Competing length scales and 2D versus 3D dimensionality in relatively thick superconducting NbN films

Magneto-transport characteristics of 2D and 3D superconducting layers, in particular, temperature and angular dependences of the upper critical field H_c2, are usually considered to be fundamentally different. In the work, using non-local resistance measurements at temperatures near the normal-to-superconducting transition, we probed an effective dimensionality of nm-thick NbN films. It was found that in relatively thick NbN layers, the thicknesses of which varied from 50 to 100 nm, the temperature effect on H_c2 certainly pointed to the three-dimensionality of the samples, while the angular dependence of H_c2 revealed behavior typical for 2D samples. The seeming contradiction is explained by an intriguing interplay of three length scales in the dimensionally confined superconducting films: the thickness, the Ginzburg-Landau coherence length, and the magnetic-field penetration depth. Our results provide new insights into the physics of superconducting films with an extremely large ratio of the London penetration depth to the Ginzburg-Landau coherence length exhibiting simultaneously 3D isotropic superconducting properties and the 2D transport regime.