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

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