A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $δ$ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes. We use the Levy laws to investigate the statistical properties of the eigenstates. We found the possibility of an Anderson transition even in 1D meaning that the disorder can also provide constructive quantum interferences. We found at this transition that the conductance probability distribution has a system-size independent shape with large fluctuations in good agreement with previous works. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results for the conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models.
Although topological Anderson insulator has been predicted in 2009, the lasting investigations of this disorder established nontrivial state results in only two experimental observations in cold atoms [Science, {\bf 362 },929 (2018)] and in photonic crystals [Nature, {\bf 560}, 461 (2018)] recently. In this paper, we study the topological Anderson transition in electric circuits. By arranging capacitor and inductor network, we construct a disordered Haldane model. Specially, the disorder is introduced by the grounding inductors with random inductance. Based on non-commutative geometry method a…
Skin-Anderson localization transitions in disordered hybrid-nonreciprocal systems
Tianjin University（天津大学）；Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University（新加坡国立大学与天津大学联合学院，天津大学国际校区）
An interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of the Anderson transitions driven by non-Hermitian disorders for three dimensional (3D) Anderson model and 3D U(1) model, which belong to 3D class ${\rm AI}^{\dagger}$ and 3D class A in the classification of non-Hermitian systems, respectively. Based on level statistics and finite-size scaling analysis, the critical exponent for length scale is estimated as $ν=0.99\pm 0.05$ for class ${\rm AI}^{\dagger}$, and $ν=1.09\pm 0.05 $ for class A, bot…
We investigate the effect of spatially correlated disorder on the Anderson transition of phonons in three dimensions using a Greens function based approach, namely, the typical medium dynamical cluster approximation (TMDCA), in mass-disordered systems. We numerically demonstrate that correlated disorder with pairwise correlations mitigates the localization of the vibrational modes. A correlation driven localization-delocalization transition can emerge in a three-dimensional disordered system with an increase in the strength of correlations.
Localization due to disorder has been one of the most intriguing theoretical concepts evolved in condensed matter. Here, we expand the theory of localization by considering two types of disorder at the same time, namely the original Anderson's disorder and the structural defect disorder, which has been suggested to be a key component in recently discovered two-dimensional amorphous materials. While increasing the degree of both disorders could induce localization of wavefunction in real space, we find that a small degree of structural defect disorder can significantly enhance the localization.…
Different disorders lead to various localization and topological phenomena in condensed matter and artificial systems. Here we study the topological and localization properties in one-dimensional Su-Schrieffer-Heeger model with spatially correlated random binary disorders. It is found that random binary disorders can induce the topological Anderson insulating phase from the trivial insulator in various parameter regions. The topological Anderson insulators are characterized by the disorder-averaged winding number and localized bulk states revealed by the inverse participation ratio in both rea…
Interplay of Flat-band and Anderson localizations in disordered moire superlattices
Guangxi University（广西大学）；Anqing Normal University（安庆师范大学）；Nankai University（南开大学）；Nottingham Trent University（诺丁汉特伦特大学）；East China Normal University（华东师范大学）
Anderson localization is a striking phenomenon wherein transport of light is arrested due to the formation of disorder-induced resonances. Hitherto, Anderson localization has been demonstrated separately in two limits of disorder, namely, amorphous disorder and nearly-periodic disorder. However, transport properties in the two limits are yet unstudied, particularly in a statistically consistent manner. Here, we experimentally measure light transport across two-dimensional open mesoscopic structures, wherein the disorder systematically ranges from nearly-periodic to amorphous. We measure the ge…
We explore the interplay of disorder and topological phenomena in honeycomb lattices of atoms coupled by the electromagnetic field. On the one hand, disorder can trigger transitions between distinct topological phases and drive the lattice into the topological Anderson insulator state. On the other hand, the nontrivial topology of the photonic band structure suppresses Anderson localization of modes that disorder introduces inside the band gap of the ideal lattice. Furthermore, we discover that disorder can both open a topological pseudogap in the spectrum of an otherwise topologically trivial…
It is well known that Anderson transition is a disorder-induced metal-insulator transition.Contrary to this conventional wisdom, some investigations have shown that disorders could destroy the phase coherence of localized modes in flatbands, making the localized states melt into extended states. This phenomenon is called the inverse Anderson transition. While, to date, the experimental observation of inverse Anderson transitions is still lacking. In this work, we report the implementation of inverse Anderson transitions based on Aharonov-Bohm topolectrical circuits. Different types of disorder…
How large is large? Estimating the critical disorder for the Anderson model
完全本地化的$d$维安德森模型与均匀分布的随机电位提供的无序强度$λ>λ_{And}$，其中$λ_{\text{And}}$满足$λ_{\text{And}}=μ_d e \ln λ_{\text{And}}$与$μ_d$的自避免行走连接常数的晶格$\mathbb{Z}^d$。值得注意的是，$λ_{\text{And}}$正是Anderson在1958年提出的大无序阈值。
