Recently, topological corner states have been extensively investigated in second-order topological photonic crystals (STPCs). However, most square lattice STPCs are proposed based on the two-dimensional (2D) Su-Schrieffer–Heeger (SSH) model. In this work, we propose a photonic crystal (PC) that goes beyond the 2D SSH model. The unit cell (UC) of the PC is only composed of a dielectric cylinder in an air background (or an air hole in a dielectric slab). The topological trivial or nontrivial photonic band gap of the cylinder-in-air or hole-in-slab UC can be confirmed from the value of 2D polarization. Remarkably, photonic band gaps form directly without any intermediate transition. 2D bulk states, one-dimensional edge states, and zero-dimensional corner states are generated hierarchically in the box-type combination structures composed of trivial and nontrivial PCs. By comparing the perfect and defective structures, the corner states show strong robustness against the defects. The proposed configurations provide a simpler platform for exploring topological corner states in photonic systems, which have great potential for application in integrated nanophotonic devices.

• Received 9 September 2021
• Revised 4 April 2022
• Accepted 28 June 2022

DOI:https://doi.org/10.1103/PhysRevA.106.013510