Time-quasiperiodic topological superconductors with Majorana Multiplexing

TL;DR

This paper introduces time-quasiperiodic Majoranas in superconducting systems driven at multiple irrational frequencies, revealing their stability, coexistence, and potential for quantum braiding in complex driven systems.

Contribution

It demonstrates the existence of multiple stable time-quasiperiodic Majoranas in multi-frequency driven systems and relates them to the time quasicrystal phase, expanding topological superconductivity.

Findings

Up to 2^d types of Majoranas can coexist in d-frequency driven systems.

Time-quasiperiodic Majoranas are stable despite dense quasienergy spectra.

Multiple Majoranas are related to the time quasicrystal phase.

Abstract

Time-quasiperiodic Majoranas are generalizations of Floquet Majoranas in time-quasiperiodic superconducting systems. We show that in a system driven at $d$ mutually irrational frequencies, there are up to $2^d$ types of such Majoranas, coexisting despite spatial overlap and lack of time-translational invariance. Although the quasienergy spectrum is dense in such systems, the time-quasiperiodic Majoranas can be stable and robust against resonances due to localization in the periodic-drives induced synthetic dimensions. This is demonstrated in a time-quasiperiodic Kitaev chain driven at two frequencies. We further relate the existence of multiple Majoranas in a time-quasiperiodic system to the time quasicrystal phase introduced recently. These time-quasiperiodic Majoranas open a new possibility for braiding which will be pursued in the future.