  Exotic band features, such as Dirac cones and flat bands, arise directly from
the lattice symmetry of materials. The Lieb lattice is one of the most
intriguing topologies, because it possesses both Dirac cones and flat bands
which intersect at the Fermi level. However, materials with Lieb lattice remain
experimentally unreached. Here, we explore two-dimensional poly-mers (2DPs)
derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice
(sql) as potential electronic Lieb lattice materials. By systematically varying
the linker lengths (ZnPc-xP), we found that some ZnPc-xP exhibit a
characteristic Lieb lattice band structure. Interestingly though, fes bands are
also observed in ZnPc-xP. The coexistence of fes and Lieb in sql 2DPs
challenges the conventional perception of the structure-electronic structure
relation. In addition, we show that manipula-tion of the Fermi level, achieved
by electron removal or atom substitution, effectively preserves the unique
characteristics of Lieb bands. Chern number calculations confirm the
non-trivial nature of the Lieb Dirac bands. Our discoveries provide a fresh
perspective on 2D polymers and redefine the search for Lieb lattice materials
into a well-defined chemical synthesis task.
