kagome晶格及其类似物的隐藏手性对称性
Hidden chiral symmetry for kagome lattice and its analogs
AI总结：
本文利用分子轨道表示揭示含平带的非二分kagome晶格及其一维类似物中隐藏的手性对称性，并提出毕达哥拉斯关系以解释拓扑边缘模和多平带结构。
摘要：
手性对称性在凝聚态物理中起着至关重要的作用。在紧束缚模型中，它通常归因于二分晶格结构，其典型结果是“粒子-空穴对称”的能带结构，即正本征能量和负本征能量成对出现。在本工作中，我们探讨具有平带的非二分晶格模型的手性对称性。我们的论证依赖于所谓的分子轨道表示，借助该表示可以保证平带的存在。我们表明，当分子轨道被归一化并划分为两个集合、且每个集合内部的分子轨道彼此不重叠时，非平带保持手性对称性。手性算子由与 Hamiltonian 相同的分子轨道构造。这导致手性算子与 Hamiltonian 之间的一种特征关系，我们称之为毕达哥拉斯关系。我们给出了此类模型的例子，即 kagome 晶格及其一维类似物，并探讨了源于手性对称性的特征，例如拓扑边缘模的出现。我们还展示了一个例子，其中两个集合中的分子轨道数量彼此不同，从而产生具有不同能量的多个平带。
英文摘要：
Chiral symmetry plays an essential role in condensed matter physics. In tight-binding models, it is often attributed to bipartite lattice structures, and its typical consequence is the ``particle-hole symmetric" band structures, that is, the positive and negative eigenenergies appear in a pairwise manner. In this work, we address the chiral symmetry for non-bipartite lattice models with flat bands. Our argument relies on what we call the molecular-orbital representation, by which we can guarantee the existence of the flat band. We show that the chiral symmetry is preserved for the non-flat bands when the molecular orbitals are normalized and divided into two sets within which they are non-overlapping. The chiral operator is constructed by the same molecular orbitals as the Hamiltonian. This results in the characteristic relation between the chiral operator and the Hamiltonian, which we call the Pythagoras relation. We present the examples of such models, i.e., the kagome lattice and its one-dimensional analog, and address the characteristics originating from the chiral symmetry, such as the emergence of the topological edge modes. We also show an example where the numbers of molecular orbitals in each set are different from each other, resulting in multiple flat bands with different energies.
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