  The ability to tune material properties using gate electric field is at the
heart of modern electronic technology. It is also a driving force behind recent
advances in two-dimensional systems, such as gate-electric-field induced
superconductivity and metal-insulator transition. Here we describe an ionic
field-effect transistor (termed "iFET"), which uses gate-controlled lithium ion
intercalation to modulate the material property of layered atomic crystal
1T-TaS$_2$. The extreme charge doping induced by the tunable ion intercalation
alters the energetics of various charge-ordered states in 1T-TaS$_2$, and
produces a series of phase transitions in thin-flake samples with reduced
dimensionality. We find that the charge-density-wave states in 1T-TaS$_2$ are
three-dimensional in nature, and completely collapse in the two-dimensional
limit defined by their critical thicknesses. Meanwhile the ionic gating induces
multiple phase transitions from Mott-insulator to metal in 1T-TaS$_2$ thin
flakes at low temperatures, with 5 orders of magnitude modulation in their
resistance. Superconductivity emerges in a textured charge-density-wave state
induced by ionic gating. Our method of gate-controlled intercalation of 2D
atomic crystals in the bulk limit opens up new possibilities in searching for
novel states of matter in the extreme charge-carrier-concentration limit.
