Semimetallic square-octagon two-dimensional polymer with high mobility

The electronic properties of π -conjugated two-dimensional (2D) polymers near the Fermi level are determined by structural topology and chemical composition. Thus tight-binding (TB) calculations of the corresponding fundamental network can be used to explore the parameter space to find configurations with intriguing properties before designing the atomistic 2D polymer network. The vertex-transitive fes lattice, which is also called a square-octagon, 4-8, or 4.8_{2<\sup> lattice, is rich in interesting topological features including Dirac points and flat bands. Herein, we study its electronic and topological properties within the TB framework using representative parameters for chemical systems. Secondly, we demonstrate that the rational implementation of band structure features obtained from TB calculations in 2D polymers is feasible with a family of 2D polymers possessing fes structure. A one-to-one band structure correspondence between the fundamental network and 2D polymers is found. Moreover, changing the relative length of linkers connecting the triangulene units in the 2D polymers reflects tuning of hopping parameters in the TB model. These perturbations allow sizable local band gaps to open at various positions in the Brillouin zone. From analysis of the Berry curvature flux, none of the polymers exhibits a large topologically nontrivial band gap. However, we find a particular configuration of semimetallic characteristics with separate electron and hole pockets, which possess very low effective masses
both for electrons (as small as m^{∗<\sup> e<\sub> = 0.05) and for holes (as small as m∗<\sup> h<\sub> = 0.01).}}