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 = ± 1 chirality, is determined by the defect Frank angle sign F and emergent gauge field flux W = ± i through the expression q_M = − iFW. 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.