Topological superconductivity in Fibonacci quasicrystals

TL;DR

This paper explores how Fibonacci quasicrystals influence topological superconductivity, revealing a complex interplay that can enhance the stability and occurrence of Majorana bound states despite mutual exclusivity.

Contribution

It demonstrates that Fibonacci quasicrystals can expand the parameter space for topological superconductivity and increase the topological gap, especially in short approximants.

Findings

No Majorana bound states inside QC gaps

QC enhances topological regions with MBS in parameter space

Short approximants of Fibonacci QC show the greatest benefits

Abstract

We investigate the properties of a Fibonacci quasicrystal (QC) arrangement of a one-dimensional topological superconductor, such as a magnetic atom chain deposited on a superconducting surface. We uncover a general mutually exclusive competition between the QC properties and the topological superconducting phase with Majorana bound states (MBS): there are no MBS inside the QC gaps and the MBS never behaves as QC subgap states, and likewise, no critical, or winding, QC subgap states exist inside the topological superconducting gaps. Surprisingly, despite this competition, we find that the QC is still highly beneficial for realizing topological superconductivity with MBS. It both leads to additional large nontrivial regions with MBS in parameter space, that are topologically trivial in crystalline systems, and increases the topological gap protecting the MBS. We also find that shorter approximants of the Fibonacci QC display the largest benefits. As a consequence, our results promote QCs, and especially their short approximants, as an appealing platform for improved experimental possibilities to realize MBS as well as generally highlights the fundamental interplay between different topologies.