Phases of Mott-Hubbard bilayers: Theoretical model

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 interlayer 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 interlayer interaction strength. In the t-J 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 nonsuperconducting and charge gapped, still shows an electromagnetic response similar to that of a superfluid due to the exciton transport. Including antiferromagnetic order in the t-J model introduces magnetically ordered phases at low doping and pushes the spin-liquid phase to a larger interlayer interaction strength and higher doping concentrations.