Enhanced superconductivity due to spectrum-wide wavefunction criticality in quasiperiodic and power-law random hopping models

There has been a surge of interest in quasiperiodic systems, with applications in ultracold atoms, many-body localization, and twisted bilayer systems at larger twist angles. The Aubry-André(AA) model is a canonical example of a 1D quasiperiodic system, and its entire spectrum of single-particle wave functions is critical (multifractal) at the metal-insulator transition (“spectrum-wide criticality”). This strange feature also occurs in the ensemble of power-law random banded matrices (PRBM), and was very recently discovered to occur generically at the 2D surface of 3D topological superconductors [1]. Here we study the interplay of critical wave functions and superconductivity in AA and PRBM models with attractive interactions via self-consistent BCS theory. Spectrum-wide criticality survives the incorporation of attractive interactions, and we show that superconducting pairing is most enhanced for the interaction-dressed spectrum-wide critical condition. Finally, we examine the interplay of Chalker scaling between critical wave functions and the enhancement of pairing in both models.