Electronic Lieb lattice signatures embedded in two-dimensional polymers with square lattice

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.