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 Tc monotonically decreased with increasing 1/d. Regarding the suppression of Tc, the sheet resistance Rsq dependence of Tc 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 Rc, at which the superconducting–insulator transition was expected, was approximately one-third of the universal value Rq = h/4e2 suggested by the dirty boson model for self-duality. It is concluded that Tc depression in the present NbN system is determined by localization theory but not the dirty boson model.