Chiral spin liquid instability of the Kitaev honeycomb model with crystallographic defects

TL;DR

This work shows that dilute Stone-Wales-type lattice defects in the Kitaev honeycomb model can induce a finite-temperature phase transition from a gapless spin liquid to a non-Abelian chiral spin liquid. The mechanism hinges on defect-bound Majorana masses that generate a topological Chern number $C=\pm1$ via a dominant $t_2$ mass term, with defect chiralities $\mu^z_r=\pm1$ acting as an emergent Ising field. Defect defects couple through a long-range ferromagnetic interaction $J(r) \sim (r_0/r)^{\gamma}$ (with $\gamma\approx2.7$), yielding a finite $T_c$ that scales as $T_c \sim 2 n_d J_K$ and can be enhanced by tuning $\gamma$; the transition exhibits mean-field critical behavior due to the long-range coupling. The defect-induced chiral QSL manifests in scalar spin chirality and orbital magnetization, offering observable signatures such as zero-field orbital effects and possible Chern mosaics near defects, with potential relevance for real Kitaev materials that host crystallographic defects.

Abstract

We study the spin-1/2 Kitaev honeycomb gapless spin liquid in the presence of Stone-Wales-type local lattice defects with odd-sided plaquettes. While the clean Kitaev model has no finite-temperature phase transitions, we find that introducing a finite defect density $n_d\approx 10^{-4}$--$10^{-2}$ produces a true phase transition with a sizeable $T_c \approx 2 n_d$ in units of the Kitaev exchange. The resulting non-Abelian chiral quantum spin liquid exhibits scalar spin chirality and electron orbital magnetization which peak near lattice defects. This disorder-driven instability relies on an emergent long range ferromagnetic interaction $r^{-γ}$ ($γ\approx 2.7$) between defect chiralities, mediated by the nearly-gapless fermions, with implications for topology generation in Dirac cones with fluctuating mass terms.

Figures (3)

• Figure 1: Local crystallographic defects generating a chiral spin liquid instability. (a) Stone-Wales (SW) defect as a local 90$^\circ$ bond rotation preserving Kitaev 3-coloring. (b) Resulting phase diagram with temperature $T$ (in units of Kitaev exchange $J_K$) and defect density per site $n_d$. Spatially random defects generate a finite temperature phase transition with $T_c\approx 2 n_d$. Additional lines show various gaps and $T_c$ for spatially correlated disorder discussed elsewhere seth_generation_2025.
• Figure 2: Chirality generation from local lattice defects. (a) A density $n_d$ superlattice of $\mu^z_r=1$ defects produces a finite Majorana gap ($\approx 11 n_d$, dotted line). (b) This gap is topological, giving Majorana fermions a quantized Chern number $C=1$. (c,d,e) The resulting chirality is observable in scalar spin chirality (SSC) from individual defects. (c) Average SSC density per site ($\approx 5.3 n_d$, dotted line). (d,e) SSC of each 3-spin trio (plotted at NNN bonds of honeycomb sites [green dots]) for two SW defects with $\mu^z$ aligned (d) and antialigned (e). Inner core SSC omitted for clarity.
• Figure 3: Emergent long-range interaction between defect chiralities. (a) Energy differences $\Delta E$ between aligned and antialigned $\mu^z$ for two SW defects separated by $\vec{r}$ in finite PBC systems of linear length $L$ can be modeled as $\Delta E/2 = J(r)+J(L-r)+J_0$, with $r{=}|\vec{r}|,L$ measured in real space (NN bond length 1). The data ($\Delta E/2{-}J(L{-}r){-}J_0)$ for $L_x {\times} L_y$ systems is well fitted by $J(r) = (r_0/r)^\gamma$ with $r_0=0.75$ and $\gamma=2.7$ (dotted line). (b) To verify the long range form of $J(r)$ we numerically computed $\Delta E$ for infinite defect arrays of density $n_d$ (blue crosses). The data shows remarkable agreement with an analytical infinite sum of the approximated $J=(r_0/r)^\gamma$ (red line). The exponent $\gamma\approx 2.7$ is renormalized from $\gamma_0=3$ by finite $n_d$, as visible from the $n_d$ array data (inset). See Ref. seth_generation_2025 for discussions of the $J(r)$ array sum, $J(\vec{r})$ anisotropies, generation of $J_0$ by PBC, as well as a third independent method of extracting $J(r)$ which shows similar results.