Interaction-tuned pattern-selective superconductivity: Application to the dodecagonal quasicrystal

Quasicrystals exhibit superconductivity under the unique interplay of long-range order and strong inhomogeneity, distinguishing them from both crystalline and amorphous systems. Understanding how this structural complexity affects superconducting states and phase transitions remains an important open question. Here, we unveil anomalous superconductivity in a dodecagonal quasicrystal using the attractive Hubbard model within the Bogoliubov--de Gennes framework. We show that both the gap structure and critical temperature depend on the local pattern due to inhomogeneous charge distribution and kinetic terms. This leads to unconventional phase transitions between mixed phases where superconducting and normal regions coexist, even without external fields, which we term pattern-selective superconductivity. Alongside the local superconducting transition, the tiny spectral gaps---a hallmark of quasicrystals---allow thermally excited insulating regions to turn metallic. Furthermore, superconductivity can be anomalously suppressed even under stronger attractive interactions due to the alignment of the Fermi level with a spectral gap in the fragmented Hartree-shifted spectrum. These findings, not observed in conventional crystals, amorphous systems, or previous studies of quasicrystal superconductivity, highlight the distinct role of quasicrystalline order.