  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.
