On the microscopics of proximity effects in one-dimensional superconducting hybrid systems

TL;DR

This paper develops a microscopic framework using Keldysh Green's functions to analyze the proximity effect in one-dimensional superconductor-normal heterostructures, revealing disorder effects and spectral properties relevant for quantum device experiments.

Contribution

It introduces a detailed microscopic approach to study proximity effects beyond the Andreev approximation, including disorder effects, in one-dimensional hybrid superconducting systems.

Findings

Disorder induces a crossover in correlation patterns.

Spectral analysis reveals the distribution of induced pair amplitude.

Theoretical insights support recent experimental observations of enhanced Cooper pair injection.

Abstract

Investigating the microscopic details of the proximity effect is crucial for both key experimental applications and fundamental inquiries into nanoscale devices featuring superconducting elements. In this work, we develop a framework motivated by experiments to study induced superconducting correlations in hybrid nanoscale devices featuring layered superconductor-normal heterostructures using the Keldysh non-equilibrium Green's functions. Following a detailed method for analyzing the induced pair amplitude in a prototypical one-dimensional hybrid, we provide insights into the proximity effect within and outside the Andreev approximation. Our analysis also uncovers a disorder-induced crossover in the correlation patterns of the system. By elucidating the spectral distribution of the induced pair amplitude, we investigate the pair correlations established in a recent experiment [Phys.Rev.Lett.128,127701], providing a theoretical basis for the enhanced Cooper pair injection demonstrated through the lens of the induced pair correlations, thereby establishing the promise of our methods in guiding new experiments in hybrid quantum devices.