Abstract
We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not suffer from decoherence and heating.
Highlights
In Appendix E, we show how changing the higher-order topological insulators (HOTIs) parameters leads to topological phase transitions of the reflection matrix, signaled by changes in its topological invariants
We have shown that back-scattering from the boundary of a static 2D HOTI is described by a reflection matrix which is topologically equivalent to a 1D nontrivial Floquet system
Our work introduces a dimensional reduction procedure based on the scattering matrix, which maps the 2D Hamiltonian of a HOTI into the 1D Floquet operator of a nontrivial chain
Summary
Topology provides a common tool set for analyzing the properties of both static and dynamical systems. Bulk-boundary correspondence predicts the appearance of gapless modes both in the spectra of time-independent Hermitian Hamiltonians [1, 2], as well as in those of the unitary time-evolution (or Floquet) operators describing periodically-driven systems [3, 4]. We first present our main idea in a generic setting (Sec. 2) before proceeding with a concrete example of a two-dimensional (2D) particle-hole symmetric HOTI For the latter system, we show that the reflection matrix is topologically equivalent to a 1D Floquet Kitaev chain [60,61,62], realizing the same topological phases (Sec. 3).
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