  A1-xFe2-ySe2 (A = K, Cs, Rb, Tl) are recently discovered iron-based
superconductors with critical temperatures (Tc) ranging up to 32 K. Their
parent phases have unique properties when compared with other iron-based
superconductors; e.g., their crystal structures include ordered Fe vacancies,
their normal states are antiferromagnetic (AFM) insulating phases, and they
have extremely high N\'eel transition temperatures. However, control of carrier
doping into the parent AFM insulators has been difficult due to their intrinsic
phase separation. Here, we fabricated an Fe-vacancy-ordered TlFe1.6Se2
insulating epitaxial film with an atomically flat surface and examined its
electrostatic carrier doping using an electric double-layer transistor (EDLT)
structure with an ionic liquid gate. The positive gate voltage gave conductance
modulation of three orders of magnitude at 25 K, and further induced and
manipulated a phase transition; i.e., delocalized carrier generation by
electrostatic doping is the origin of the phase transition. This is the first
demonstration, to the authors' knowledge, of an EDLT using a Mott insulator
iron-selenide channel and opens a way to explore high-Tc superconductivity in
iron-based layered materials, where carrier doping by conventional chemical
means is difficult.
