations

The observation of spin resonances around the corner of the unfolded Brillouin zone in intercalated iron-selenide high-T_c superconductors is consistent with the presence of low-energy hidden spin fluctuations in these materials. We develop an Eliashberg theory based on the exchange of hidden spin fluctuations by electrons in the principal 3d_xz and 3d_yz orbitals of the iron atom. At half filling, and in the absence of interactions, an electron-type Fermi surface exists at the center of the unfolded Brillouin zone and a hole-type Fermi surface exists at the corner of the unfolded Brillouin zone. As the interaction strength grows strong, Eliashberg theory predicts a Lifshitz transition to electron/hole Fermi surface pockets at the corner of the folded Brillouin zone. They are extremely faint because of wavefunction renormalization. The Eliashberg theory also predicts a rigid shift of the renormalized band structure upon electron doping, resulting in small but faint hole Fermi surface pockets, and in larger electron Fermi surface pockets. Last, the Eliashberg theory predicts an instability to S-wave Cooper pairing that alternates in sign between the electon-type and the hole-type Fermi surface pockets.