Suppression of Unconventional Superconductivity in Quasicrystals

Anderson's theorem states that conventional superconductors are robust to non-magnetic random disorder, while unconventional (non-s-wave) superconductors are not. In this work, we consider the robustness of conventional and unconventional superconductors to quasiperiodicity. This is done in the context of the Aubry-André (AA) model in 2D and 3D: a square/cubic lattice with an incommensurate non-magnetic potential. Like disordered lattices, the AA model does not have lattice translation symmetry, but unlike disordered lattices, the AA model is ordered, i.e. it is a quasicrystal. We show that if the strength of the incommensurate potential is below a critical value, both conventional and unconventional superconductivity is robust. Above the critical value, unconventional superconductivity becomes fragile, signaled by a lack of the low temperature divergence of the pair susceptibility. The critical value of the incommensurate potential also marks a crossover from ballistic to diffusive behavior of the free fermions. Based on this, we speculate that the superconductivity observed in quasicrystalline moiré systems is likely s-wave.