Robustness of symmetry-protected topological states against time-periodic perturbations

Abstract

The existence of gapless boundary states is a key attribute of any topological insulator. Topological band theory predicts that these states are robust against static perturbations that preserve the relevant symmetries. In this article, using Floquet theory, we examine how chiral symmetry-protection extends also to states subject to time-periodic perturbations $-$ in one-dimensional Floquet topological insulators as well as in ordinary one-dimensional time-independent topological insulators. It is found that, in the case of the latter, the edge modes are resistant to a much larger class of time-periodic symmetry-preserving perturbations than in Floquet topological insulators. Notably, boundary states in chiral time-independent topological insulators also exhibit an unexpected resilience against a certain type of symmetry-breaking time-periodic perturbations. We argue that this is a generic property for topological phases protected by chiral symmetry. Implications for experiments are discussed.

10 pages, 7 figures; published version

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• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Thermoelectric performance of topological boundary modes
• Localization counteracts decoherence in noisy Floquet topological chains
• Edge mode manipulation through commensurate multifrequency driving
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
• Robust topological feature against non-Hermiticity in Jaynes-Cummings Model
• Topological phase transition in commensurate multi-frequency Floquet Su-Schrieffer-Heeger model
• Transport signatures of symmetry protection in 1D Floquet topological insulators
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Anomalous Floquet Phases. A resonance phenomena
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
• Robust Bulk States
• Topological states at exceptional points
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Spectral Form Factors of Topological Phases