Absence of Anderson localization in certain random lattices

Abstract

We report on the transition between an Anderson localized regime and a conductive regime in a 1D scattering system with correlated disorder. We show experimentally that when long-range correlations are introduced, in the form of a power-law spectral density with power larger than 2, the localization length becomes much bigger than the sample size and the transmission peaks typical of an Anderson localized system merge into a pass band. As other forms of long-range correlations are known to have the opposite effect, i.e. to enhance localization, our results show that care is needed when discussing the effects of correlations, as different kinds of long-range correlations can give rise to very different behavior.Wave transport in multiply scattering media is a complex phenomenon. If the scattering is weak enough the interference effects can be neglected and the wave transport can be described in terms of a diffusion equation [1,2]. As the scattering strength increases interference effects reduce the diffusion coefficient, an effect known as weak localization [3]. Once the scattering strength overcomes a certain threshold the diffusion coefficient goes to zero, the system becomes Anderson localized, and no macroscopic transport is possible [4,5].Anderson localization is quintessentially an interference effect that can occur for any kind of wave and thus, although it was originally proposed for electrons [6], it has been observed for mechanical waves [7,8], BoseEinstein condensates [9] and electromagnetic waves [10]. It is well understood that the dimensionality of the system plays a major role when it comes to Anderson localization. For 3D systems, when the disorder increases, there is a phase transition between a conductive phase, where all the eigenmodes are extended, and an insulating phase, where the eigenmodes become exponentially localized in regions of size ∼ ξ (the localization length) [11].For 1D systems, the scaling theory of localization predicts that no such transition occurs, and the localization length ξ is always finite [12]. Despite its simplicity, the scaling theory of localization relies on several hypotheses, one of which is that, if one could switch off interference, the transport would be properly described by a diffusion equation, i.e. that the scattering potential can be described as white noise. Once correlations are introduced in the scattering potential the picture becomes much less clear, and it is possible to have frequency bands where the system is localized co-existing with frequency bands where all the eigenmodes are extended [13,14], discrete sets of extended modes in an otherwise localized spectrum [15], enhanced localization [16], or even fully extended Bloch modes in random-like potentials [17].In this article we study experimentally the case where the scattering potential is described by colored noise instead of white noise, i.e. when the power spectrum of the random potential is not flat. We show that, as the disorder becomes more colored, the localization length becomes longer,...

Anderson localization and delocalization of massless two-dimensional Dirac electrons in random one-dimensional scalar and vector potentials

“…[1][2][3][4][5][6][7][8][9][10][11] Though the basic origin of Anderson localization, which is the interference of wave components multiply scattered by randomly placed scattering centers, is wellunderstood, new and surprising aspects of the phenomenon have been discovered continually. [12][13][14][15][16][17][18][19][20] Differences in the types of wave equations, the material properties and the nature of disorder all affect Anderson localization strongly and can cause conceptually new phenomena to occur. Recently, much interest has been paid to the localization arising in new kinds of condensed-matter materials and artificially fabricated metamaterials.…”

Wave Propagation and Localization in a Complex Random Potential with Power-law Correlations: A Numerical Study

“…Email address: nguyenbaphi@muce.edu.vn https//doi.org / 10.25073/2588-1124/vnumap.4498 During the recent few decades, the influence of spatially correlated disorder on the wave propagation and localization properties has been attracted much attention from theoretical as well as experimental researchers [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. It has been demonstrated that some special kinds of short-range correlated disorder can produce delocalized eigenstates even in one dimension [7,8].…”

Anderson localization of two-dimensional massless pseudospin-1 Dirac particles in a correlated random one-dimensional scalar potential

“…Recently, there has been much interest in the roles of short-range and long-range disorder correlations in localization phenomena [33,[44][45][46]. In this paper, we extend this approach to the localization in Dirac systems.…”