Localization and transport in a strongly driven Anderson insulator

Localization and transport in a strongly driven Anderson insulator We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focusing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We show that (i) resonances in this model correspond to adiabatic Landau-Zener (LZ) transitions that occur due to level crossings between lattice sites over the course of dynamics; (ii) the proliferation of these resonances leads to dynamics that appear diffusive over a single drive cycle, but the system always remains localized; (iii) actual charge transport occurs over many drive cycles due to slow dephasing between these LZ orbits and is logarithmic in time, with a crucial role being played by far-off Mott-like resonances; and (iv) applying a spatially varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We derive the conditions for the strong-driving regime, determining the parametric dependencies of the size of Floquet eigenstates, and time scales associated with the dynamics, and corroborate the findings using both numerical scaling collapses and analytical arguments. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Localization and transport in a strongly driven Anderson insulator

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Localization and transport in a strongly driven Anderson insulator

Abstract

We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focusing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We show that (i) resonances in this model correspond to adiabatic Landau-Zener (LZ) transitions that occur due to level crossings between lattice sites over the course of dynamics; (ii) the proliferation of these resonances leads to dynamics that appear diffusive over a single drive cycle, but the system always remains localized; (iii) actual charge transport occurs over many drive cycles due to slow dephasing between these LZ orbits and is logarithmic in time, with a crucial role being played by far-off Mott-like resonances; and (iv) applying a spatially varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We derive the conditions for the strong-driving regime, determining the parametric dependencies of the size of Floquet eigenstates, and time scales associated with the dynamics, and corroborate the findings using both numerical scaling collapses and analytical arguments.
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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.014201
Publisher site
See Article on Publisher Site

Abstract

We study localization and charge dynamics in a monochromatically driven one-dimensional Anderson insulator focusing on the low-frequency, strong-driving regime. We study this problem using a mapping of the Floquet Hamiltonian to a hopping problem with correlated disorder in one higher harmonic-space dimension. We show that (i) resonances in this model correspond to adiabatic Landau-Zener (LZ) transitions that occur due to level crossings between lattice sites over the course of dynamics; (ii) the proliferation of these resonances leads to dynamics that appear diffusive over a single drive cycle, but the system always remains localized; (iii) actual charge transport occurs over many drive cycles due to slow dephasing between these LZ orbits and is logarithmic in time, with a crucial role being played by far-off Mott-like resonances; and (iv) applying a spatially varying random phase to the drive tends to decrease localization, suggestive of weak-localization physics. We derive the conditions for the strong-driving regime, determining the parametric dependencies of the size of Floquet eigenstates, and time scales associated with the dynamics, and corroborate the findings using both numerical scaling collapses and analytical arguments.

Journal

Physical Review BAmerican Physical Society (APS)

Published: Jul 10, 2017

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