Diamagnetic Response of an N-S-Proximity System at Arbitrary Impurity Concentration

TL;DR

This paper explores how the magnetic response of normal-metal--superconductor proximity systems varies with impurity levels and temperature, revealing a transition from non-local to local screening regimes.

Contribution

It derives a general linear-response formula for arbitrary impurity concentrations and temperatures, bridging clean and dirty limit behaviors in proximity systems.

Findings

Finite mean free path enhances screening in the ballistic regime.

Non-locality range is temperature-dependent in the ballistic regime.

Cross-over from local to non-local screening occurs in the diffusive limit.

Abstract

We investigate the magnetic response of normal-metal--superconductor proximity systems for arbitrary concentrations of impurities and at arbitrary temperatures. Using the quasiclassical theory a general linear-response formula is derived which yields a non-local current-field relation in terms of the zero-field Green's functions. Various regimes between clean-limit and (local) dirty-limit response are investigated by analytical methods and by solving the general formula numerically. In the ballistic regime we find that a finite mean free path reduces the non-locality and leads to a stronger screening than in the clean limit even for a mean free path much larger than the system size. Additionally, the range of the kernel describing the non-locality is strongly temperature-dependent in this case. In the diffusive limit we find a cross-over from local to non-local screening, which restricts the applicability of the dirty-limit theory.