  A self-doped bilayer t-t'-J model of an electron- and a hole-doped planes is
studied by the slave-boson mean-field theory. A hopping integral between the
differently doped planes, which are generated by a site potential, are
renormalized by the electron-electron correlation. We find coexistent phases of
antiferromagnetic (AFM) and superconducting orders, although the magnitudes of
order parameters become more dissimilar in the bilayer away from half-filling.
Fermi surfaces (FS's) with the AFM order show two pockets around the nodal and
the anti-nodal regions. These results look like a composite of electron- and
hole-doped FS's. In the nodal direction, the FS splitting is absent even in the
bilayer system, since one band is flat due to the AFM order.
