Exactly solvable spin liquids in Kitaev bilayers and moir\'e superlattices

TL;DR

This paper introduces an exactly solvable Kitaev-type model on bilayer honeycomb lattices, revealing diverse spin liquid phases, flux arrangements, and edge states in moiré superlattices through simulations.

Contribution

It develops a new exactly solvable model for Kitaev interactions on bilayer and moiré superlattices, exploring their complex phase diagrams and topological properties.

Findings

Discovery of various gapped and gapless spin liquid phases.

Identification of flux arrangements correlated with stacking regions.

Observation of edge and corner modes in moiré superlattices.

Abstract

Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer $\mathbb{Z}_2$ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by $C_{3z}$ and $C_{6z}$ of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.