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 gapped within a stable ${\mathbb{Z}}_2$ spin liquid phase. 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 two-vison gap on finite lattices with the result from an analytical approach based on Green's function techniques. We find that the two-vison gap decreases as the size of the Fermi surface increases, signaling 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.

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• Fractionalization
• Quantum spin liquid
• Kagome lattice
• Kitaev model