Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices

Abstract

Building on the recent advancements on moiré superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moiré 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 moiré 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 moiré unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moiré 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.

15 pages, 12 figures

References in corpus (24)

• Flat Bands in Slightly Twisted Bilayer Graphene
• Graphene Bilayers with a Twist
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Vaporization of Kitaev spin liquids
• Synthesis, Engineering, and Theory of 2D van der Waals Magnets
• A $\Gamma$-matrix generalization of the Kitaev model
• Skyrmions in twisted van der Waals magnets
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Thermal transport in a two-dimensional ${\mathbb{Z}}_2$ spin liquid
• Quantum critical phase transition between two topologically-ordered phases in the Ising toric code bilayer
• Further insights into the thermodynamics of the Kitaev honeycomb model
• Kitaev spin-orbital bilayers and their moiré superlattices
• Multiplicative topological phases
• A Kitaev-type spin liquid on a quasicrystal
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Low temperature properties in the Bilayer Kitaev model
• Magnetic fragmentation and fractionalized Goldstone modes in a bilayer quantum spin liquid
• Fragility of surface states in non-Wigner Dyson topological insulators
• Floating Edge Bands in the Bernevig-Hughes-Zhang model with Altermagnetism
• Microscopic Roadmap to a Yao-Lee Spin-Orbital Liquid
• Topological and magnetic phase transitions in the bilayer Kitaev-Ising model
• Quantum phase transitions in the $K$-layer Ising toric code
• A primer on Kitaev Model: Basic aspects, material realization, and recent experiments