Induced superconducting pair correlations in a quasicrystal coupled to a BCS superconductor

TL;DR

This paper investigates how superconducting correlations are induced in a one-dimensional Fibonacci quasicrystal when coupled to a BCS superconductor, revealing long-range proximity effects and topological signatures.

Contribution

It demonstrates the long-range proximity effect and topological features in a Fibonacci quasicrystal using self-consistent Bogoliubov-de Gennes equations.

Findings

Proximity effect in Fibonacci chain is long-ranged.

Induced superconductivity reflects topological properties.

Edge states' winding numbers influence the superconducting order.

Abstract

In this report, we describe the proximity effect which arises when a quasicrystal is placed in contact with a superconductor. We consider the simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all states are known to be critical. A hybrid ring is made by connecting a finite piece of such a Fibonacci chain to a BCS-type superconductor. Solving the resulting Bogoliubov-de Gennes equations self-consistently, we show that the proximity effect in the Fibonacci chain is long ranged, and that the induced superconducting order carries information on topological properties, namely, the winding numbers of edge states of the Fibonacci chain.