Localization and interaction effects in ultrathin epitaxial NbN superconducting films

For epitaxial NbN films with thickness d, 2.0 nm <= d <= 20.5 nm, we observed a sharp superconducting transition, for which the transition temperature T-c monotonically decreased with increasing 1/d. Regarding the suppression of T-c, the sheet resistance R-sq dependence of T-c closely fitted the Finkel'stein formula from localization theory, with a reasonable value of the electron mean free path comparable to atomic distance, which was used as a fitting parameter. On the other hand, the critical sheet resistance R-c, at which the superconducting-insulator transition was expected, was approximately one-third of the universal value R-q =h/4e(2) suggested by the dirty boson model for self-duality. It is concluded that T-c depression in the present NbN system is determined by localization theory but not the dirty boson model.