Topological defects in Floquet systems: Anomalous chiral modes and topological invariant

TL;DR

This paper introduces a topological invariant for Floquet systems that counts chiral modes along defects created by spatially modulated periodic driving, enabling new ways to generate chiral modes in 3D materials.

Contribution

It defines a novel topological invariant for Floquet topological defects and demonstrates how to create chiral modes in bulk materials through modulated driving.

Findings

Defined a topological invariant on a five-dimensional parameter space.

Showed the creation of chiral modes via spatially modulated Floquet driving.

Provided a framework for future studies of Floquet topological defects.

Abstract

Backscattering-immune chiral modes arise along certain line defects in three-dimensional materials. In this paper, we study Floquet chiral modes along Floquet topological defects, namely, the defects come entirely from spatial modulations of periodic driving. We define a precise topological invariant that counts the number of Floquet chiral modes, which is expressed as an integral on a five-dimensional torus parameterized by $(k_x,k_y,k_z,\theta,t)$. This work demonstrates the possibility of creating chiral modes in three-dimensional bulk materials by modulated driving. We hope that it will stimulate further studies of Floquet topological defects.