We study the effects of quasiperiodicity on the stability of conventional and unconventional superconductors. Quasiperiodicity is modeled using the three-dimensional Aubry-André (AA) 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 ballistic to diffusive character. We find that, in the ballistic regime, the system a weak-coupling instability towards both $s$-wave and $p$-wave superconductivity. In contrast, only the conventional $s$-wave instability survives in the diffusive regime. Our result suggest a version of Anderson's theorem for quasiperiodic systems, relating the normal state dynamics to the stability of conventional and unconventional superconductivity.

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• Superconductivity
• Disordered alloys
• Quasicrystals
• BCS theory
• Mean field theory