Real-space chirality from crystalline topological defects in the Kitaev spin liquid

Abstract

We show that certain crystalline topological defects in the gapless Kitaev honeycomb spin liquid model generate a chirality and Majorana fermion orbital magnetization that depends in a universal manner on their emergent flux. Focusing on 5-7 dislocations as building blocks, consisting of pentagon and heptagon disclinations, we identify the Kitaev bond label configurations that preserve solvability. By computing two formulations of local markers $M(r)$ we find that the 5 and 7 lattice defects generate a real-space contribution to Chern number and an associated Majorana fermion orbital magnetization proportional to $M(r)$. The sign of the $M(r)$ contribution from each 5/7 defect, i.e. its $q_M=\pm 1$ chirality, is determined by the defect Frank angle sign $F$ and emergent gauge field flux $W = \pm i$ through the expression $q_M = - i F W$. Remarkably, though lattice curvature and torsion can interplay with the surrounding gapless background to modify the profile of $M(r)$, its sign $q_M$ is determined locally, implying that crystalline defects in the Kitaev spin liquid can generate a robust and observable chirality.