At the edge of mobility

Sanchez-Palencia, Laurent

doi:10.1038/nphys3379

Cited by 9 publications

(5 citation statements)

References 17 publications

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“…Anderson localization [1][2][3][4], i.e., the inhibition of wave diffusion in disordered media via destructive interference of multiply scattered waves is a universal phenomenon observed in a variety of classical and quantum systems with experimental demonstrations reported in different areas of physics ranging from photonics [5][6][7], acoustics [8], matter waves [9][10][11][12][13], and quantum matter [14], to mention a few. The kind of disorder and the spatial dimension of the system are pivotal to Anderson localization since they strongly affect the appearance of localization transitions and the existence of mobility edges [2][3][4][15][16][17], i.e., critical energies separating extended and localized states in the spectrum. In low-dimensional systems with uncorrelated disorder, localization transitions and mobility edges are prevented [4,15].…”

Section: Introductionmentioning

confidence: 99%

Absence of mobility edges in mosaic Wannier-Stark lattices

Longhi

2023

Phys. Rev. B

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Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of certain one-dimensional models with quasiperiodic disorder. Recently, some works claimed rather unexpectedly that mobility edges can exist even in disorder-free one-dimensional models, suggesting as an example the so-called mosaic Wannier-Stark lattice where a Stark potential is applied on every M site of the lattice. Here, we present an exact spectral analysis of the mosaic Wannier-Stark Hamiltonian and prove that, strictly speaking, there are not mobility edges, separating extended and localized states. Specifically, we prove that the energy spectrum is almost pure point with all the wave functions displaying a higher than exponential localization with the exception of (M − 1)-isolated extended states at energies around which a countably infinite number of localized states with a diverging localization size condense.

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Section: Introductionmentioning

confidence: 99%

Absence of mobility edges in mosaic Wannier-Stark lattices

Longhi

2023

Phys. Rev. B

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“…Various AA-like models hosting mobility edges have been discussed, such as slow-varying potentials, [17] off-diagonal disorder, [18,19] long-range hoppings, [20] and other generalized quasiperiodic potentials. [21] Liu et al [22] numerically found the simultaneous occurrence of the localization transition and the 𝒫𝒯 -symmetry breaking. Zeng et al [23] demonstrated the correspondence between the winding number and the localization transition, and numerically uncovered mobility edges in the spectrum with or without the 𝒫𝒯 -symmetry.…”

Section: Introductionmentioning

confidence: 99%

Mobility edges generated by the non-Hermitian flatband lattice

Liu¹,

Cheng²

2023

Chinese Phys. B

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We study the cross-stitch flatband lattice subject to the quasiperiodic complex potential exp(ix). We first identify the exact expression of quadratic mobility edges through analytical calculation, then verify theoretical predictions by numerically calculating the inverse participation ratio. Further more, we study the relationship between the real-complex spectrum transition and the localization-delocalization transition, and demonstrate that mobility edges in this non-Hermitian model not only separate localized from extended states but also indicate the coexistence of complex and real spectrum.

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“…Anderson localization [7] has now been demonstrated in a variety of experiments, using photonic systems [8][9][10], acoustic waves [11], ultracold atoms [12][13][14][15][16], and quantum wires [17]. However, a direct experimental observation of MEs remains a challenge [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Anomalous mobility edges in one-dimensional quasiperiodic models

et al. 2022

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Mobility edges, separating localized from extended states, are known to arise in the single-particle energy spectrum of disordered systems in dimension strictly higher than two and certain quasiperiodic models in one dimension. Here we unveil a different class of mobility edges, dubbed anomalous mobility edges, that separate energy intervals where all states are localized from energy intervals where all states are critical in diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable quasi-periodic diagonal model and analytically demonstrate the existence of anomalous mobility edges. Moreover, numerical multifractal analysis of the corresponding wave functions confirms the emergence of a finite energy interval where all states are critical. We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and show numerical evidence of anomalous mobility edges. We finally discuss possible experimental realizations of quasi-periodic models hosting anomalous mobility edges. These results shed new light on the localization and critical properties of low-dimensional systems with aperiodic order.

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At the edge of mobility

Cited by 9 publications

References 17 publications

Absence of mobility edges in mosaic Wannier-Stark lattices

Absence of mobility edges in mosaic Wannier-Stark lattices

Mobility edges generated by the non-Hermitian flatband lattice

Anomalous mobility edges in one-dimensional quasiperiodic models

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