Zero-index topological interface states in a distorted Kekulé photonic crystal

Topological interface states (TISs) and zero-index behavior are two unique phenomena in photonic systems. TISs enable robust wave propagation along a topological interface, while zero-index behavior allows waves to travel without phase variation. However, photonic structures that simultaneously exhibit both topological properties and zero-index behavior remain largely unexplored. In this work, we present two distorted Kekul\'e photonic crystals capable of supporting a pair of gapless pseudospin TISs. Since this degeneracy occurs at the center of the Brillouin zone, the TISs inherently combine topological protection with a zero-index response, which we refer to as zero-index TISs. This enables unidirectional wave propagation with minimal phase variation while maintaining robustness against interface corners. Our work offers an effective approach to achieving zero-index topological mode, with potential applications in signal transmission, qubit entanglement, and beyond.