修正 Haldane-Dice 模型中的奇异平带
Singular flat bands in the modified Haldane-Dice model
AI总结：
本文研究受单轴应变和 Haldane 型次近邻作用调控的修正 Haldane-Dice 模型，通过拓扑相图、紧致局域态与 Hilbert–Schmidt 量子距离证明中心平带在所有接触点均奇异，并给出不可收缩环态。
摘要：
平带可根据其 Bloch 波函数在动量空间中能带交叉点附近的行为划分为奇异平带和非奇异平带。我们分析了 Dice 模型中的平带，该平带可通过锯齿方向的单轴应变以及 Haldane 型次近邻相互作用进行调控，并推导了修正 Haldane-Dice 模型的拓扑相图，以获得中心带的所有能带闭合点。当中心带为平带时，我们确定了其紧致局域态，并借助 Hilbert–Schmidt 量子距离对其在所有能带接触点处的行为进行分类。我们发现，对于所有能带接触点（拓扑相变），该平带均保持奇异性，并具有最大量子距离；同时给出了由此在实空间环面上产生的不可收缩环态的表达式。
英文摘要：
Flat bands can be divided into singular and non-singular ones according to the behavior of their Bloch wave function around band-crossing points in momentum space. We analyze the flat band in the Dice model, which can be tuned by a uniaxial strain in the zigzag direction and a Haldane-type next-nearest neighbor interaction, and derive the topological phase diagram of the modified Haldane-Dice model to obtain all band-gap closings with the central band. When the central band is flat, we determine its compact localized state and classify its behavior at all band-touching points by means of the Hilbert-Schmidt quantum distance. We find that the flat band remains singular for all band-touching points (topological phase transitions) with a maximal quantum distance and give expressions for the resulting non-contractible loop states on the real-space torus.
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