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.