Is spontaneous vortex generation in superconducting 4Hb-TaS2 from vison-vortex nucleation with $\mathbb{Z}_{2}$ topological order?

We propose the superconducting van der Waals material 4Hb-TaS₂ to realize the \(\mathbb{Z}_{2}\) topological order and interpret the recent discovery of the spontaneous vortex generation in 4Hb-TaS₂ as the vison-vortex nucleation. For the alternating stacking of metallic/superconducting and Mott insulating layers in 4Hb-TaS₂, we expect the local moments in the Mott insulating 1T-TaS₂ layer to form the \(\mathbb{Z}_{2}\) topological order. The spontaneous vortex generation in 4Hb-TaS₂ is interpreted from the transition or nucleation between the superconducting vortex and the \(\mathbb{Z}_{2}\) vison in different phase regimes. Differing from the single vison-vortex nucleation in the original Senthil–Fisher’s cuprate proposal, we consider such nucleation process between the superconducting vortex lattice and the vison crystal. We further propose experiments to distinguish this proposal with the \(\mathbb{Z}_{2}\) topological order from the chiral spin liquid scenarios.