  We present theoretically the electronic structure of antiferromagnetic (AFM)
FeSe monolayer on TiO$_{2}$ terminated SrTiO$_{3}$(001) surface. It is revealed
that the striking disappearance of the Fermi surface around the Brillouin zone
(BZ) center can be well explained by the antiferromatnetic (AFM) phase. We show
that the system has a considerable charge transfer from SrTiO$_{3}$(001)
substrate to FeSe monolayer, and so has a self-constructed electric field. The
FeSe monolayer band structure near the BZ center is sensitive to charge doping,
and the spin-resolved energy bands at BZ corner are distorted to be flattened
by the perpendicular electric field. We propose a tight-binding model
Hamiltonian to take these key factors into account. We also show that this
composite structure is an ideal electron-hole bilayer system, with electrons
and holes respectively formed in FeSe monolayer and TiO$_{2}$ surface layer.
