Gapless Superconductivity and Topological Phases in Ammann-Beenker Quasicrystals

Ammann-Beenker quasicrystals can host gapless superconductivity under magnetic field, originating from the interplay of broken translational symmetry and highly degenerate confined states. The gapless superconducting phase can also be topologically nontrivial when Rashba spin-orbit coupling is present.