Strongly Disordered Floquet Topological Systems

Jacob Shapiro, Clément Tauber

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


We study the strong disorder regime of Floquet topological systems in dimension two that describe independent electrons on a lattice subject to a periodic driving. In the spectrum of the Floquet propagator we assume the existence of an interval in which all states are localized—a mobility gap—extending previous studies which make the stronger spectral gap assumption. We devise a new approach to define the topological invariants by way of stretching the gap of a given system onto the whole circle. We show that such completely localized systems have natural indices that circumvent the relative construction and match with quantized magnetization and pumping observables from the physics literature. These indices obey a bulk-edge correspondence, which carries over to the stretched systems as well. Finally, these invariants are shown to coincide with those associated with the usual relative construction, which we also extend to the mobility gap regime.

Original languageEnglish (US)
Pages (from-to)1837-1875
Number of pages39
JournalAnnales Henri Poincare
Issue number6
StatePublished - Jun 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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