  We study superconductivity in a family of one dimensional incommensurate
system with $s$-wave pairing interaction. The incommensurate potential can
alter the spatial characteristics of electrons in the normal state, leading to
either extended, critical, or localized wave functions. We find that
superconductivity is significantly enhanced when the electronic wave function
exhibits a critical multifractal structure. This criticality also manifests
itself in the power-law dependence of superconducting temperature on the
pairing strength. As a consequence, an extended superconducting domain is
expected to exist around the localization-delocalization transition, which can
be induced by either tuning the amplitude of the incommensurate potential, or
by varying the chemical potential across a mobility edge. Our results thus
suggest a novel approach to enhance superconducting transition temperature
through engineering of incommensurate potential.
