Gapless superconductivity and its real-space topology in quasicrystals - Kazuma Saito; Masahiro Hori; Ryo Okugawa; K. Tanaka; Takami Tohyama (Physical Review Research, 2025)
We study superconductivity in Ammann-Beenker quasicrystals under magnetic field. By assuming an intrinsic s-wave pairing interaction and solving for mean-field equations self-consistently, we find gapless superconductivity in the quasicrystals at and near half filling. We show that gapless superconductivity results from the combination of broken translational symmetry and confined states that is characteristic of the quasicrystals. When Rashba spin-orbit coupling is present, the quasicrystalline gapless superconductor can be topologically nontrivial and characterized by a nonzero pseudospectrum invariant given by a spectral localizer. The gapless topological superconducting phase exhibits edge states with near-zero energy. These findings suggest that quasicrystals can be a unique platform for realizing gapless superconductivity with nontrivial topology.