  Superconductivity in the cuprate superconductors and the Fe-based
superconductors is realized by doping the parent compound with charge carriers,
or by application of high pressure, to suppress the antiferromagnetic state.
Such a rich phase diagram is important in understanding superconductivity
mechanism and other physics in the Cu- and Fe-based high temperature
superconductors. In this paper, we report a phase diagram in the single-layer
FeSe films grown on SrTiO3 substrate by an annealing procedure to tune the
charge carrier concentration over a wide range. A dramatic change of the band
structure and Fermi surface is observed, with two distinct phases identified
that are competing during the annealing process. Superconductivity with a
record high transition temperature (Tc) at ~65 K is realized by optimizing the
annealing process. The wide tunability of the system across different phases,
and its high-Tc, make the single-layer FeSe film ideal not only to investigate
the superconductivity physics and mechanism, but also to study novel quantum
phenomena and for potential applications.
