Self-consistent study of topological superconductivity in two-dimensional quasicrystals

Abstract

We study two-dimensional s-wave topological superconductivity with Rashba spin-orbit coupling and Zeeman field in Penrose and Ammann-Beenker quasicrystals. By solving the Bogoliubov–de Gennes equations self-consistently for not only the superconducting order parameter, but also the spin-dependent Hartree potential, we show the stable occurrence of topological superconductivity with broken time-reversal symmetry in both Penrose and Ammann-Beenker quasicrystals. The topological nature of the quasicrystalline system is signified by the Bott index B. Topological phase transitions are found to occur, where B changes between 0 and ±1, as the chemical potential or Zeeman field is varied. In terms of self-consistent solutions, we demonstrate the existence of a Majorana zero mode per edge or vortex when B=±1, consistently with the bulk-edge/defect correspondence for periodic systems.

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