Kitaev spin-orbital bilayers and their moiré superlattices

Abstract We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped {Z}₂ Z 2 quantum spin liquid phase emerges at a finite J c. We show that this phase survives in the well-controlled large- J limit, where an isotropic honeycomb toric code emerges. For moiré superlattices, a finite- q inter-layer hybridization is stabilized. This connects inequivalent Dirac points, effectively ‘untwisting’ the system. Our study thus provides insight into the spin-liquid phases of bilayer spin-orbital Kitaev materials.