Visons in Kitaev Spin Liquids with Majorana Fermi Surfaces

TL;DR

This paper studies visons in Kitaev quantum spin liquids with Majorana Fermi surfaces, revealing how their gaps and local correlations are affected by Fermi surface size and finite-size effects.

Contribution

It introduces an analytical approach to understand vison behavior in Kitaev models with Majorana Fermi surfaces, highlighting their instability and impact on spin correlations.

Findings

Vison gap decreases with increasing Fermi surface size.

Larger Fermi surfaces suppress changes in local spin correlations.

Finite-size effects are significant due to gapless modes.

Abstract

The excitation spectrum of Kitaev quantum spin liquids consists of itinerant Majorana fermions, which can be gapless or gapped, and vortices of a $\mathbb{Z}_2$ gauge field, known as visons, which are always gapped. In this work, we investigate visons in Kitaev-type models where the Majorana fermions form a Fermi surface. In this case, the creation of a vison pair is analogous to introducing a local impurity potential in a metal. Since the gapless modes lead to strong finite-size effects, we compare the numerical calculation of the vison gap on finite lattices with the result from an analytical approach based on Green's function techniques. We find that the vison gap decreases as the size of the Fermi surface increases, signalling an instability of the quantum spin liquid ground state. We also show that larger Fermi surfaces tend to suppress the change in local spin correlations due to the Majorana-vison scattering potential.