  A general feature of unconventional superconductors is the existence of a
superconducting dome in the phase diagram as a function of carrier
concentration. For the simplest iron-based superconductor FeSe (with transition
temperature Tc ~ 8 K), its Tc can be greatly enhanced by doping electrons via
many routes, even up to 65 K in monolayer FeSe/SiTiO3. However, a clear phase
diagram with carrier concentration for FeSe-derived superconductors is still
lacking. Here, we report the observation of a series of discrete
superconducting phases in FeSe thin flakes by continuously tuning carrier
concentration through the intercalation of Li and Na ions with a solid ionic
gating technique. Such discrete superconducting phases are robust against the
substitution of Se by 20% S, but are vulnerable to the substitution of Fe by 2%
Cu, highlighting the importance of the iron site being intact. A complete
superconducting phase diagram for FeSe-derivatives is given, which is distinct
from other unconventional superconductors.
