Abstract
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.
