We report the successful growth of tetragonal FeS film with one or two unit-cell (UC) thickness on SrTiO3(001) substrate by molecular beam epitaxy. Large lattice constant mismatch with the substrate leads to high density of defects in single UC FeS, while it has been significantly reduced in double UC thick film due to the lattice relaxation. The scanning tunneling spectra on the surface of FeS thin film reveal the electronic doping effect of single UC FeS from the substrate. In addition, at the Fermi level, the energy gaps of approximate 1.5 meV are observed in films of both thicknesses at 4.6 K and below. The absence of coherence peaks of gap spectra may be related to the preformed Cooper-pairs without phase coherence.
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