Topological superconductivity in quasicrystals

TL;DR

This paper demonstrates that non-Abelian topological superconductivity can be realized in two-dimensional quasicrystals, such as Penrose and Ammann-Beenker, using mechanisms similar to those in crystalline materials, confirmed by topological invariants and Majorana modes.

Contribution

It introduces a method to achieve topological superconductivity in quasicrystals with specific parameters, expanding the scope of topological phases beyond periodic crystals.

Findings

Topological superconductivity with broken time-reversal symmetry is realized in quasicrystals.

Presence of zero-energy surface bound states and chiral wave propagation confirms topological nature.

Existence of Majorana zero modes in vortices and along surfaces indicates non-Abelian statistics.

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.