Fermi surface pockets in electron-doped iron superconductor by Lifshitz transition

The Fermi surface pockets that lie at the corner of the two-iron Brillouin zone in heavily electron-doped iron selenide superconductors are accounted for by an extended Hubbard model over the square lattice of iron atoms that includes the principal 3d xz and 3d yz orbitals. At half filling, and in the absence of intra-orbital next-nearest neighbor hopping, perfect nesting between electron-type and hole-type Fermi surfaces at the the center and at the corner of the one-iron Brillouin zone is revealed. It results in hidden magnetic order in the presence of magnetic frustration within mean field theory. An Eliashberg-type calculation that includes spin-fluctuation exchange finds that the Fermi surfaces undergo a Lifshitz transition to electron/hole Fermi surface pockets centered at the corner of the two-iron Brillouin zone as on-site repulsion grows strong. In agreement with angle-resolved photoemission spectroscopy on iron selenide high-temperature superconductors, only the two electron-type Fermi surface pockets remain after a rigid shift in energy of the renormalized band structure by strong enough electron doping. At the limit of strong on-site repulsion, a spin-wave analysis of the hidden-magnetic-order state finds a "floating ring" of low-energy spin excitations centered at the checkerboard wavenumber (pi,pi). This prediction compares favorably with recent observations of low-energy spin resonances around (pi,pi) in intercalated iron selenide by inelastic neutron scattering.