Dynamics of visons and thermal Hall effect in perturbed Kitaev models

Abstract

A vison is an excitation of the Kitaev spin liquid which carries a ${\mathbb{Z}}_2$ gauge flux. While immobile in the pure Kitaev model, it becomes a dynamical degree of freedom in the presence of perturbations. We study an isolated vison in the isotropic Kitaev model perturbed by a small external magnetic field $h$, an offdiagonal exchange interactions $\Gamma$ and a Heisenberg coupling $J$. In the ferromagnetic Kitaev model, the dressed vison obtains a dispersion linear in $\Gamma$ and $h$ and a fully universal low-$T$ mobility, $\mu =6v_m^2/T^2$, where $v_m$ is the velocity of Majorana fermions. In contrast, in the antiferromagnetic Kitaev model interference effects suppress the coherent propagation and an incoherent Majorana-assisted hopping leads to a $T$-independent mobility. The motion of a single vison due to Heisenberg interactions is strongly suppressed for both signs of the Kitaev coupling. Vison bands in the antiferromagnetic Kitaev models can be topological and may lead to a characteristic features in thermal Hall effects in Kitaev materials.

arXiv comment8+11 pages, 10 figures. Corrected an error in the field-induced vison hopping related to large finite size effects. Modified conclusions on Chern numbers and vison Hall effect. Added discussion on how vison diffusion acts as bottleneck for equilibration

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