论文标题
通过旋转的D-轨道在Kagome金属中实现理想平坦带
Realization of ideal flat band by rotated d-orbitals in Kagome metals
论文作者
论文摘要
最近，人们对Kagome金属产生了浓厚的兴趣，这些金属有望容纳平坦的乐队（FBS）。但是，观察到的FBS是非理想的，因为它们在整个2D Brillouin区域都不平坦，并且与其他频段强烈重叠。最关键的是，除了最简单的kagome晶格模型之外，在Kagome金属中存在理想FB的理论条件是未知的。在这里，基于D-轨对称性和基础Kagome晶格对称性之间相互作用的紧密结合模型分析，我们建立了这样的条件。我们表明，对于一个纯的过渡金属（TM）kagome晶格，只有DZ2轨道会产生Fb。而dxy，dx2-y2，dxz和dyz轨道却没有。后四个轨道产生FB的条件是旋转它们，以便它们与下面的Kagome晶格对称性符合。有趣的是，具有旋转DXY（DXZ）和DX2-Y2（DYZ）轨道的晶格分别导致坐在Dirac Band上方和下方的相反手性的FB。对于插入的TM Kagome晶格，Kagome-Hexagonal Intercalation始终表现出FB，而Kagome-Trigonal插入的情况是条件。隔离单个D轨道产生的FB的另一个条件是增加晶体场的分裂，例如在分层金属有机框架的Kagome金属中。
Recently there has been intense interest in Kagome metals, which are expected to host flat bands (FBs). However, the observed FBs are non-ideal as they are not flat over the whole 2D Brillouin zone and overlap strongly with other bands. Most critically, the theoretical conditions for the existence of ideal FB in Kagome metals, beyond the simplest Kagome lattice model, are unknown. Here, based on tight-binding model analyses of the interplay between d-orbital symmetry and underlying Kagome lattice symmetry, we establish such conditions. We show that for a pure transition-metal (TM) Kagome lattice, only dz2 orbital gives rise to a FB; while dxy, dx2-y2, dxz, and dyz orbitals do not. The condition for the latter four orbitals to produce a FB is to rotate them so that they will conform with the underlying Kagome lattice symmetry. Interestingly, the lattice having rotated dxy (dxz) and dx2-y2 (dyz) orbitals leads to a FB of opposite chirality sitting above and below the Dirac bands, respectively. For intercalated TM Kagome lattices, the Kagome-hexagonal intercalation exhibits always a FB, while the case for the Kagome-trigonal intercalation is conditional. Another condition to isolate the FB arising from individual d-orbitals is to increase the crystal field splitting, such as in Kagome metals of layered metalorganic frameworks.
