边膨胀晶格中的定位与平带
Localization and Flat Bands in Bond-Inflated Lattices
AI总结：
研究边膨胀晶格中平带的形成机制，揭示几何结构对有序和随机系统中局域化的调控作用。
摘要：
我们研究了通过重复边膨胀生成的正方形、蜂窝状和三角形母晶格中的定位和平带形成。将每条键替换为有限的tight-binding链产生了几类不同的平带：链诱导的平带位于插入链的本征能量处，双分边膨胀晶格中的对称保护零能量平带，以及足够长的链附近的近平带连接带。我们分析了这些机制在有序Lieb-L、超Honeycomb和超Triangular晶格中的响应，并检验了键失序、位点失序、随机磁通量和膨胀过程自身随机性的影响。尽管键和位点失序会拓宽大多数平带，零能量手性带和连接诱导的平带在某些扰动下仍保持稳健。值得注意的是，随机边膨胀图中仍存在显著的平带特征，即使没有平移对称性。特别是零能量态的数量被发现由匹配缺陷N-2ν(G)很好地估计，表明局部树状结构继续控制低能空缺。这些结果将边膨胀晶格识别为一类系统，其中几何结构本身能生成有序和随机设置中的稳健局域化。
英文摘要：
We study localization and flat-band formation in lattices generated by repeated bond inflation of square, honeycomb, and triangular parent lattices. Replacing each bond by a finite tight-binding chain produces several distinct classes of flat bands: chain-induced flat bands at the eigenenergies of the inserted chains, symmetry-protected zero-energy flat bands in bipartite bond-inflated lattices, and nearly flat junction bands near the spectral edges for sufficiently long chains. We analyze these mechanisms for ordered Lieb-$L$, super$^{L}$honeycomb, and super$^{L}$triangular lattices, and examine their response to bond disorder, site disorder, random magnetic flux, and randomness in the inflation process itself. While bond and site disorder broaden most flat bands, the zero-energy chiral band and the junction-induced flat bands remain robust under certain perturbations. Remarkably, substantial flat-band features also persist in randomly bond-inflated graphs, even in the absence of translational symmetry. In particular, the number of zero-energy states is found to be well estimated by the matching deficiency $N-2ν(G)$, indicating that local tree-like structure continues to control the low-energy nullity. These results identify bond-inflated lattices as a broad class of systems in which geometry alone generates robust localization in both ordered and random settings.
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