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Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: Engineering of mobility gaps and multifractal states

Aditya, S and Sengupta, K and Sen, D (2023) Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: Engineering of mobility gaps and multifractal states. In: Physical Review B, 107 (3).

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Official URL: https://doi.org/10.1103/PhysRevB.107.035402


In this study, we examine whether periodic driving of a model with a quasiperiodic potential can generate interesting Floquet phases that have no counterparts in the static model. Specifically, we consider the Aubry-André model, which is a one-dimensional time-independent model with an on-site quasiperiodic potential V0 and a nearest-neighbor hopping amplitude that is taken to have a staggered form. We add a uniform hopping amplitude that varies in time either sinusoidally or as a square pulse with a frequency ω. Unlike the static Aubry-André model, which has a simple phase diagram with only two phases (only extended or only localized states), we find that the driven model has four possible phases for the Floquet eigenstates: a phase with gapless quasienergy bands and only extended states, a phase with multiple mobility gaps separating different quasienergy bands, a mixed phase with coexisting extended, multifractal, and localized states, and a phase with only localized states. The multifractal states have generalized inverse participation ratios that scale with the system size with exponents that are different from the values for both extended and localized states. In addition, we observe intricate reentrant transitions between the different kinds of states when ω and V0 are varied. The appearance of such transitions is confirmed by the behavior of the Shannon entropy. Many of our numerical results can be understood from an analytic Floquet Hamiltonian derived using a Floquet perturbation theory that uses the inverse of the driving amplitude as the perturbation parameter. In the limit of high frequency and large driving amplitude, we find that the Floquet quasienergies match the energies of the undriven system, but the Floquet eigenstates are much more extended. We also study the spreading of a one-particle wave packet, and we find that it is always ballistic but the ballistic velocity varies significantly with the system parameters, sometimes showing a nonmonotonic dependence on V0 that does not occur in the static model. Finally, we compare the results for the driven model, which has a static staggered hopping amplitude, with a model that has a static uniform hopping amplitude, and we find some significant differences between the two cases. All of our results are found to be independent of the driving protocol, either sinusoidal or square pulse. We conclude that the interplay of the quasiperiodic potential and driving produces a rich phase diagram that does not appear in the static model. © 2023 American Physical Society.

Item Type: Journal Article
Publication: Physical Review B
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Author(s).
Keywords: Fractals; Hamiltonians; Perturbation techniques, Eigenstates; Floquet; Hopping amplitude; Localized state; Mobility gap; Multi fractals; Quasi-energy; Quasiperiodic potential; Square pulse; Static modelling, Ballistics
Department/Centre: Division of Chemical Sciences > Solid State & Structural Chemistry Unit
Date Deposited: 09 Feb 2023 05:39
Last Modified: 09 Feb 2023 05:39
URI: https://eprints.iisc.ac.in/id/eprint/80106

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