Topological superconductivity in quasicrystals

準結晶におけるトポロジカル超伝導

Ghadimi, R.*; 杉本 貴則*; 田中 佳織*; 遠山 貴己

Ghadimi, R.*; Sugimoto, Takanori*; Tanaka, Kaori*; Toyama, Takami

We propose realization of non-Abelian topological superconductivity in two-dimensional quasicrystals by the same mechanism as in crystalline counterparts. Specifically, we study a two-dimensional electron gas in Penrose and Ammann-Beenker quasicrystals with Rashba spin-orbit coupling, perpendicular Zeeman magnetic field, and conventional -wave superconductivity. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling, where the Bott index is unity. The topological nature of this phase is confirmed by the existence of a zero-energy surface bound state and the chiral propagation of a wave packet projected onto the midgap bound state along the surfaces. Furthermore, we confirm the existence of a single Majorana zero mode each in a vortex at the center of the system and along the surfaces, signifying the non-Abelian character of the system when the Bott index is unity.