  The Hohenberg-Mermin-Wagner theorem states that a two-dimensional system
cannot spontaneously break a continuous symmetry at finite temperature. This is
supported by the observation of layer-dependent superconductivity in the
quasi-two-dimensional superconductor NbSe2, in which the superconducting
transition temperature (Tc) is reduced by about 60% in the monolayer limit.
However, for the extremely anisotropic copper-based high-Tc superconductor
Bi2Sr2CaCu2O8+{\delta} (Bi-2212), the Tc of the monolayer is almost identical
to that of its bulk counterpart. To clarify the effect of dimensionality on
superconductivity, here we successfully fabricate ultrathin flakes of
CsCa2Fe4As4F2, a highly anisotropic iron-based high-Tc superconductor, down to
monolayer. The monolayer flake exhibits the highest Tc of 24 K (after tuning to
the optimal doping by ionic liquid gating), which is about 20% lower than that
of the bulk crystal. We also fabricate ultrathin flakes of CaKFe4As4, another
iron-based superconductor with much smaller anisotropy. The Tc of the 3-layer
flake decreases by 46%, showing a more pronounced dimensional effect than that
of CsCa2Fe4As4F2. By carefully examining their anisotropy and the c-axis
coherence length, we reveal the general trend and empirical law of the
layer-dependent superconductivity in these quasi-two-dimensional
superconductors. From this, the Tc of a new monolayer superconductor can be
extrapolated.
