# The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring

## TL;DR

This study investigates how the superconducting order parameter penetrates a Fibonacci quasicrystal in a hybrid ring, revealing dependence on structural parameters and topological edge states, with notable fluctuations and enhanced penetration at specific configurations.

## Contribution

It introduces a self-consistent method to analyze the superconducting order parameter in a superconductor-quasicrystal hybrid, highlighting the influence of quasicrystal structure and topological states on superconducting proximity effects.

## Key findings

- Order parameter decay follows a power law with distance.
- Large fluctuations in order parameter for individual chains.
- Enhanced penetration at specific phason angles.

## Abstract

We compute the real-space profile of the superconducting order parameter (OP) in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter $\phi$, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on $\phi$ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly $larger$ than in a normal periodic conductor for special values of $\phi$.