Kitaev spin-orbital bilayers and their moire superlattices

We determine the phase diagram of a bilayer, Yao-Lee spin-orbital model with inter-layer interactions (J), for several stackings and moire superlattices. For AA stacking, a gapped Z₂ 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 moire 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.