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
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.