Superconducting energy gap distribution in c-axis oriented MgB${}_2$ thin film from point contact study

We have analyzed about 100 voltage-dependent differential resistance dV/dI(V) curves of metallic point contacts between c-axis oriented MgB${}_2$ thin film and Ag, which exhibit clear Andreev reflection features connected with the superconducting gap. About one half of the curves show the presence of a second larger gap. The histogram of the double-gap distribution reveals distinct maxima at 2.4 and 7 meV, while curves with a single-gap features result in more broad maximum at 3.5 meV. The double-gap distribution is in qualitative agreement with the distribution of gap values over the Fermi surface calculated by H. J. Choi et al. (cond-mat/0111183). The data unequivocally show the presence of two gaps ${\mathrm{\Delta }}_S=2.45\pm 0.15$ meV and ${\mathrm{\Delta }}_L=7.0\pm 0.45$ meV in MgB${}_2$ with gap ratio $2.85\pm 0.15$. Our observations prove further a widely discussed multi-gap scenario for MgB${}_2$, where two distinct gaps are seen in the clean limit, while a single averaged gap is present in the dirty one.