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

TL;DR

This paper demonstrates that crystalline topological defects in the Kitaev spin liquid induce a universal chirality and Majorana fermion orbital magnetization, which are locally determined and potentially observable.

Contribution

It reveals how specific lattice defects generate a universal chirality and magnetization in the Kitaev spin liquid, linking defect properties to emergent topological features.

Findings

Defects produce a real-space contribution to Chern number.

The sign of the magnetization is determined by defect flux and Frank angle.

Crystalline defects can generate observable chirality in the 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.