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

## TL;DR

This paper investigates how topological insulator boundary states, protected by chiral symmetry, withstand time-periodic perturbations, revealing greater robustness in static systems and unexpected resilience against symmetry-breaking perturbations.

## Contribution

It demonstrates that chiral symmetry-protected topological states exhibit significant robustness against time-periodic perturbations, extending understanding of their stability beyond static conditions.

## Key findings

- Edge states resist a broader class of time-periodic perturbations in static topological insulators.
- Boundary states show resilience against certain symmetry-breaking time-periodic perturbations.
- Chiral symmetry provides a generic protection mechanism for topological phases under dynamic 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.