# Spectroscopic evidence for strong correlations between local superconducting gap and local Altshuler-Aronov density-of-states suppression in ultrathin NbN films

## TL;DR

This study uses scanning tunneling spectroscopy to reveal that local superconducting gap variations in ultrathin NbN films are strongly linked to Altshuler-Aronov density-of-states suppression caused by electronic interactions, explained through a local Finkelstein mechanism.

## Contribution

It demonstrates a purely fermionic explanation for superconducting inhomogeneities in disordered NbN films based on local LDOS suppression and resistivity variations.

## Key findings

- Local superconducting gap correlates with LDOS depletion.
- LDOS suppression can be modeled as local resistivity changes.
- Resistivity variations induce local gap variations via Finkelstein mechanism.

## Abstract

Disorder has different profound effects on superconducting thin films. For a large variety of materials, increasing disorder reduces electronic screening which enhances electron-electron repulsion. These fermionic effects lead to a mechanism described by Finkelstein: when disorder combined to electron-electron interactions increases, there is a global decrease of the superconducting energy gap $\Delta$ and of the critical temperature $T_c$, the ratio $\Delta$/$k_BT_c$ remaining roughly constant. In addition, in most films an emergent granularity develops with increasing disorder and results in the formation of inhomogeneous superconducting puddles. These gap inhomogeneities are usually accompanied by the development of bosonic features: a pseudogap develops above the critical temperature $T_c$ and the energy gap $\Delta$ starts decoupling from $T_c$. Thus the mechanism(s) driving the appearance of these gap inhomogeneities could result from a complicated interplay between fermionic and bosonic effects. By studying the local electronic properties of a NbN film with scanning tunneling spectroscopy (STS) we show that the inhomogeneous spatial distribution of $\Delta$ is locally strongly correlated to a large depletion in the local density of states (LDOS) around the Fermi level, associated to the Altshuler-Aronov effect induced by strong electronic interactions. By modelling quantitatively the measured LDOS suppression, we show that the latter can be interpreted as local variations of the film resistivity. This local change in resistivity leads to a local variation of $\Delta$ through a local Finkelstein mechanism. Our analysis furnishes a purely fermionic scenario explaining quantitatively the emergent superconducting inhomogeneities, while the precise origin of the latter remained unclear up to now.