Hierarchy of higher-order Floquet topological phases in three dimensions

TL;DR

This paper develops a hierarchy of higher-order Floquet topological phases in three dimensions by periodically driving static topological states with symmetry-breaking masses, leading to dynamic hinge and corner modes.

Contribution

It introduces a systematic protocol to realize second- and third-order Floquet topological states in 3D, expanding the understanding of dynamic boundary modes in driven systems.

Findings

Realization of second-order Floquet topological states with hinge modes.

Demonstration of third-order Floquet topological states with corner modes.

Application to 3D topological insulators and Dirac semimetals.

Abstract

Following a general protocol of periodically driving static first-order topological phases (supporting surface states) with suitable discrete symmetry breaking Wilson-Dirac masses, here we construct a hierarchy of higher-order Floquet topological phases in three dimensions. In particular, we demonstrate realizations of both second-order and third-order Floquet topological states, respectively supporting dynamic hinge and corner modes at zero quasienergy, by periodically driving their static first-order parent states with one and two discrete symmetry breaking Wilson-Dirac mass(es). While the static surface states are characterized by codimension $d_c=1$, the resulting dynamic hinge (corner) modes, protected by \emph{antiunitary} spectral or particle-hole symmetries, live on the boundaries with $d_c=2$ $(3)$. We exemplify these outcomes for three-dimensional topological insulators and Dirac semimetals, with the latter ones following an arbitrary spin-$j$ representation.