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Anomalous Levitation and Annihilation in Floquet Topological Insulators

János Asbóth

Recently, the anomalous Floquet Anderson insulator (AFAI)[1] has attracted significant attention due to the coexistence of chiral edge modes and fully localized bulk. We show[2] that an AFAI can be obtained by time-periodically applying disordered phase "kicks" (via onsite potential) to a clean Chern insulator, a next-nearest neighbor hopping Hamiltonian with staggered flux. By computing the transmission through the system, we find that tuning the time period between the kicks leads to AFAI phases with different topological invariants, even in the limit of complete disorder (uniformly distributed phases). Disorder-induced transitions to these phases occur by "levitation and pair annihilation" of extended states carrying the Chern numbers, but these transitions can be anomalous, with the two annihilating states coming from different Floquet zones. Our results are applicable to a variety of Floquet topological systems, and may provide a more accessible way to construct AFAIs in cold-atom experiments.

[1] : P. Titum et al, Phys. Rev. X 6, 021013 (2016)
[2] : Hui Liu, Ion Cosma Fulga, J.K. Asboth (unpublished)


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