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.
We investigated the magnetoconductivity Δσ(H)≡1/ρ(H)−1/ρ(0) in a wide range of magnetic fields for three-dimensional indium oxide films doped with zinc, tin, or gallium in the range of resistivity ρ(300K) between 4.1×10−6 Ωm and 1.7×10−3 Ωm. The weak localization theory was fitted to data for Δσ(H) at various temperatures in the range 2.0 K≤T≤50 K by the use of suitable characteristics Dτin(T) and Dτso, where D, τin, and τso are the electron diffusion constant, inelastic scattering time, and spin-orbit (s-o) scattering time, respectively. It was found that (i) for films with a large value of ρ, the sign of Δσ(H) changes from positive to negative with decreasing temperature as a precursor to an anti-weak localization effect; (ii) the ratio τso/τin decreases from ≈4000 to≈4.0 with increasing ρ; (iii) the strong ρ dependence of Dτso cannot be explained by the model with a constant atomic number Z in a formula τso∝1/Z4 proposed by Abrikozov and Gorkov Zh. Eksp. Teor. Fiz. 42, 1088 (1962); [Sov. Phys. JETP 15, 752 (1962)]. As a reason for this ρ dependence, we suggest that the s-o scattering changes with increasing ρ from light oxygen atoms to heavy atoms, i.e., indium, zinc, and gallium, because of the decrease in the number of oxygen vacancies acting as s-o scattering centers.
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