Wave transport in one-dimensional disordered systems with finite-width potential steps

Díaz, Marlos; Mello, Pier A.; Yépez, M.; Tomsovic, Steven

doi:10.1209/0295-5075/97/54002

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…Such a peculiarity of the lowest resonance ϕ = π occurring in the model has been predicted in Ref. [11].…”

Section: Non-resonant Localization Lengthsupporting

confidence: 58%

“…Recently, the detailed study of the transmittance and reflectance in the vicinity of the lowest resonance has been performed in Ref. [11]. The authors where able to develop the theory and obtain the analytical results for a quite simple model for which the potential consists of barriers and wells of a fixed thickness d, however, with a weak variation of their heights and depths.…”

Section: Introductionmentioning

confidence: 99%

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Resonant enhancement of Anderson localization: Analytical approach

2013

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We study localization properties of the eigenstates and wave transport in a one-dimensional system consisting of a set of barriers and/or wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between the wells and/or barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.

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“…Such a peculiarity of the lowest resonance ϕ = π occurring in the model has been predicted in Ref. [11].…”

Section: Non-resonant Localization Lengthsupporting

confidence: 58%

Section: Introductionmentioning

confidence: 99%

Resonant enhancement of Anderson localization: Analytical approach

2013

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“…In the present paper we build on previous work [16] to study the simplest extension of the problems contemplated in Refs. [7,8]: the problem of wave transport in 1D disordered systems, in which the various scatterers have a finite size.…”

Section: Introductionmentioning

confidence: 99%

Wave transport in one-dimensional disordered systems with finite-size scatterers

et al. 2015

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We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are n barriers and wells with statistically independent intensities and with a spatial extension l c which may contain an arbitrary number δ/2π of wavelengths, where δ = kl c .We analyze the average Landauer resistance and transmission coefficient of the chain as a function of n and the phase parameter δ. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with n, ii) a regime, to be called II, for δ in the vicinity of π, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for δ very close to π, the formation of a band gap, which becomes ever more conspicuous as n increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with n and δ. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.

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“…Anderson localization in disordered 1D systems has been extensively investigated. In particular, the model of successive 1D barriers (or wells) of fixed thickness ℓ and random heights is known to lead to resonant localization whenever the accumulated phase in the distance ℓ is an integer multiple of π [14][15][16]. We show below that the segmented wire exhibits resonant localization when the segment lengths are narrowly distributed around a given value ℓ 0 .…”

Section: Introductionmentioning

confidence: 79%

Resonant Anderson localization in segmented wires

Estarellas

Serra

2016

Phys. Rev. E

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We discuss a model of random segmented wire, with linear segments of two-dimensional wires joined by circular bends. The joining vertices act as scatterers on the propagating electron waves. The model leads to resonant Anderson localization when all segments are of similar length. The resonant behavior is present with one and also with several propagating modes. The probability distributions evolve from diffusive to localized regimes when increasing the number of segments in a similar way for long and short localization lengths. As a function of the energy, a finite segmented wire typically evolves from localized to diffusive to ballistic behavior in each conductance plateau.

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Wave transport in one-dimensional disordered systems with finite-width potential steps

Cited by 4 publications

References 13 publications

Resonant enhancement of Anderson localization: Analytical approach

Resonant enhancement of Anderson localization: Analytical approach

Wave transport in one-dimensional disordered systems with finite-size scatterers

Resonant Anderson localization in segmented wires

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