  The electronic properties of Mott insulators realized in (111) bilayers of
perovskite transition-metal oxides are studied. The low-energy effective
Hamiltonians for such Mott insulators are derived in the presence of a strong
spin-orbit coupling. These models are characterized by the antiferromagnetic
Heisenberg interaction and the anisotropic interaction whose form depends on
the $d$ orbital occupancy. From exact diagonalization analyses on finite
clusters, the ground state phase diagrams are derived, including a Kitaev spin
liquid phase in a narrow parameter regime for $t_{2g}$ systems. Slave-boson
mean-field analyses indicate the possibility of novel superconducting states
induced by carrier doping into the Mott-insulating parent systems, suggesting
the present model systems as unique playgrounds for studying
correlation-induced novel phenomena. Possible experimental realizations are
also discussed.
