Gauge Field Dynamics in Multilayer Kitaev Spin Liquids

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.

arXiv comment13 pages with 9 figures. Substantially extended new version with newly identified conservation laws for AB and ABC stacking that profoundly influence excitation dynamics. Possible experimental consequences are discussed

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