  Superconductivity originates from pairing of electrons. Pairing channel on
Fermi surface and pairing glue are thus two pivotal issues for understanding a
superconductor. Recently, high-temperature superconductivity over 40 K was
found in electron-doped FeSe superconductors including K$_x$Fe$_{2-y}$Se$_2$,
Li$_{0.8}$Fe$_{0.2}$OHFeSe, and 1 monolayer FeSe thin film. However, their
pairing mechanism remains controversial. Here, we studied the systematic
evolution of electronic structure in potassium-coated FeSe single crystal. The
doping level is controlled precisely by in situ evaporating potassium onto the
sample surface. We found that the superconductivity emerges when the
inter-pocket scattering between two electron pockets is turned on by a Lifshitz
transition of Fermi surface. The nematic order suppresses remarkably at the
same doping and strong nematic fluctuation remains in a wide doping range of
the phase diagram. Our results suggest an underlying correlation among
superconductivity, inter-pocket scattering, and nematic fluctuation in
electron-doped FeSe superconductors.
