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 ∝ J_⊥. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. Conservation laws and topology keep single visons immobile. However, an inter-layer vison pairs can hop with a hopping amplitude linear in J_⊥ 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 AB or ABC stacking, sheet conservation laws restrict its motion to a one-dimensional channel within the plane. For all stacking types, 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_⊥. We use our results to identify the leading instabilities of the spin liquid phase induced by the inter-layer coupling.

基塔耶夫自旋液体通过与马约拉纳费米子耦合的视觉激励实现了新兴的静态\({{\mathbb{Z}}}_{2}\)规范场。我们考虑相互堆叠的 Kitaev 模型，通过海森堡相互作用∝ J _⊥弱耦合。这种层间耦合破坏了模型的可积性，并使规范场变得动态。守恒定律和拓扑结构使单一视觉保持不动。然而，层间视觉对可以以J _⊥中线性的跳跃幅度跳跃，但它们的运动受到堆叠类型的强烈影响。对于 AA 堆叠，中间层对具有二维运动，但对于 AB 或 ABC 堆叠，片材守恒定律将其运动限制在平面内的一维通道。对于所有堆叠类型，层内视觉对仅限于在平面外移动。根据 Kitaev 耦合K _x 、 K _y 、 K _z的各向异性，层内视觉对可以显示相干隧道或纯粹非相干跳跃。当磁场为马约拉纳费米子打开一个间隙时，就会存在两种类型的层内视觉对——玻色子和费米子。只有玻色子对获得与J _⊥呈线性关系的跳跃率。我们利用我们的结果来识别由层间耦合引起的自旋液相的主要不稳定性。