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

We study the spin-1/2 Kitaev honeycomb model in the presence of dilute crystallographic defects with odd sided plaquettes. In addition to disclination and dislocation topological defects, we define and analyze a locally realizable "Stone-Wales" defect which can be experimentally relevant for Kitaev materials. The emergent flux on an odd plaquette breaks time-reversal symmetry and shows a real-space chirality. We find that the chiralities of distant defects couple through an emergent long range power law interaction with ferromagnetic sign. While the clean Kitaev model has no finite-temperature phase transitions, we find that introducing a finite defect density n_d ~ 10^-4 -- 10^-2 produces a true phase transition with a sizeable T_c ~ 2 n_d in units of the Kitaev exchange. The resulting non-Abelian chiral quantum spin liquid (with nonzero Majorana fermion Chern number) exhibits scalar spin chirality and electron orbital magnetization at T < T_c even without external magnetic fields.