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.