Topological superconductivity in Fibonacci quasicrystals

In this work, we explore the topological properties of a one-dimensional topological superconductor arranged in a Fibonacci quasicrystal (QC) configuration, which models a magnetic atom chain placed on a superconducting surface. We reveal an aparent mutually exclusive competition between the quasicrystalline order and the topological superconducting phase with Majorana bound states (MBS), which turns out to be beneficial in a broader perspective supplied by topological diagrams. Specifically, no MBS are found within the QC gaps, and MBS never exhibit quasicrystalline subgap behavior. Similarly, critical or winding QC subgap states do not exist within the topological superconducting gaps.

Despite this competition, we discover that the QC structure offers significant advantages for realizing topological superconductivity with MBS. It expands the parameter space to include large nontrivial regions supporting MBS, which remain topologically trivial in crystalline systems. Furthermore, the underlying quasicrystal structure enhances the topological gap, ensuring ncreased robustness of the MBS. Notably, shorter approximants of the Fibonacci QC yield the most pronounced benefits.

These findings position quasicrystals, particularly their shorter approximants, as promising platforms for experimental realization of MBS. They also highlight the intriguing interplay between distinct gapped systems influencing the topological superconductivity and paving the way for novel approaches in topological quantum systems.