Kitaev spin-orbital bilayers and their moiré superlattices

We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moir\'e superlattices. For AA stacking, gapped Z2 quantum spin liquid emerges at finite Jc. show that this survives in well-controlled large-J limit, where an isotropic honeycomb toric code emerges. superlattices, finite-q hybridization is stabilized. This connects inequivalent Dirac points, effectively `untwisting' system. Our study thus provides insight into spin-liquid phases bilayer Kitaev materials.