Square-root Floquet topological phases and time crystals

TL;DR

This paper introduces a method to create square-root versions of Floquet topological phases, leading to richer physics, including new topological superconductors and time crystals, with robustness and potential for systematic phase construction.

Contribution

It presents a general approach to generate square-root Floquet phases, expanding the landscape of topological and time crystalline phenomena in driven quantum systems.

Findings

Discovery of Floquet topological superconductors with multiple edge modes

Identification of 4T-period Floquet time crystals in various systems

Method to iteratively construct nth-root Floquet phases

Abstract

Periodically driven (Floquet) phases are attractive due to their ability to host unique physical phenomena with no static counterparts. We propose a general approach in nontrivially devising a square-root version of existing Floquet phases, applicable both in noninteracting and interacting setting. The resulting systems are found to yield richer physics that is otherwise absent in the original counterparts and is robust against parameter imperfection. These include the emergence of Floquet topological superconductors with arbitrarily many zero, $\pi$, and $\pi/2$ edge modes, as well as $4T$-period Floquet time crystals in disordered and disorder-free systems ($T$ being the driving period). Remarkably, our approach can be repeated indefinitely to obtain a 2nth-root version of a given system, thus allowing for the discovery and systematic construction of a family of exotic Floquet phases.