We use sub-Kelvin scanning tunneling spectroscopy to investigate the suppression of superconductivity in homogeneously disordered ultrathin MoC films. We observe that the superconducting state remains spatially homogeneous even on the films of 3 nm thickness. The vortex imaging suggests the global phase coherence in our films. Upon decreasing thickness, when the superconducting transition drops from 8.5 to 1.2 K, the superconducting energy gap  follows perfectly T c . All this is pointing to a two-stage fermionic scenario of the superconductor-insulator transition (SIT) via a metallic state as an alternative to the direct bosonic SIT scenario with a Cooper-pair insulating state evidenced by the last decade STM experiments. [7][8][9][10][11][12][13] bring evidences that upon increasing disorder decreases more slowly than T c , the variation of on a scale of the superconducting coherence length  increases, a pseudogap appears above T c in the tunneling spectra, the spectral coherence peaks are suppressed, and the vortex lattice is fading out. This phenomenology strongly supports the bosonic scenario and raises the question about the universality of the bosonic SIT [14]. On the other hand, potential evidence for the fermionic mechanism was provided even sooner by the tunneling experiments on planar junctions on amorphous Bi and PbBi/Ge films [15,16] indicating that the Cooper pair amplitude vanishes at SIT. But the unambiguousness of these results was challenged by the fact that the spatially averaged tunneling spectra were gapless. This gaplessness could be explained by a very inhomogeneous gap distribution due to phase fluctuations. Then, superconducting pair correlations might also exist in insulators close to SIT, contradicting the fermionic scenario. KeywordsHere, we present sub-Kelvin STM experiments on ultra thin superconducting MoC films with atomic spatial resolution. We demonstrate the spatial homogeneity of the superconducting state for film thicknesses down to 3 nm and the closing of the superconducting energy gap/order parameter as T c vanishes, in agreement with the fermionic scenario. Thus, we bring the first direct evidence on the local behavior of the superconducting order parameter in this class of the transition.The MoC films were prepared by the magnetron reactive sputtering from a Mo target in an argon-acetylene atmosphere onto a sapphire c-cut substrate. The details can be found elsewhere [17]. The preparation followed the procedure of Lee and Ketterson [18] who manufactured continuous MoC films down to 0.4 nm thickness showing

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We studied a thin superconducting NbN film in magnetic fields up to 8 T above the zerotemperature limit by means of time-domain terahertz and scanning tunneling spectroscopies in order to understand the vortex response. Scanning tunneling spectroscopy was used to determine the optical gap and the upper critical field of the sample. The obtained values were subsequently used to fit the terahertz complex conductivity spectra in the magnetic field in the Faraday geometry above the zero temperature limit. These spectra are best described in terms of the Coffey-Clem self-consistent solution of a modified London equation in the flux creep regime. 74.25.Gz, 74.55.+v,