Vortex creation and control in the Kitaev spin liquid by local bond modulations

TL;DR

This paper proposes a theoretical method to create and manipulate vortices in the Kitaev spin liquid using local bond modulations, with potential applications in topological quantum computation.

Contribution

It introduces a novel approach to generate and control vortices in the Kitaev model via local exchange interaction modulations, including Dzyaloshinskii-Moriya interactions, supported by ab initio calculations.

Findings

Local bond modulations can induce vortices in the Kitaev spin liquid.

Dzyaloshinskii-Moriya interactions effectively flip the sign of the Kitaev interaction.

Vortices can be braided through adiabatic local bond changes.

Abstract

The Kitaev model realizes a quantum spin liquid where the spin excitations are fractionalized into itinerant Majorana fermions and localized $\mathbb{Z}_2$ vortices. Quantum entanglement between the fractional excitations can be utilized for decoherence-free topological quantum computation. Of particular interest is the anyonic statistics realized by braiding the vortex excitations under a magnetic field. Despite the promising potential, the practical methodology for creation and control of the vortex excitations remains elusive thus far. Here we theoretically propose how one can create and move the vortices in the Kitaev spin liquid. We find that the vortices are induced by a local modulation of the exchange interaction; especially, the local Dzyaloshinskii-Moriya (symmetric off-diagonal) interaction can create vortices most efficiently in the (anti)ferromagnetic Kitaev model, as it effectively flips the sign of the Kitaev interaction. We test this idea by performing the {\it ab initio} calculation for a candidate material $\alpha$-RuCl$_3$ through the manipulation of the ligand positions that breaks the inversion symmetry and induces the local Dzyaloshinskii-Moriya interaction. We also demonstrate a braiding of vortices by adiabatically and successively changing the local bond modulations.