Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models

TL;DR

This paper investigates how spectrum-wide quantum criticality (SWQC) in one-dimensional models with attractive interactions enhances superconductivity, showing that SWQC persists at localization transitions and maximizes pairing amplitude.

Contribution

It demonstrates that SWQC, previously observed in 2D topological systems, can robustly enhance superconductivity in 1D models with attractive interactions.

Findings

SWQC survives at the Anderson localization transition.

Pairing amplitude is maximized near the localization transition.

SWQC can robustly enhance superconductivity.

Abstract

We study the interplay of superconductivity and a wide spectrum of critical (multifractal) wave functions ("spectrum-wide quantum criticality," SWQC) in the one-dimensional Aubry-Andr\'e and power-law random-banded matrix models with attractive interactions, using self-consistent BCS theory. We find that SWQC survives the incorporation of attractive interactions at the Anderson localization transition, while the pairing amplitude is maximized near this transition in both models. Our results suggest that SWQC, recently discovered in two-dimensional topological surface-state and nodal superconductor models, can robustly enhance superconductivity.