Destruction of superconductivity in disordered materials : a dimensional crossover

Abstract

The disorder-induced Superconductor-to-Insulator Transition in amorphous Nb${}_x$Si${}_{1-x}$ two-dimensional thin films is studied for different niobium compositions $x$ through a variation of the sample thickness $d$. We show that the critical thickness $d_c$, separating a superconducting regime from an insulating one, increases strongly with diminishing $x$, thus attaining values of over 100 Ã . The corresponding phase diagram in the $(d,x)$ plane is inferred and related to the three-dimensional situation. The two-dimensional Superconductor-to-Insulator Transition well connects with the three-dimensional Superconductor-to-Metal Transition.