A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system

Elizabeth J. Dresselhaus, Alexander Avdoshkin, Zhetao Jia, Matteo Secli, Boubacar Kante, Joel E. Moore
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Abstract

Emerging experimental platforms use amorphousness, a constrained form of disorder, to tailor meta-material properties. We study localization under this type of disorder in a class of $2D$ models generalizing recent experiments on photonic systems. We explore two kinds of localization that emerge in these models: Anderson localization by disorder, and the existence of compact, macroscopically degenerate localized states as in many crystalline flat bands. We find localization properties to depend on the symmetry class within a family of amorphized kagom\'{e} tight-binding models, set by a tunable synthetic magnetic field. The flat-band-like degeneracy innate to kagom\'{e} lattices survives under amorphousness without on-site disorder. This phenomenon arises from the cooperation between the structure of the compact localized states and the geometry of the amorphous graph. For particular values of the field, such states emerge in the amorphous system that were not present on the kagom\'{e} lattice in the same field. For generic states, the standard paradigm of Anderson localization is found to apply as expected for systems with particle-hole symmetry (class D), while a similar interpretation does not extend to our results in the general unitary case (class A). The structure of amorphous graphs, which arise in current photonics experiments, allows exact statements about flat-band-like states, including such states that only exist in amorphous systems, and demonstrates how the qualitative behavior of a disordered system can be tuned at fixed graph topology.
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两种局域化的故事:光子学启发的非晶系统中平带和安德森局域化的共存
新出现的实验平台利用无定形这种受约束的无序形式来定制元材料特性。我们在一类 2D$ 模型中研究了这种无序状态下的定位,该模型概括了最近关于光子系统的实验。我们探讨了这些模型中出现的两种局域化现象:我们发现局域化特性取决于一系列非晶化 kagom\'{e} 紧束缚模型中的对称类,并由可调合成磁场设定。在没有现场无序的非晶态条件下,卡格姆({e})晶格与生俱来的平带变性仍然存在。这种现象源于紧凑局部态的结构与非晶态图形几何之间的合作。在特定的场值下,非晶态系统中会出现在同一场中的卡戈姆(kagom\'{e})晶格上不存在的状态。对于一般态,我们发现安德森局域化的标准范式如预期般适用于具有粒子-空穴对称性(D类)的系统,而类似的解释并没有延伸到我们在一般单元情况(A类)下的结果。当前光子学实验中出现的非晶态图的结构允许对平带样态(包括只存在于非晶态系统中的此类态)做出精确陈述,并证明了在固定的图拓扑结构下如何调整无序系统的定性行为。
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