Nature of visons in the perturbed ferromagnetic and antiferromagnetic Kitaev honeycomb models

TL;DR

This paper investigates how vison particles behave differently in ferromagnetic and antiferromagnetic Kitaev honeycomb models under perturbations, revealing distinct symmetries and thermal Hall effects.

Contribution

It uncovers the contrasting vison symmetry properties and thermal Hall responses in ferromagnetic versus antiferromagnetic Kitaev models under Zeeman perturbation.

Findings

Visons in ferromagnetic models have trivial translational symmetry and zero Berry curvature.

Visons in antiferromagnetic models exhibit projective translational symmetry with $ ext{π}$-flux and non-zero Chern numbers.

Antiferromagnetic visons contribute intrinsically to the thermal Hall effect.

Abstract

The Kitaev honeycomb model hosts a fascinating fractionalized state of matter featuring emergent Majorana fermions and a vison particle that carries the flux of an emergent gauge field. In the exactly solvable model these visons are static but certain perturbations can induce their motion. We show that the nature of the vison motion induced by a Zeeman field is sharply distinct in the ferromagnetic vs the antiferromagnetic Kitaev models. Namely, in the ferromagnetic model the vison has a trivial non-projective translational symmetry, whereas in the antiferromagnetic Kitaev model it has a projective translational symmetry with $\pi$-flux per unit cell. The vison band of the ferromagnetic case has zero Berry curvature, and no associated intrinsic contribution to the thermal Hall effect. In contrast, in the antiferromagnetic case there are two gapped vison bands with opposite Chern numbers and an associated intrinsic vison contribution to the thermal Hall effect. We discuss these findings in the light of the physics of the spin liquid candidate $\alpha$-RuCl$_3$.