Phases of Mott-Hubbard bilayers

TL;DR

This paper explores the phase diagram of two interacting Mott-Hubbard layers, revealing exciton formation, a spin liquid insulator phase, and a transition to d-wave superconductivity influenced by doping and inter-layer interactions.

Contribution

It introduces a comprehensive phase diagram for coupled Mott-Hubbard planes, highlighting exciton effects and the conditions for spin liquid and superconducting phases.

Findings

Exciton formation occurs due to Coulomb attraction between holons and doublons.

A spin liquid insulator phase exists without lattice frustration.

The critical doping for phase transition depends on inter-layer interaction strength.

Abstract

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.