Topological reflection matrix

Physical review. B./Physical review. B, vol. 105

Abstract

While periodically driven phases offer a unique insight into nonequilibrium 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 nontrivial 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.

Authors 3

1. Selma Franca

   Leibniz Institute for Solid State and Materials Research · Complexity and Topology in Quantum Matter

   Affiliation as printed

   IFW Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtzstraße 20, 01069 Dresden, Germany

2. Fabian Hassler Aachen JARA-Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   JARA-Institute for Quantum Information, RWTH Aachen University, 52056 Aachen, Germany

3. Ion Cosma Fulga

   Leibniz Institute for Solid State and Materials Research · Complexity and Topology in Quantum Matter

   Affiliation as printed

   IFW Dresden and Würzburg-Dresden Cluster of Excellence ct.qmat, Helmholtzstraße 20, 01069 Dresden, Germany