Symmetry Analysis of Anomalous Floquet Topological Phases

TL;DR

This paper introduces a practical symmetry analysis method to distinguish anomalous Floquet topological phases from normal insulators in nonequilibrium systems, revealing unique dynamic features despite similar symmetry eigenvalues.

Contribution

It develops an enhanced symmetry analysis approach for Floquet topological phases, especially in the presence of crystal symmetry, to identify topological states via microscopic dynamics.

Findings

Anomalous Floquet states share symmetry eigenvalues with normal insulators.

Stable symmetry inversion points in dynamics distinguish topological states.

The approach explains coexistence of boundary and bulk states in Floquet phases.

Abstract

The topological characterization of nonequilibrium topological matter is highly nontrivial because familiar approaches designed for equilibrium topological phases may not apply. In the presence of crystal symmetry, Floquet topological insulator states cannot be easily distinguished from normal insulators by a set of symmetry eigenvalues at high symmetry points in the Brillouin zone. This work advocates a physically motivated, easy-to-implement approach to enhance the symmetry analysis to distinguish between a variety of Floquet topological phases. Using a two-dimensional inversion-symmetric periodically-driven system as an example, we show that the symmetry eigenvalues for anomalous Floquet topological states, of both first-order and second-order, are the same as for normal atomic insulators. However, the topological states can be distinguished from one another and from normal insulators by inspecting the occurrence of stable symmetry inversion points in their microscopic dynamics. The analysis points to a simple picture for understanding how topological boundary states can coexist with localized bulk states in anomalous Floquet topological phases.