论文标题
平带发生器
Flatband generators
论文作者
论文摘要
平板（FBS）是翻译不变紧密结合网络的单粒子光谱中的无分散能带。 FB由于破坏性干扰而发生，导致宏观退化的本征态居住在有限数量的单位细胞中，这些单元被称为紧凑型局部状态（CLS）。这种宏观的退化性通常对扰动高度敏感，因此即使轻微的扰动也可以提高堕落性并导致各种有趣的物理现象。 在本论文中，我们开发了一种方法来识别和构建在1d，2d Hermitian和1d Non-Hermitian系统中的FB Hamiltonians。首先，我们通过其CLS属性引入了FB晶格的系统分类，并提出了一种计划，以生成具有给定CLS属性的FB的紧密结合的汉密尔顿人--- FB发电机。将此FB发电机应用于1D系统，我们确定了具有任意数量的带和CLS尺寸的1D晶格的所有可能的FB哈密顿量。扩展了1D方法，我们为2D FB Hamiltonians建立了一个FB发电机，其CLS在$ 2 \ times2 $ plaquette中最多占据了四个单位单元。我们在非炎热制度中采用了这种方法，我们实现了一个FB发电机，用于使用两个频段的一维非晶格。最终，我们将方法应用于提出一个紧密结合模型，该模型解释了微波光子晶体的光谱特性。 我们在本文中的结果和方法进一步了解了我们对FB晶格及其CLS的性质的理解，为在实验中设计FB晶格提供了更大的灵活性，并为未来的研究开放了新的途径。
Flatbands (FBs) are dispersionless energy bands in the single-particle spectrum of a translational invariant tight-binding network. The FBs occur due to destructive interference, resulting in macroscopically degenerate eigenstates living in a finite number of unit cells, which are called compact localized states (CLSs). Such macroscopic degeneracy is in general highly sensitive to perturbations, such that even slight perturbation lifts the degeneracy and leads to various interesting physical phenomena. In this thesis, we develop an approach to identify and construct FB Hamiltonians in 1D, 2D Hermitian, and 1D non-Hermitian systems. First, we introduce a systematic classification of FB lattices by their CLS properties, and propose a scheme to generate tight-binding Hamiltonians having FBs with given CLS properties---a FB generator. Applying this FB generator to a 1D system, we identify all possible FB Hamiltonians of 1D lattices with arbitrary numbers of bands and CLS sizes. Extending the 1D approach, we establish a FB generator for 2D FB Hamiltonians that have CLSs occupying a maximum of four unit cells in a $2\times2$ plaquette. Employing this approach in the non-Hermitiaon regime, we realize a FB generator for a 1D non-Hermitian lattice with two bands. Ultimately, we apply our methods to propose a tight-binding model that explains the spectral properties of a microwave photonic crystal. Our results and methods in this thesis further our understanding of the properties of FB lattices and their CLSs, provide more flexibility to design FB lattices in experiments, and open new avenues for future research.
