Localization, Topology, and Quantized Transport in Disordered Floquet Systems

Wauters, Matteo M.; Russomanno, Angelo; Citro, Roberta; Santoro, Giuseppe E.; Privitera, Lorenzo

doi:10.1103/physrevlett.123.266601

Cited by 34 publications

(24 citation statements)

References 51 publications

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“…Crucially, even in this region, quantized pumping persists, as will be shown below. This agrees with the analysis of [44], where the breakdown of quantized pumping has been linked to a delocalizationlocalization transition of Floquet eigenstates, which occurs deep in the regime of localized single-particle Hamiltonian eigenstates.…”

Section: B Localization Of Single-particle Statessupporting

confidence: 90%

“…The shaded region indicates the point where the mode of the minimum gap along the pump cycle closes at w/J ≈ 2.95 ± 0.05. Similar results for the critical disorder strength were obtained in[44] from Floquet states for different parameters. At larger values of w 8J, one finds C = 0[44].…”

supporting

confidence: 84%

“…A very appealing perspective on a disordered charge pump, modeled by the Rice-Mele model, has been put forward in Ref. [44]: While the Hamiltonian eigenstates are fully localized in one dimension with random onsite disorder for any disorder strength [45], there is a delocalization-localization transition in the Floquet eigenstates at the point where quantized pumping breaks down. Our work extends the analysis and theoretical understanding in several ways.…”

Section: Introductionmentioning

confidence: 99%

“…We show that the disorder average of the bulk gap overestimates the critial disorder strength, while the mode, the most likely value, agrees very well with the point at which the disorder-averaged measures for topological charge pumping start to deviate from integer values. This insight may be relevant for the analysis of experimental data [32] as well as of numerical studies of finite systems [44].…”

Section: Introductionmentioning

confidence: 99%

“…(see also the discussion in [32,44]). Finally, the stability of topological pumping in quasiperiodic potentials will be interesting as well (see, e.g., [69,70]).…”

mentioning

confidence: 99%

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Effect of disorder on topological charge pumping in the Rice-Mele model

et al. 2021

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Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. In the instantaneous basis, we compute the polarization, the entanglement spectrum, and the local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations, we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes and is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution.

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Section: B Localization Of Single-particle Statessupporting

confidence: 90%

supporting

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…(see also the discussion in [32,44]). Finally, the stability of topological pumping in quasiperiodic potentials will be interesting as well (see, e.g., [69,70]).…”

mentioning

confidence: 99%

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Effect of disorder on topological charge pumping in the Rice-Mele model

et al. 2021

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Topology, Oxidation States, and Charge Transport in Ionic Conductors

2022

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Recent theoretical advances, based on a combination of concepts from Thouless' topological theory of adiabatic charge transport and a newly introduced gauge‐invariance principle for transport coefficients, have permitted to connect (and reconcile) Faraday's picture of ionic transport—whereby each atom carries a well‐defined integer charge—with a rigorous quantum description of the electronic charge‐density distribution, which hardly suggests its partition into well defined atomic contributions. In this paper, these progresses are reviewed; in particular, it is shown how, by relaxing some general topological conditions, charge may be transported in ionic conductors without any net ionic displacements. After reporting numerical experiments which corroborate these findings, a new connection between the topological picture and the well‐known Marcus–Hush theory of electron transfer is introduced in terms of the topology of adiabatic paths drawn by atomic trajectories. As a significant byproduct, the results reviewed here permit to classify different regimes of ionic transport according to the topological properties of the electronic structure of the conducting material. Finally, a few recent applications to energy materials and planetary sciences are reported.

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Perspective: Floquet engineering topological states from effective models towards realistic materials

Zhan,

Chen,

Ning

et al. 2024

Quantum Front

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With significant advances in classifying and cataloguing topological matter, the focus of topological physics has shifted towards quantum control, particularly the creation and manipulation of topological phases of matter. Floquet engineering, the concept of tailoring a system by periodic fields, offers a powerful tool to manipulate electronic properties of condensed systems, and even to create exotic non-equilibrium topological states that are impossibly present in equilibrium scenarios. In this perspective, we give a brief review of recent progress in theoretical investigations of Floquet engineering topological states from effective models towards realistic materials. We show that light irradiation can realize various desired topological states through the introduction of symmetry breaking, such as first- and higher-order Weyl fermions, quadrupole topological insulator with periodic driving and disorder, quantum anomalous Hall effects with a tunable Chern number, as well as beyond. Moreover, based on first-principles calculations and Floquet theorem, we show several realistic material candidates proposed as potential hosts for promising Floquet topological states, facilitating their verification in experiments. We believe that our perspective on Floquet engineering of topological states will advance further studies of rich exotic light-induced phenomena in condensed matter physics.

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Localization, Topology, and Quantized Transport in Disordered Floquet Systems

Cited by 34 publications

References 51 publications

Effect of disorder on topological charge pumping in the Rice-Mele model

Effect of disorder on topological charge pumping in the Rice-Mele model

Topology, Oxidation States, and Charge Transport in Ionic Conductors

Perspective: Floquet engineering topological states from effective models towards realistic materials

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