Self-consistent study of topological superconductivity in quasicrystals

Quasicrystals are emerging topological materials which defy all the laws of crystallography, with aperiodic long-range order and higher-dimensional symmetry. We study topological superconductivity with broken time-reversal symmetry in prototypal two-dimensional quasicrystals, Penrose and Ammann-Beenker quasicrystals. By solving the Bogoliubov-de Gennes equations self-consistently for the mean fields, we show the stable occurrence of TSC in both Penrose and Ammann-Beenker quasicrystals. The topological nature of TSC in a quasicrystal is signified by the Bott index. We confirm the appearance of zero-energy Majorana fermions at surface boundaries when the Bott index is unity, in accordance with the bulk-boundary correspondence and the non-Abelian character of the system.