Second-order topological insulator in two-dimensional C2N and its derivatives

The high-order topological phase exhibits nontrivial gapless states at the boundaries whose dimension is lower than bulk by two. However, this phase has not been observed experimentally in two-dimensional (2D) materials up to now. In this paper, using first-principles calculations and the tight-binding model, we propose that the experimentally synthesized ${\mathrm{C}}_{2}\mathrm{N}$ is a 2D second-order topological insulator (SOTI) with one-dimensional gapped edge states and zero-dimensional gapless corner states. ${\mathrm{C}}_{2}\mathrm{N}$ exhibits a large bulk gap of 2.45 eV and an edge gap of 0.32 eV, making it an excellent candidate to evidently present the nontrivial corner states in experiments. The robustness of the corner states against the edge disorders has been explicitly identified. Moreover, another three ${\mathrm{C}}_{2}\mathrm{N}$-like materials are also found to host the nontrivial SOTI phase including an experimentally synthesized material aza-fused $\ensuremath{\pi}$-conjugated microporous polymers. The four 2D SOTIs proposed in our present paper provide excellent candidates for studying the novel high-order topological properties in future experiments.