Superconductivity across Lifshitz transition and anomalous insulating state in surface K-dosed (Li_0.8Fe_0.2OH)FeSe

In iron-based superconductors, understanding the relation between superconductivity and electronic structure upon doping is crucial for exploring the pairing mechanism. Recently, it was found that, in iron selenide (FeSe), enhanced superconductivity (T_c of more than 40 K) can be achieved via electron doping, with the Fermi surface only comprising M-centered electron pockets. By using surface K dosing, scanning tunneling microscopy/spectroscopy, and angle-resolved photoemission spectroscopy, we studied the electronic structure and superconductivity of (Li_0.8Fe_0.2OH)FeSe in the deep electron-doped regime. We find that a Γ-centered electron band, which originally lies above the Fermi level (E_F), can be continuously tuned to cross E_F and contribute a new electron pocket at Γ. When this Lifshitz transition occurs, the superconductivity in the M-centered electron pocket is slightly suppressed, and a possible superconducting gap with a small size (up to ~5 meV) and a dome-like doping dependence is observed on the new Γ electron pocket. Upon further K dosing, the system eventually evolves into an insulating state. Our findings provide new clues to understand superconductivity versus Fermi surface topology and the correlation effect in FeSe-based superconductors.