Upper critical field in nanostructured Nb: Competing effects of the reduction in density of states and the mean free path

We show that the upper critical field in nanometer-sized Nb particles is governed by the changes in the effective Ginzburg-Landau coherence length occurring due to two competing factors: (i) the decrease in the grain size and consequent increase of disorder, and (ii) the effective decrease in the density of states at the Fermi level due to the formation of a Kubo gap. As a result, the upper critical field (H-C2) and irreversibility fields (H-irr) in nanostructured Nb show nonmonotonic grain size dependences. Between 60 and 20 nm, H-C2 is found to increase by 2.5 times, while there is no appreciable decrease in the superconducting transition temperature (T-C) from its bulk value of 9.4 K. This can be ascribed to a decrease in the coherence length due to a reduction in the mean free path with decreasing size. Below 20 nm, however, H-C2 decreases with decreasing size. In this size range (< 20 nm), there also occurs a decrease in the T-C as well as the superconducting energy gap. The decrease in H-C2 in this regime can be ascribed to the decrease in the density of states at the Fermi level due to a quantization in the electronic energy levels.