Anomalous transport in low-dimensional systems with correlated disorder

Izrailev, F. M.; Makarov, N. M.

doi:10.1088/0305-4470/38/49/010

Cited by 45 publications

(69 citation statements)

References 73 publications

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“…This phenomenon, known as the mobility edge, is discussed, for instance, in Ref. 27. These findings have revised a previously accepted belief that any randomness ͑no matter how weak the randomness is͒ in 1D structures results in Anderson localization.…”

Section: Introductionsupporting

confidence: 53%

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

et al. 2007

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A fundamental property of wave propagation is Anderson localization, which affects the transfer of information, energy, mass, and charge in disordered media. This localization can manifest itself via, e.g., the metal-insulator transition. We exactly map the behavior of a quantum particle moving in a potential with correlated disorder to the sub-terahertz wave propagation in either Josephson chains or superconducting multilayers. When the Josephson junction parameters vary randomly, the sub-THz electromagnetic waves cannot propagate through these Josephson structures due to localization. For parameter variations with long-range correlations, we predict sharp transitions from transparent to reflective frequency regions for Josephson plasma waves. With appropriate choices of the correlation function, frequency windows with targeted or designed transparencies for THz or sub-THz electromagnetic waves could be achieved. This could be useful for tailoring the electromagnetic wave spectrum of Josephson arrays within the THz frequency range, which is important for applications in physics, astronomy, chemistry, biology, and medicine.

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Section: Introductionsupporting

confidence: 53%

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

et al. 2007

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“…[171] (see Ref. [172] for review). Special attention is deserved also for disordered systems with chiral symmetries [173].…”

Section: Resultsmentioning

confidence: 99%

“…Right: The same data plotted as a function of L/ξ(W ), Eq. (172). Note the logarithmic scale on the horizontal axis.…”

Section: Scaling Of the Smallest Lyapunov Exponentmentioning

confidence: 99%

Numerical analysis of the Anderson localization

Markoš¹

2006

Acta Physica Slovaca. Reviews and Tutorials

138

242

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The aim of this paper is to demonstrate, by simple numerical simulations, the main transport properties of disordered electron systems. These systems undergo the metal insulator transition when either Fermi energy crosses the mobility edge or the strength of the disorder increases over critical value. We study how disorder affects the energy spectrum and spatial distribution of electronic eigenstates in the diffusive and insulating regime, as well as in the critical region of the metal-insulator transition. Then, we introduce the transfer matrix and conductance, and we discuss how the quantum character of the electron propagation influences the transport properties of disordered samples. In the weakly disordered systems, the weak localization and anti-localization as well as the universal conductance fluctuation are numerically simulated and discussed. The localization in the one dimensional system is described and interpreted as a purely quantum effect. Statistical properties of the conductance in the critical and localized regimes are demonstrated. Special attention is given to the numerical study of the transport properties of the critical regime and to the numerical verification of the single parameter scaling theory of localization. Numerical data for the critical exponent in the orthogonal models in dimension 2 < d ≤ 5 are compared with theoretical predictions. We argue that the discrepancy between the theory and numerical data is due to the absence of the self-averaging of transmission quantities. This complicates the analytical analysis of the disordered systems. Finally, theoretical methods of description of weakly disordered systems are explained and their possible generalization to the localized regime is discussed. Since we concentrate on the one-electron propagation at zero temperature, no effects of electronelectron interaction and incoherent scattering are discussed in the paper.

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“…Among the setups studied in this direction one can mention the tight-binding Anderson model with two-coupled chains 19 , the models with stratified or layered disorder 20,21 , and multi-mode waveguides with long-range correlations in surface profiles 20,22 .…”

Section: Introductionmentioning

confidence: 99%

Transport through quasi-one-dimensional wires with correlated disorder

Herrera-González

2014

Phys. Rev. E

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We study transport properties of bulk-disordered quasi-one-dimensional (Q1D) wires paying main attention to the role of long-range correlations embedded into the disorder. First, we show that for stratified disorder for which the disorder is the same for all individual chains forming the Q1D wire, the transport properties can be analytically described provided the disorder is weak. When the disorder in every chain is not the same, however, has the same binary correlator, the general theory is absent. Thus, we consider the case when only one channel is open and all others are closed. For this situation we suggest a semi-analytical approach which is quite effective for the description of the total transmission coefficient. Our numerical data confirm the validity of our approach. Such Q1D disordered structures with anomalous transport properties can be the subject of an experimental study.

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Anomalous transport in low-dimensional systems with correlated disorder

Cited by 45 publications

References 73 publications

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

Numerical analysis of the Anderson localization

Transport through quasi-one-dimensional wires with correlated disorder

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