We determine the phase diagram of a bilayer, Kitaev spin-orbital model with inter-layer interactions (J), for several stackings and moiré superlattices. For AA stacking, a gapped Z2 quantum spin liquid phase emerges at a finite Jc. 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.

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 $${{\mathbb{Z}}}_{2}$$ Z 2 quantum spin liquid phase emerges at a finite Jc. 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.

We study the phase diagram of a bilayer quantum spin liquid model with Kitaev-type interactions on a square lattice. We show that the low energy limit is described by a π-flux Hubbard model with an enhanced SO(4) symmetry. The antiferromagnetic Mott transition of the Hubbard model signals a magnetic fragmentation transition for the spin and orbital degrees of freedom of the bilayer. The fragmented "Néel order" features a non-local string order parameter for an in-plane Néel component, in addition to an anisotropic local order parameter. The associated quantum order is characterized by an emergent Z2 × Z2 gauge field when the Néel vector is along the ẑ direction, and a Z2 gauge field otherwise. We underpin these results with a perturbative calculation, which is consistent with the field theory analysis. We conclude with a discussion on the low energy collective excitations of these phases and show that the Goldstone boson of the Z2 ×Z2 phase is fractionalized and non-local.

No abstract