  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.
