A prominent characteristic of two-dimensional higher-order topological insulators (2D-HOTIs) is the topologically protected corner modes associated with gapped edge states. Opening the gap of bulk and edge states is a key to realizing 2D-HOTIs. In this paper, we theoretically propose that 2D-HOTIs can be realized on porous network models. We consider two porous network models, the graphenylenelike and the porous-honeycomb models, which respectively contain 12 and 18 atoms in supercells. These superstructures can open the bulk gap as well as the edge gap and induce HOTIs. Experimentally, graphene nanomesh, other 2D porous materials, and organic molecules naturally host supercells with regular nanoholes, which can be candidates to realizing HOTIs. Our studies reveal that 2D-HOTIs can be realized on some 2D porous network models and provide a promising route to explore HOTI states in real materials.

• Received 6 April 2021
• Accepted 12 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.165416