Kondo enabled transmutation between spinons and superconducting vortices: origin of magnetic memory in 4Hb-$mathrm{TaS_2}$*

Recent experiments [Persky {it{et al.}}, Nature {f{607}}, 692 (2022)] demonstrate a magnetic memory effect in 4Hb-$mathrm{TaS_2}$ above its superconducting transition temperature, where Abriokosov vortices are generated spontaneously by lowering temperature at zero magnetic field after field training the normal state. Motivated by the experiment, we propose the chiral quantum spin liquid (QSL) stabilized in the constituent layers of 4Hb-$mathrm{TaS_2}$ as a mechanism. We model 4Hb-$mathrm{TaS_2}$ as coupled layers of the chiral QSL and superconductor. Through the Kondo coupling between the localized moments and conduction electrons, there is mutual transmutation between spinons and vortices during the thermal cycling process, which yields magnetic memory effect as observed in experiments. We also propose a mechanism to stabilize the chiral and nematic superconductivity in 4Hb-$mathrm{TaS_2}$ through the Kondo coupling of conduction electrons to the chiral QSL. Our results suggest 4Hb-$mathrm{TaS_2}$ as an exciting platform to explore the interplay between QSL and superconductivity through the Kondo effect.