  We theoretically study, through combining the density functional theory and
an unfolding technique, the electronic band structure and the charge doping
effects for the deposition of potassium (K) on multilayer FeSe films grown on
SrTiO3 (001) surface. These results form a theoretical base line for further
detailed studies of low-temperature electronic properties and their multiway
quantum engineering of FeSe thin films. We explain the Fermi surface topology
observed in experiment and formulate the amount of doped electrons as a
function of atomic K coverage. We show that the atomic K deposition efficiently
dopes electrons to top layer FeSe. Both checkerboard and pair-checkerboard
antiferromagnetic (AFM) FeSe layers show electron pockets at M point and no
Fermi pocket at $\Gamma$ point with moderate atomic K coverage. The electron
transfer from K adsorbate to FeSe film introduces a strong electric field,
which leads to a double-Weyl cone structure at M point in the Brillouin zone of
checkerboard-AFM FeSe. We demonstrate that with experimentally accessible heavy
electron doping, an electron-like Fermi pocket will emerge at $\Gamma$ point,
which should manifest itself in modulating the high-temperature
superconductivity of FeSe thin films.
