Published Tunneling Results of Binnig et al Interpreted as Related to Surface Superconductivity in SrTiO3

In 1980, Binnig et al. reported tunneling measurements on Nb-doped SrTiO3, and interpreted their results as indicating two-band superconductivity in the bulk of SrTiO3. However, (1) effective masses determined from tunneling results in the normal state by Sroubek in 1969 and 1970 are much smaller than those determined by most other methods. The much smaller masses were attributed to properties of a surface layer by the present author in 1971. (2) The only other reports of two-band superconductivity in bulk SrTiO3 can be used to infer much smaller values for the band separations than found by Binnig et al. In this paper, we give an alternative explanation of the results of Binnig et al. in terms of superconductivity in a surface layer. We obtain fair fits to the band gaps versus Fermi energy for the two bands in the three samples where two surface subbands are occupied and to the temperature dependence of the gaps in one crystal, using a model with three adjustable interaction parameters, an adjustable energy for the phonons which dominate the pairing, and an adjustable ratio of the mean-field Tc to the actual Tc. We show results for a combined fit to the low-temperature band gaps and to the T-dependence in one crystal. The phonon energy which gives the best fit is 21 meV. This is probably an appropriate average over the three longitudinal polar modes and acoustic modes in the material. A large value of about two is found for the ratio Tcmf/Tc, and we conjecture that this arises because a band with a small Fermi energy, not seen in the tunneling results, plays a part in increasing Tcmf/Tc.