Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585, Japan1
Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan2
Department of Physics and Engineering Physics, and Centre for Quantum Topology and Its Applications (quanTA), University of Saskatchewan, 116 Science Place, Saskatoon, Saskatchewan, Canada S7N 5E23
The appearance of superconductivity in quasicrystals opens a lot of questions regarding the effect of aperiodicity in superconducting related phenomena. The topological superconducting phase is one of flourishing phenomena that may happen even in quasicrystals. Here, we extend a conventional way constructing an s-wave topological superconductor under Rashba spin-orbit coupling, perpendicular Zeeman magnetic field from periodic lattice to two different quasicrystals, Amman-Beenker and Penrose lattices [1]. We find that topological superconductivity with broken time-reversal symmetry is realized in both Penrose and Ammann-Beenker quasicrystals at low filling. 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.
[1] R. Ghadimi, T. Sugimoto, K. Tanaka, and T. Tohyama, arXiv:2006.06952.
Keywords: quasicrystal, topological superconductor