SciPost Physics Core

Simulating Floquet topological phases in static systems

Selma Franca, Fabian Hassler, Ion Cosma Fulga

SciPost Phys. Core 4, 007 (2021) · published 15 April 2021

• doi: 10.21468/SciPostPhysCore.4.2.007
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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.

• Franca et al., Topological reflection matrix
  Phys. Rev. B 105, 155121 (2022) [Crossref]
• Xu et al., Topological micromotion of Floquet quantum systems
  Phys. Rev. B 105, 045139 (2022) [Crossref]
• Dabiri et al., Electric circuit simulation of Floquet topological insulators in Fourier space
  134, 084303 (2023) [Crossref]
• Shukla et al., Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains
  Phys. Rev. B 105, 224307 (2022) [Crossref]
• Zhu et al., Scattering theory of delicate topological insulators
  Phys. Rev. B 107, 195110 (2023) [Crossref]
• Franca et al., Non-Hermitian Physics without Gain or Loss: The Skin Effect of Reflected Waves
  Phys. Rev. Lett. 129, 086601 (2022) [Crossref]
• Zhou, Generating Many Majorana Corner Modes and Multiple Phase Transitions in Floquet Second-Order Topological Superconductors
  Symmetry 14, 2546 (2022) [Crossref]