  A phase diagram of two Mott-Hubbard planes interacting with a short-range
Coulomb repulsion is presented. Considering the case of equal amount of doping
by holes in one layer as electrons in the other, a holon-doublon inter-layer
exciton formation is shown to be a natural consequence of Coulomb attraction.
Quasiparticle spectrum is gapped and incoherent below a critical doping
$\delta_c$ due to the formation of excitons. A spin liquid insulator (SLI)
phase is thus realized without the lattice frustration. The critical value
$\delta_{c}$ sensitively depends on the inter-layer interaction strength. In
the $tJ$ model description of each layer with the d-wave pairing, $\delta_{c}$
marks the crossover between SLI and d-wave superconductor. The SLI phase,
despite being non-superconducting and charge-gapped, still shows
electromagnetic response similar to that of a superfluid due to the exciton
transport. Including antiferromagnetic order in the $tJ$ model introduces
magnetically ordered phases at low doping and pushes the spin liquid phase to a
larger inter-layer interaction strength and higher doping concentrations.
