We uncover the low-energy spectrum of a t-J model for electrons on a square
lattice of spin-1 iron atoms with 3dxz and 3dyz orbital character by applying
Schwinger-boson-slave-fermion mean-field theory and by exact diagonalization of
one hole roaming over a 4 x 4 x 2 lattice. Hopping matrix elements are set to
produce hole bands centered at zero two-dimensional (2D) momentum in the
free-electron limit. Holes can propagate coherently in the t-J model below a
threshold Hund coupling when long-range antiferromagnetic order across the d+ =
3d(x+iy)z and d- = 3d(x-iy)z orbitals is established by magnetic frustration
that is off-diagonal in the orbital indices. This leads to two hole-pocket
Fermi surfaces centered at zero 2D momentum. Proximity to a commensurate
spin-density wave (cSDW) that exists above the threshold Hund coupling results
in emergent Fermi surface pockets about cSDW momenta at a quantum critical
point (QCP). This motivates the introduction of a new Gutzwiller wavefunction
for a cSDW metal state. Study of the spin-fluctuation spectrum at cSDW momenta
indicates that the dispersion of the nested band of one-particle states that
emerges is electron-type. Increasing Hund coupling past the QCP can push the
hole-pocket Fermi surfaces centered at zero 2D momentum below the Fermi energy
level, in agreement with recent determinations of the electronic structure of
mono-layer iron-selenide superconductors.Comment: 41 pages, 12 figures, published versio