Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

Abrahams, Elihu; Anderson, Philip W.; Licciardello, D.C.; Ramakrishnan, T. V.

doi:10.1103/physrevlett.42.673

Cited by 5,977 publications

(4,219 citation statements)

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“…! , which is conventionally referred to as single parameter scaling [12]. Our calculations corroborate the log-normal statistics, single parameter scaling, and self-averaging properties of P[ln ! ]…”

supporting

confidence: 75%

Anderson Localization of Thermal Phonons Leads to a Thermal Conductivity Maximum

Mendoza

Chen

2016

Nano Lett.

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Our elastic model of ErAs disordered GaAs/AlAs superlattices exhibits a local thermal conductivity maximum as a function of length due to exponentially suppressed Anderson-localized phonons. By analyzing the sample-to-sample fluctuations in the dimensionless conductance, !, the transition from diffusive to localized transport is identified as the crossover from the multi-channel to single-channel transport regime ! ≈ 1. Single parameter scaling is shown to hold in this crossover regime through the universality of the probability distribution of ! that is independent of system size and disorder strength.

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supporting

confidence: 75%

Anderson Localization of Thermal Phonons Leads to a Thermal Conductivity Maximum

Mendoza

Chen

2016

Nano Lett.

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“…For normal diffusion it is well known that quantum corrections (interference) may modify substantially the semiclassical results. For instance in a 2d disordered system [22,13], a simple calculation of the one-loop perturbative quantum correction shows that the diffusion constant is smaller than in the classical case, β(g) becomes negative and the semiclassical metal-insulator transition is destroyed by quantum corrections.…”

Section: Stability Of the Semiclassical Predictionsmentioning

confidence: 99%

“…In this paper we aim to address these questions by using ideas and techniques originally developed in the theory of disordered systems [12] such as the one--parameter scaling theory [13].…”

Section: Introductionmentioning

confidence: 99%

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Anderson Localization in Quantum Chaos: Scaling and Universality

García-García

Wang

2007

Acta Phys. Pol. A

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The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.

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“…Another seminal work along this direction is the scaling theory of localization [5], which indicates that all electronic states are exponentially localized in low-dimensional noninteracting systems even for infinitesimal disorder and become localized in three-dimensional (3D) systems with sufficiently large disorder strength. In fact, Anderson localization is a universal wave phenomenon and has been observed experimentally in a wide variety of systems, including light [6][7][8][9], microwaves [10], acoustic waves [11,12], and matter waves [13][14][15][16][17].…”

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Universal scheme to generate metal–insulator transition in disordered systems

Guo

Xiong

Xie

et al. 2013

J. Phys.: Condens. Matter

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We propose a scheme to generate metal-insulator transition in random binary layer (RBL) model, which is constructed by randomly assigning two types of layers. Based on a tight-binding Hamiltonian, the localization length is calculated for a variety of RBLs with different cross section geometries by using the transfer-matrix method. Both analytical and numerical results show that a band of extended states could appear in the RBLs and the systems behave as metals by properly tuning the model parameters, due to the existence of a completely ordered subband, leading to a metal-insulator transition in parameter space. Furthermore, the extended states are irrespective of the diagonal and off-diagonal disorder strengths. Our results can be generalized to two-and three-dimensional disordered systems with arbitrary layer structures, and may be realized in Bose-Einstein condensates.

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Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

Cited by 5,977 publications

References 8 publications

Anderson Localization of Thermal Phonons Leads to a Thermal Conductivity Maximum

Anderson Localization of Thermal Phonons Leads to a Thermal Conductivity Maximum

Anderson Localization in Quantum Chaos: Scaling and Universality

Universal scheme to generate metal–insulator transition in disordered systems

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