Fig. 2. Evolution of the superfluid density in the ion-gated FeSe film.

(A) Temperature-dependent superfluid density, ρ_s(T), for the ion-gated FeSe film with T_c systematically tuned from ~11 to 43 K. The dashed lines are the nodeless-gap fits to the first 10% drop in ${\mathrm{\rho }}_{\mathrm{s}}\left(T\right)/{\mathrm{\rho }}_{\mathrm{s}}(T\to 0)$ , as depicted in the expanded view of the ρ_s data at low temperatures in (B). arb. units, arbitrary units. (C) Dependence of T_c on the zero-temperature superfluid density, ${\mathrm{\rho }}_{\mathrm{s}0}\equiv {\mathrm{\rho }}_{\mathrm{s}}(T\to 0)$ , where ρ_s0 is determined from the nodeless-gap fit. The blue squares represent the experimental data; the red solid line is the fit to $T_{\mathrm{c}}=\mathrm{\gamma }{\mathrm{\rho }}_{\mathrm{s}0}^{0.55}$ , where γ is the fit parameter. (D) Uemura plot: T_c versus Fermi temperature, T_F, for various superconductors (59). The ion-gated FeSe with T_c > 39 K, as well as other FeSe-based superconductors, i.e., monolayer FeSe on SrTiO₃ substrate [1 unit cell (uc) FeSe] and (Li_0.8Fe_0.2)OHFeSe (FeSe-11111) are located closer to the BEC limit for 3D bosonic gas (T_c = 0.218T_F, the dashed line) than cuprate and heavy-fermion superconductors (the shaded region). The large ratio of Δ/E_F ≈ 0.23 for ion-gated FeSe also indicates that it lies in the BCS-BEC crossover regime (see the inset). T_F and E_F are obtained from ρ_s0 using the formula given in (32), i.e., E_F = k_BT_F = $\frac{\mathrm{\pi }{\mathrm{\hslash }}^{2}d}{{\mathrm{\mu }}_0{e}^2}$ ρ_s0, where $d$ is the interlayer distance. The values of Δ are obtained from the nodeless-gap fits in (B).