Observation of a new possible superconducting state and anomalous insulating state in surface K-dosed (Li$_{\mathrm{\mathbf{1-x}}}$\textbf{Fe}$_{\mathrm{\mathbf{x}}}$\textbf{OH)FeSe}

By using scanning tunneling microscopy/spectroscopy, we studied the evolution of electronic structure and superconductivity of (Li$_{\mathrm{\mathbf{1-x}}}$\textbf{Fe}$_{\mathrm{\mathbf{x}}}$\textbf{OH)FeSe via surface potassium (K) dosing. We found that the }$\Gamma $\textbf{-centered electron band, which was 70meV above Fermi level (}\textbf{\textit{E}}$_{\mathbf{F}}$\textbf{), can be tuned to cross }\textbf{\textit{E}}$_{\mathbf{F}}$\textbf{ by K dosing, and contributes a new electron pocket at }$\Gamma $\textbf{ When such Lifshitz transition happens, the superconducting gap on M-centered electron pocket is slightly suppressed. With further K dosing, a new superconducting-like gap gradually opens on the }$\Gamma $\textbf{ electron pocket, and forms a dome like doping behavior. After that, the system eventually evolves into an insulating phase with gradually depleted density of states near E}$_{\mathrm{\mathbf{F}}}$\textbf{. Our results provide more detailed phase diagram of FeSe in the deep electron doping region. The novel Fermi surface with electron pockets at both }$\Gamma $\textbf{ and M points will provide more clues to understand superconductivity of Fe-based superconductors.}