Emergent topological interfacial states in 3D photonic crystals via half-period structural shifts.

While higher-order two-dimensional (2D) topological photonic crystals have been extensively explored, 3D analogues remain scarce despite their potential for richer topological phenomena and applications in robust 3D photonic networks. In this work, we propose a strategy to engineer 3D topological photonic crystals by constructing interfaces between inversion-symmetric lattices and their half-lattice-shifted counterparts - a 3D generalization of the topological interfaces in the Su-Schrieffer-Heeger model. By designing a hexagonal lattice photonic crystal with tunable band gaps, we demonstrate that either the original or half-period-shifted configurations exhibit a non-trivial Zak phase of π along all three primitive lattice directions. Numerical simulations reveal the emergence of surface states at planar interfaces, hinge states at 1D corners, and also 0D corner states, indicative of higher-order topology. This work not only advances the designs of 3D topological photonic crystals but also opens avenues for applications in fault-tolerant photonic circuits and multidimensional light trapping.