Enhancement of Superconductivity in the Fibonacci Chain

TL;DR

This paper investigates how quasi-periodic disorder following Fibonacci sequence influences superconductivity in a 1D model, revealing enhanced critical temperatures and significant sample-to-sample fluctuations due to multifractality.

Contribution

It provides a numerical analysis of superconducting transition temperatures in a Fibonacci chain, highlighting deviations from traditional assumptions and uncovering disorder-induced enhancements.

Findings

Critical temperature is enhanced compared to analytical predictions.

Sample-to-sample fluctuations become prominent at weak coupling.

Multifractality correlates with superconducting properties.

Abstract

We study the interplay between quasi-periodic disorder and superconductivity in a 1D tight-binding model with the quasi-periodic modulation of on-site energies that follow the Fibonacci rule and all the eigenstates are multifractal. As a signature of multifractality, we observe the power-law dependence of the correlation between different single-particle eigenstates as a function of their energy difference. By computing numerically the superconducting transition temperature, we find the distribution of critical temperatures, analyze their statistics and estimate the mean value and variance of critical temperatures for various regimes of the attractive coupling strength and quasi-periodic disorder. We find an enhancement of the critical temperature as compared to the analytical results that are based on strong assumptions of absence of correlations and self-averaging of multiple characteristics of the system, which are not justified for the Fibonacci chain. For the very weak coupling regime, we observe a crossover where the self-averaging of the critical temperature breaks down completely and a strong sample-to-sample fluctuations emerge.