Two different superconducting states and possible antiferromagnetic quantum critical points in S-doped FeSe under pressure

We performed $^{77}$Se-NMR measurements on FeSe$_{1-x}$S$_x$, ($x$ = 0.12) up to 3.0 GPa at an applied magnetic field of 6.02 T, and found that the superconducting (SC) phase exhibits a remarkable double-dome structure in the pressure($P$)-temperature($T$) phase diagram which is hidden at 0 T. From the relaxation rate $1/T_1$ divided by $T$, $1/T_1T$, a Lifshitz transition may occur at 1.0 GPa, and the dominant nesting vector could change due to topological changes in Fermi surfaces. In other words, two types of antiferromagnetic (AFM) fluctuations would exist in the $P-T$ phase diagram. We conclude that the SC double domes in 12%-S doped FeSe consist of two SC states each of which correlates to a different type of AFM fluctuation. Furthermore, the strong AFM fluctuation at ambient pressure could originate from a possible hidden AFM quantum critical point.