  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.
