Gauge Field Dynamics in Multilayer Kitaev Spin Liquids

TL;DR

This paper studies how stacking multiple Kitaev spin liquids with weak inter-layer interactions makes gauge fields dynamic, revealing complex vison pair motions and potential instabilities in the phase.

Contribution

It introduces a model of multilayer Kitaev spin liquids with weak Heisenberg coupling, analyzing the resulting gauge dynamics and vison pair mobility depending on stacking and anisotropy.

Findings

Inter-layer vison pairs can hop with amplitude linear in $J_ot$

Stacking type influences vison pair motion, from 2D to 1D channels

Magnetic field induces different behaviors for bosonic and fermionic vison pairs

Abstract

The Kitaev spin liquid realizes an emergent static $\mathbb{Z}_2$ gauge field with vison excitations coupled to Majorana fermions. We consider Kitaev models stacked on top of each other, weakly coupled by Heisenberg interaction $\propto J_\perp$. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. \new{Conservation laws and topology keeps single visons immobile. However, an inter-layer vison pairs can hop with a hopping amplitude linear in $J_\perp$ confined to the layer, but their motion is strongly influenced by the type of stacking. For AA stacking, an interlayer pair has a two-dimensional motion but for the AB or ABC stacking, sheet conservation laws restrict its motion to a one-dimensional channel within the plane. For all stackings, an intra-layer vison-pair is constrained to move out-of-plane only.} Depending on the anisotropy of the Kitaev couplings $K_x, K_y, K_z$, the intra-layer vison pairs can display either coherent tunnelling or purely incoherent hopping. When a magnetic field opens a gap for Majorana fermions, there exist two types of intra-layer vison pairs - a bosonic and a fermionic one. Only the bosonic pair obtains a hopping rate linear in $J_\perp$. We use our results to identify the leading instabilities of the spin liquid phase induced by the inter-layer coupling.