# Strongly Disordered Floquet Topological Systems

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## Abstract

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.

## Notes

### Acknowledgements

The authors thank Gian Michele Graf for many useful discussions. J. S. thanks Netanel H. Lindner for his hospitality at the Technion in Israel and for elaborations on the completely localized edge index. C. T. thanks Alain Joye for his invitation at institut Fourier and fruitful discussions on localization for unitary operators.

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