Igor Valery Yurkevich

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.

1 Introduction The physics of (quasi-) 1D systems is extremely rich and exhibits itself in a variety of phenomena, from edge states in quantum Hall effects[1] and topological insulators[2] to the most recent experimental results of the enhancement of superconductivity by disorder in quasi-1D materials[3] and zero-magnetic field fractional conductance in GaAs/AlGaAs heterostructures.[4] Strongly interacting electrons in 1D systems are described by Luttinger liquid (LL) theory.[5-8] Seminal...