二维以下类分形晶格中手征边缘模的鲁棒性：一个实例研究
Robustness of chiral edge modes in fractal-like-lattices below two dimensions: A case study
摘要：
二维量子霍尔系统最显著的特征之一是手征边缘模。它们的存在是体边界对应的结果，它们的稳定性保证了横向电导的量子化。在这项工作中，我们研究了两个微观模型，Hofstadter晶格模型和扩展版本的Halfman的陈氏绝缘体。这两种模型都在二维空间中拥有量子霍尔相位。我们将它们转移到一个和两个之间的维度分形的晶格实现，并研究其边缘状态的存在性和鲁棒性。我们的主要观察结果是，相反，他们的二维对应，有没有在分形边缘模式的普遍行为。相反，它们的存在和稳定性严重依赖于模型的细节和分形的晶格实现。
英文摘要：
One of the most prominent characteristics of two-dimensional Quantum Hall systems are chiral edge modes. Their existence is a consequence of the bulk-boundary correspondence and their stability guarantees the quantization of the transverse conductance. In this work, we study two microscopic models, the Hofstadter lattice model and an extended version of Haldane's Chern insulator. Both models host Quantum Hall phases in two dimensions. We transfer them to lattice implementations of fractals with a dimension between one and two and study the existence and robustness of their edge states. Our main observation is that, contrary to their two-dimensional counterpart, there is no universal behavior of the edge modes in fractals. Instead, their presence and stability critically depends on details of the models and the lattice realization of the fractal.
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