Topological Insulating Phase in Single-Layer Pentagonal Covalent Organic Frameworks: A Reticular Design Using Metal Phthalocyanine

Abstract

Organic topological insulators have received tremendous attention lately due to their designability and highly chemical diversity. In this work, we propose an isoreticular series of single-layer π-conjugated covalent organic frameworks with the Cairo pentagonal tiling, termed mcm-ZnPc-1, mcm-ZnPc-2, mcm-ZnPc-3, and mcm-ZnPc-3N, where mcm is the crystal net’s symbol and ZnPc stands for zinc phthalocyanine. First-principles calculations using density functional theory show that mcm-ZnPc-1 and mcm-ZnPc-2 are trivial insulators with band gaps of 0.96 and 1.18 eV, respectively. Interestingly, expanding the π-conjugated system of mcm-ZnPc-2, followed by a chemical substitution, results in mcm-ZnPc-3 and mcm-ZnPc-3N with a distorted Dirac point and a quadratic band-crossing point in their band structures, respectively. The topological analyses indicate that mcm-ZnPc-3N is a Z2 topological insulator with a nontrivial gapless edge state. Our tight-binding model for the pentagonal lattice suggests that the topologically trivial-to-nontrivial transition can be attributed to the sufficient electronic coupling between two adjacent linkers and to the fact that the band-crossing point locates at the Fermi level. Remarkably, we show that replacing Zn in mcm-ZnPc-3N with Cd and Hg can substantially enlarge the nontrivial band gap from 0.3 meV up to 10 meV due to strong spin–orbit coupling strengths although a biaxial strain is necessary to tune the Fermi level of mcm-HgPc-3N in order to enter its topological insulating phase. Our proposed materials are predicted to be dynamically, thermally, and mechanically stable, thus paving the way for their experimental realization. This work not only introduces the pentagonal lattice as a building motif for framework structures but also demonstrates a strategy to engineer the exotic band structure of organic materials.