Kitaev spin-orbital bilayers and their moir\'e superlattices

TL;DR

This paper explores the phase diagram of bilayer Kitaev spin-orbital models with moiré superlattices, revealing a gapped Z2 quantum spin liquid phase and its stability, providing insights into spin-liquid phases in these materials.

Contribution

It introduces the phase diagram of a bilayer Yao-Lee model with inter-layer interactions, highlighting the emergence and stability of a Z2 quantum spin liquid phase in various stacking configurations.

Findings

Gapped Z2 quantum spin liquid appears at finite Jc in AA stacking.

The spin liquid phase persists in the large-J limit, forming a honeycomb toric code.

Moiré superlattices stabilize finite-q inter-layer hybridization, 'untwisting' the system.

Abstract

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, 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 moir\'e 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.