Topological reflection matrix

TL;DR

This paper extends a decoherence-free method using reflection matrices to simulate and analyze three-dimensional higher-order topological phases, including corner and hinge modes, with potential for experimental realization.

Contribution

It generalizes the reflection matrix approach to 3D HOTPs, enabling simulation of both first- and second-order Floquet phases with complex symmetry protections.

Findings

Reflection processes can simulate 3D Floquet topological phases.

Both first- and second-order Floquet phases are realizable.

Topological invariants are computed using nested scattering matrices.

Abstract

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