Abstract

Recently there has been intense interest in kagome metals, which are expected to host flat bands (FBs). However, the observed ``FBs'' are not flat over the whole two-dimensional Brillouin zone and overlap strongly with other bands. In fact, the FB does not truly exist in a default $d$-orbital kagome lattice, and the conditions for its existence in kagome metals are unknown. Here, based on tight-binding model analyses of the interplay between orbital and lattice symmetry, we establish such conditions. We show that for a single $d$-orbital kagome lattice assuming large crystal field splitting (CFS), only the ${d}_{{z}^{2}}$ orbital gives rise to a FB, while ${d}_{xy}, {d}_{{x}^{2}\ensuremath{-}{y}^{2}}, {d}_{xz}$, and ${d}_{yz}$ orbitals can only produce a FB with a rotated $d$-orbital basis so that they conform with the underlying kagome lattice symmetry. Most importantly, we demonstrate that both conditions of $d$-orbital rotation and large CFS can be ideally satisfied by intercalating the kagome lattice with a hexagonal sublattice without disrupting the destructive interference of FB wave function. Furthermore, we propose layered metalorganic frameworks as promising candidate kagome metals to realize FBs.

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