Tunable Fragile Topology in Floquet Systems

TL;DR

This paper introduces and demonstrates the existence of fragile topological phases in periodically-driven Floquet systems, revealing rich phase diagrams and tunable phase transitions with potential experimental signatures.

Contribution

It extends fragile topology to Floquet systems, showing how driving amplitudes can tune between various topological and trivial phases with distinct boundary features.

Findings

Discovery of Floquet fragile topological phases protected by symmetries

Identification of phase transitions driven by tuning amplitudes

Observation of corner fractional charges as topological signatures

Abstract

We extend the notion of fragile topology to periodically-driven systems. We demonstrate driving-induced fragile topology in two different models, namely, the Floquet honeycomb model and the Floquet $\pi$-flux square-lattice model. In both cases, we discover a rich phase diagram that includes Floquet fragile topological phases protected by crystalline rotation or mirror symmetries, Floquet Chern insulators, and trivial atomic phases, with distinct boundary features. Remarkably, the transitions between different phases can be feasibly achieved by simply tuning the driving amplitudes, which is a unique feature of driving-enabled topological phenomena. Moreover, corner-localized fractional charges are identified as a ``smoking-gun'' signal of fragile topology in our systems. Our work paves the way for studying and realizing fragile topology in Floquet systems.