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We propose the superconducting van der Waals material 4Hb-TaS$_2$ to realizethe $\mathbb{Z}_2$ topological order and interpret the recent discovery of thespontaneous vortex generation in 4Hb-TaS$_2$ as the vison-vortex nucleation.For the alternating stacking of metallic/superconducting and Mott insulatinglayers in 4Hb-TaS$_2$, we expect the local moments in the Mott insulating1T-TaS$_2$ layer to form the $\mathbb{Z}_2$ topological order. The spontaneousvortex generation in 4Hb-TaS$_2$ is interpreted from the transition ornucleation between the superconducting vortex and the $\mathbb{Z}_2$ vison indifferent phase regimes. Differing from the single vison-vortex nucleation inthe original Senthil-Fisher's cuprate proposal, we consider such nucleationprocess between the superconducting vortex lattice and the vison crystal. Wefurther propose experiments to distinguish this proposal with the$\mathbb{Z}_2$ topological order from the chiral spin liquid scenarios.

Is spontaneous vortex generation in superconducting 4Hb-TaS$_2$ from vison-vortex nucleation with $\mathbb{Z}_2$ topological order?