Topological superconductivity in quasicrystals

Abstract

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 $s$-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.

11 pages, 9 figures

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Cited by in corpus (8)

• Chern insulator in a hyperbolic lattice
• Topological states in quasicrystals
• Noncrystalline topological superconductors
• Intrinsic vortex pinning in superconducting quasicrystals
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Pattern-dependent proximity effect and Majorana edge mode in one-dimensional quasicrystals
• 1D quasicrystals and topological markers
• Confined states in the tight-binding model on the hexagonal golden-mean tiling