AI 中文总结
研究具有传统二维晶格平移对称性的有限能带紧束缚模型中的理想能带，通过解析构造陈数\(|\mathrm{Ch}| = 1\)的孤立陈理想能带，证明有限范围跳跃模型中不存在非零陈数的孤立陈理想能带，并推广到总陈数为零的威尔逊回路理想能带。
AI 中文摘要
当一个能带的狄利克雷泛函达到拓扑下界时，它被称为理想能带。我们研究具有传统二维晶格平移对称性的有限能带紧束缚模型中的理想能带，允许能带具有非平坦色散。首先，我们在具有指数衰减跳跃的有限能带模型中，对陈数\(|\mathrm{Ch}| = 1\)的孤立陈理想能带进行了解析构造。此构造仅在至少两个轨道具有不同嵌入位置（模晶格向量）时适用，补充了先前已知的\(|\mathrm{Ch}|>1\)的构造。然后表明，在具有有限范围跳跃的有限能带模型中，无论嵌入轨道位置如何，都不存在具有任何非零陈数的孤立陈理想能带。即使存在孤立能带接触点，只要布里渊区中任何地方的贝里曲率不发散，该结论仍然成立。最后，我们将结论推广到总陈数为零的威尔逊回路理想能带，如凯恩 - 梅勒\(\mathbb{Z}_2\)理想能带。
英文摘要
A band is called ideal when its Dirichlet functional saturates the topological lower bound. We study ideal bands in finite-band tight-binding models with conventional two-dimensional lattice translation symmetries, allowing the bands to have non-flat dispersion. We first provide an analytic construction of isolated Chern-ideal bands with Chern number $|\mathrm{Ch}|=1$ in finite-band models with exponentially decaying hopping. This construction applies only when at least two orbitals have different embedded positions (modulo lattice vectors), complementing the previously known construction for $|\mathrm{Ch}|>1$. We then show that isolated Chern-ideal bands with any nonzero Chern number cannot exist in finite-band models with finite-range hopping, regardless of the embedded orbital positions. The conclusion holds even if there are isolated band touching points, as long as the Berry curvature does not diverge anywhere in the Brillouin zone. We finally generalize the conclusions to Wilson-loop-ideal bands with zero total Chern number, such as Kane-Mele $\mathbb{Z}_2$-ideal bands.
Comments7+20 pages, no figure
