Topological reflection matrix

While periodically-driven phases offer a unique insight into non-equilibrium topology that is richer than its static counterpart, their experimental realization often hindered by ubiquitous decoherence effects. Recently, we have proposed decoherence-free approach of realizing these Floquet phases. The central the reflection matrix, being unitary for bulk insulator, plays role time-evolution operator. We shown processes off boundaries systems supporting higher-order topological (HOTPs) simulate non-trivial So far, this method was to work one-dimensional protected local symmetries. Here, extend range applicability studying three-dimensional HOTPs with corner and hinge modes. show can both first-order second-order phases, combination spatial For every phase, discuss appropriate invariants calculated nested scattering matrix method.