Realization of flat bands by lattice intercalation in kagome metals

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.