Quenched nematic criticality separating two superconducting domes in an iron-based superconductor under pressure

The nematic electronic state and its associated nematic critical fluctuations have emerged as potential candidates for superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with other magnetically-ordered phases poses significant challenges in establishing their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a clean nematic quantum phase transition in the absence of a long-range magnetic order. We find that in the proximity of the nematic phase transition, there is an unusual non-Fermi liquid behavior in resistivity at high temperatures that evolves into a Fermi liquid behaviour at the lowest temperatures. From quantum oscillations in high magnetic fields, we trace the evolution of the Fermi surface and electronic correlations as a function of applied pressure. We detect experimentally a Lifshitz transition that separates two distinct superconducting regions: one emerging from the nematic electronic phase with a small Fermi surface and strong electronic correlations and the other one with a large Fermi surface and weak correlations that promotes nesting and stabilization of a magnetically-ordered phase at high pressures. The lack of mass divergence suggests that the nematic critical fluctuations are quenched by the strong coupling to the lattice. This establishes that superconductivity is not enhanced at the nematic quantum phase transition in the absence of magnetic order.