标题： 二维量子霍尔问题与一维准晶之间的缺失链路 显示英文标题

标题： Missing link between the 2D Quantum Hall problem and 1D quasicrystals

摘要： 本文讨论了两类重要材料之间的联系，即准晶和拓扑绝缘体（以量子霍尔问题为例）。 有人指出，准晶从二维量子霍尔模型“继承”了拓扑性质。 我们通过引入Fibonacci-Hall模型作为一维准晶与磁场问题之间的桥梁，明确展示了这一点。 我们在这里展示如何计算准晶周期逼近中能带的Chern数以及间隙标签。 这些Chern数被视为由准晶在二维空间中几何缠绕引起的通量参数$\phi^S$的结果。 我们证明了该模型相空间中存在Lifshitz过渡线。 这些过渡线由Chern数的变化和边缘态的消失来标记。 所提出的外推方法可以推广到更高维度的二维和三维准晶中，在那里可以计算高阶Chern数，并与实验可测量的输运量相关联。 显示英文摘要

摘要： This paper discusses a connection between two important classes of materials, namely quasicrystals and topological insulators as exemplified by the Quantum Hall problem. It has been remarked that the quasicrystal ``inherits" topological properties from the 2D Quantum Hall model. We show this explicitly by introducing the Fibonacci-Hall model as a link between a 1D quasicrystal and the magnetic problems. We show here how Chern numbers for bands in periodic approximants of quasicrystals can be computed, along with gap labels. The Chern numbers are thus seen as a consequence of a flux parameter $\phi^S$ induced by the geometry of winding in 2D space of the quasicrystal. We show the existence of lines of Lifshitz transitions in the phase space of the model. These are marked by change of Chern number and disappearance of edge states. The proposed extrapolation method can be generalized to higher dimensional 2D and 3D quasicrystals, where higher order Chern numbers could be computed, and related to experimentally measurable transport quantities.