Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

TL;DR

This paper investigates how disorder suppresses superconductivity in thin films, revealing that three-dimensional effects near localization thresholds, rather than purely two-dimensional diffusion, dominate the critical temperature reduction.

Contribution

It demonstrates that the suppression of T_c is primarily due to small-scale electron interactions related to three-dimensional effects, challenging the traditional diffusive two-dimensional model.

Findings

Suppression of T_c is linked to small-scale electron interactions near the Fermi wavelength.

The dominant factor is the parameter k_F l, not the sheet resistance.

Most films follow a fermionic suppression scenario influenced by three-dimensional localization.

Abstract

Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the $T_c$ suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift $\delta T_c/T_{c0} \sim - 1/k_Fl$, where $k_F$ is the Fermi momentum and $l$ is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of $T_c$ suppression with decreasing the film thickness, this effect is caused by the proximity to the three-dimensional Anderson localization threshold and is controlled by the parameter $k_F l$ rather than the sheet resistance of the film.