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Simulating Floquet topological phases in static systems

by Selma Franca, Fabian Hassler, Ion Cosma Fulga

Submission summary

As Contributors: Ion Cosma Fulga
Arxiv Link: (pdf)
Date accepted: 2021-03-31
Date submitted: 2021-02-09 12:59
Submitted by: Fulga, Ion Cosma
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


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.

Published as SciPost Phys. Core 4, 007 (2021)

Author comments upon resubmission

Dear Editor,
Thank you for handling our manuscript and for sending us the referee reports.
For ease of reading, we have prepared a pdf reply, which can be accessed at the following link:

Selma Franca, Fabian Hassler, and Ion Cosma Fulga

List of changes

See our reply pdf for a detailed list of changes.

Reports on this Submission

Anonymous Report 1 on 2021-2-24 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2001.08217v3, delivered 2021-02-24, doi: 10.21468/SciPost.Report.2606


Following the comments given in the previous submission, the authors included a more detailed general description of their dimensional reduction procedure and compared it with another competing approach.

This is clearly an improvement from the previous manuscript hence I now vote to accept.

Regarding the discussion around the importance of simulating non-interacting physics, my opinion stayed as is.

  • validity: high
  • significance: ok
  • originality: good
  • clarity: top
  • formatting: perfect
  • grammar: perfect

Login to report


Ion Cosma Fulga  on 2021-02-09


Following the Editor's suggestion, we upload here the pdf of our resubmission letter.



Jian-Hua Jiang  on 2021-03-11

suggestion for further work

This is definitely an elegant theory that connects two realms of topological physics: the Hermitian systems and the unitary systems. The mapping looks interesting and encouraging. I am wondering how such a connection depends microscopic details: for instance, the size of the HOTI, the couplings between the waveguides and the HOTI, the band gap of the HOTI. In addition, there are various 2D HOTIs, how do they map to 1D Floquet topological insulators in various phases? All these aspects are important before the phenomena become reality in experiments.

Author:  Ion Cosma Fulga  on 2021-04-15

(in reply to Jian-Hua Jiang on 2021-03-11)

Thank you very much for your comment! We have replied to it in the attached pdf.



Anonymous on 2021-03-23

Following the Referee reports and the comments on the previous version of the manucript, the authors have made modfications to the manuscript, which I think has improved it quite a lot. In particular, the appendices on dimensional reduction and the fictitious time-evolution operator go a long way in improving the paper.

I find the statement of the authors' about a response (such as in frequency-dependence of spectral functions) unconvincing. Even if the the 'invariant' is a pi phase difference in the unitary reflection matrix, can it not be engineered into a signature of the topology such as in 4pi Josephson junctions?

The authors make several claims of meta-metarial realization of their protocol; however I do not think it is substantiated well. I understand that this is a theoretical paper and the scope for a full experimental proposal is limited.

The concern about the significance of the results stays unchanged.

Despite these concerns, with some reservations, I think the paper can be considered for SciPost Physics Core.