Enhancement of superconductivity in the Fibonacci chain

We study the interplay between quasiperiodic disorder and superconductivity in a one-dimensional tight-binding model with the quasiperiodic 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. We numerically compute the mean-field superconducting transition temperature for every realization of a Fibonacci chain of a given size and 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 quasiperiodic disorder. We find an enhancement of the critical temperature compared to the analytical results that are based on strong assumptions of the 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 strong sample-to-sample fluctuations emerge.