Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators

TL;DR

This paper investigates how dynamical chiral symmetry in Floquet topological insulators influences their topological phases, revealing novel phenomena like symmetry-class conversion and the emergence of topological $ ext{pi}$-modes.

Contribution

It introduces a general framework for analyzing Floquet insulators with dynamical chiral symmetry and demonstrates how driving can induce class transitions and topological $ ext{pi}$-modes.

Findings

Topological gaps at zero quasi-energy are unaffected by driving when DCS has no static analog.

Driving can open topological gaps at $ ext{pi}$ quasi-energy, especially where perturbations vanish.

Symmetry-class conversion enables topologically trivial Hamiltonians to host topological $ ext{pi}$-modes.

Abstract

In this work, we discuss properties with no static counterpart arising in Floquet topological insulators with a dynamical chiral symmetry (DCS), i.e., a chiral symmetry which is present while driving. We explore the topological properties of Floquet insulators possessing a DCS which either does or does not survive upon taking the static limit. We consider the case of harmonic drives and employ a general framework using the quasi-energy operator in frequency space. We find that for a DCS with no static analog, the presence of driving has a negligible impact on the topological phases associated with zero quasi-energy. In stark contrast, topological gaps can open at $\pi$ quasi-energy and mainly occur at momenta where the driving perturbation vanishes. We confirm the above general predictions for an extended Kitaev chain model in the BDI symmetry class. Another possibility that opens up when adding the drive, while preserving chiral symmetry, is symmetry-class conversion. We demonstrate such an effect for a static CI class Hamiltonian which is topologically trivial in 1D. By considering a suitable driving, we obtain a CI$\rightarrow$AIII transition, which now enables the system to harbor topological $\pi$-modes. Notably, the arising topological phases strongly depend on whether the DCS has a static analog or not. Our results bring Floquet insulators with nonstandard DCS forward as ideal candidate platforms for engineering and manipulating topological $\pi$-modes.