Hierarchy of higher-order Floquet topological phases in three dimensions

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 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.