  Line-graph (LG) lattices are known for having topological flat bands (FBs)
from the destructive interference of Bloch wavefunctions encoded in lattice
symmetry. Here, we develop an atomic/molecular orbital design principle for the
existence of FBs in non-LG lattices. Using a generic tight-binding model, we
demonstrate that the underlying wavefunction symmetry of FBs in a LG lattice
can be transformed into the atomic/molecular orbital symmetry in a non-LG
lattice. We show such orbital-designed topological FBs in three common 2D
non-LG, square, trigonal, and hexagonal lattices, where the chosen orbitals
faithfully reproduce the corresponding localized FB plaquette states of
checkerboard, Kagome, and diatomic-Kagome lattices, respectively. Fundamentally
our theory enriches the FB physics; practically the proposed orbital design
principle is expected to significantly expand the scope of FB materials, since
most materials have multiple atomic/molecular orbitals at each lattice site,
rather than a single s orbital mandated in graph theory.
