Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems

Abstract

We show that quasiperiodicity can enhance superconductivity in one-dimensional narrow-band systems with s-wave pairing. Using a generalized Aubry-Andr\'e-Harper model featuring quasiperiodic modulations in both the on-site potential and the hoppings, we study superconductivity across the extended, critical, and localized phases present in the noninteracting limit. Our results show that within the critical and localized phases, the superconducting critical temperature exhibits an algebraic scaling with the interaction strength, in contrast to the conventional BCS scaling observed in periodic approximants with a similar density of states. This direct comparison establishes that the enhancement originates from the nature of the single-particle eigenstates, rather than from band flattening alone. Furthermore, we find that the superfluid weight remains finite across all phases, including the localized regime, highlighting that superconducting phase coherence is retained throughout. The effects of quasiperiodicity on the superfluid weight are most pronounced in the weak-coupling regime, indicating the nontrivial role of the localization properties of the parent eigenstates in shaping the superconducting phases.