$D$维装饰金刚石和烧绿石晶格中的平带解：简化为分子问题
Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem
摘要：
平带模型从基本方面和材料实现方面都特别感兴趣。除了典型的例子，如Lieb格和线图，各种紧束缚模型被发现具有平坦的带。然而，色散关系的解析处理是有限的，特别是当有多个不同能量的平坦带。在本文中，我们提出了如何确定在一般尺寸$D \geq 2$紧束缚模型的装饰金刚石和烧绿石晶格的平带能量和波函数。对于二维和三维，这种晶格结构与各种有机和无机材料有关，因此我们的方法将有助于分析这些材料的能带结构。
英文摘要：
Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D \geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.
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