## SciPost Submission Page

# Simulating Floquet topological phases in static systems

### by Selma Franca, Fabian Hassler, Ion Cosma Fulga

### Submission summary

As Contributors: | Ion Cosma Fulga |

Arxiv Link: | https://arxiv.org/abs/2001.08217v2 (pdf) |

Date submitted: | 2020-08-03 11:55 |

Submitted by: | Fulga, Ion Cosma |

Submitted to: | SciPost Physics |

Discipline: | Physics |

Subject area: | Condensed Matter Physics - Theory |

Approach: | Theoretical |

### 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.