  We study the effects of quasiperiodicity on the stability of conventional and
unconventional superconductors. Quasiperiodicity is modelled using the
three-dimensional Aubry-Andre model, a system in which electrons are coupled to
a translation-symmetry-breaking potential that is incommensurate with the
underlying lattice. Upon increasing the strength of the quasiperiodic
potential, the single-particle eigenstates undergo a transition from a
ballistic to a diffusive character. Here, we study the instability of the model
towards superconductivity. We find that in the ballistic regime, the system is
unstable towards both $s$-wave and $p$-wave superconductivity. In contrast,
only the conventional $s$-wave instability survives in the intermediate
diffusive regime. Our results suggest a version of Anderson's theorem for
quasiperiodic systems, relating the normal state dynamics to the stability of
conventional and unconventional superconductivity. These findings are relevant
vis-a-vis recent studies of superconductivity in quasiperiodic moire
structures.
