Phase diagram of the strongly disordered<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-wave superconductor NbN close to the metal-insulator transition

Abstract

We present a phase diagram as a function of disorder in three-dimensional NbN thin films as the system enters the critical disorder for destruction of the superconducting state. The superconducting state is investigated using a combination of magnetotransport and scanning tunneling spectroscopy measurements. Our studies reveal three disorder regimes. At low disorder (${k}_{F}l$ \ensuremath{\sim} 10--4), the system follows the mean field Bardeen-Cooper-Schrieffer behavior, where the superconducting energy gap vanishes at the temperature at which electrical resistance appears. For stronger disorder ($1&lt;{k}_{F}l$ 4), a ``pseudogap'' state emerges, where a gap in the electronic spectrum persists up to temperatures much higher than ${T}_{c}$, suggesting that Cooper pairs continue to exist in the system even after the zero resistance state is destroyed. Finally, at even stronger disorder (${k}_{F}l$ 1), the global superconducting ground state is destroyed even though superconducting correlations continue to survive, as evidenced from a pronounced magnetoresistance peak at low temperatures.