Superconductivity in Fibonacci chain

Abstract

We study the interplay between the incommensurate disorder and superconductivity in the one-dimensional system with the s-wave pairing mechanism. Specifically, we consider the tight-binding model for the Fibonacci chain, which include the quasi-periodic modulation in on-site disorder. As the signature of multifractality, we observe the power-law dependence for the spatial correlation as the function of energy. By numerically calculating the transition temperature of the superconductivity, we find the enhancement of the critical temperature given by analytical prediction is underestimated. Furthermore, for the very weak coupling regime, we observe a crossover where self-averaging of the critical temperature breaks down and appears a strong fluctuation related to samples.