Direct evidence of superconductivity and determination of the superfluid density in buried ultrathin FeSe grown on SrTiO$_3$

Abstract: Bulk FeSe is superconducting with a critical temperature $T_c$ $\cong$ 8 K and SrTiO$_3$ is insulating in nature, yet high-temperature superconductivity has been reported at the interface between a single-layer FeSe and SrTiO$_3$. Angle resolved photoemission spectroscopy and scanning tunneling microscopy measurements observe a gap opening at the Fermi surface below $\approx$ 60 K. Elucidating the microscopic properties and understanding the pairing mechanism of single-layer FeSe is of utmost importance as it is a basic building block of iron-based superconductors. Here, we use the low-energy muon spin rotation/relaxation technique (LE-$\mu$SR) to detect and quantify the supercarrier density and determine the gap symmetry in FeSe grown on SrTiO$_3$ (100). Measurements in applied field show a temperature dependent broadening of the field distribution below $\sim$ 60 K, reflecting the superconducting transition and formation of a vortex state. Zero field measurements rule out the presence of magnetism of static or fluctuating origin. From the inhomogeneous field distribution, we determine an effective sheet supercarrier density $n_s^{2D} \simeq 6 \times 10^{14}$ cm$^{-2}$ at $T \rightarrow 0$ K, which is a factor of 4 larger than expected from ARPES measurements of the excess electron count per Fe of 1 monolayer (ML) FeSe. The temperature dependence of the superfluid density $n_s(T)$ can be well described down to $\sim$ 10 K by simple s-wave BCS, indicating a rather clean superconducting phase with a gap of 10.2(1.1) meV. The result is a clear indication of the gradual formation of a two dimensional vortex lattice existing over the entire large FeSe/STO interface and provides unambiguous evidence for robust superconductivity below 60 K in ultrathin FeSe.