Geometrical enhancement of the proximity effect in quantum wires with extended superconducting tunnel contacts

TL;DR

This paper investigates how the geometry of extended superconducting contacts enhances Andreev reflection in quantum wires, revealing a length-dependent increase in reflection probability due to particle-hole mixing and minigap formation.

Contribution

It introduces a geometrical perspective on the proximity effect, showing how extended contacts can significantly boost Andreev reflection beyond traditional expectations.

Findings

Andreev reflection probability $R_A$ increases with contact length $L$

A characteristic length scale $\xi_N$ determines the enhancement

Enhanced reflection occurs despite low interfacial transparency

Abstract

We study Andreev reflection in a ballistic one-dimensional channel coupled in parallel to a superconductor via a tunnel barrier of finite length $L$. The dependence of the low-energy Andreev reflection probability $R_A$ on $L$ reveals the existence of a characteristic length scale $\xi_N$ beyond which $R_A(L)$ is enhanced up to unity despite the low interfacial transparency. The Andreev reflection enhancement is due to the strong mixing of particle and hole states that builds up in contacts exceeding the coherence length $\xi_N$, leading to a small energy gap (minigap) in the density of states of the normal system. The role of the geometry of such hybrid contacts is discussed in the context of the experimental observation of zero-bias Andreev anomalies in the resistance of extended carbon nanotube/superconductor junctions in field effect transistor setups.