Simulating Floquet topological phases in static systems

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 to suffer from decoherence and heating.

31 pages, 8 figures. Updated the paper based on the referee reports at https://scipost.org/submissions/2001.08217/

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Cited by in corpus (9)

• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Electric Circuit Simulation of Floquet Topological Insulators
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Topological Micromotion of Floquet Quantum Systems
• Gapless higher-order topology and corner states in Floquet systems
• Scattering theory of delicate topological insulators
• Topological reflection matrix
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
• Noise resilience of two-dimensional Floquet topological phases