Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer

The origin of enhanced superconductivity over 50 K in the recently discovered FeSe monolayer films grown on SrTiO$_3$ (STO), as compared to 8 K in bulk FeSe, is intensely debated. As with the ferrochalcogenides A$_x$Fe$_{2-y}$Se$_2$ and potassium doped FeSe, which also have a relatively high superconducting critical temperature ($T_c$), the Fermi surface (FS) of the FeSe/STO monolayer films is free of hole-like FS, suggesting that a Lifshitz transition by which these hole FSs vanish may help increasing $T_c$. However, the fundamental reasons explaining this increase of $T_c$ remain unclear. Here we report a 15 K jump of $T_c$ accompanying a second Lifshitz transition characterized by the emergence of an electron pocket at the Brillouin zone (BZ) centre, which is triggered by high electron doping following \textit{in-situ} deposition of potassium on FeSe/STO monolayer films. Our results suggest that the pairing interactions are orbital-dependent with the $d_{xy}$ orbital playing a determining role in generating enhanced superconductivity in FeSe.