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.
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