This paper is a contribution to the Physical Review Applied collection titled Phononics and Metamaterials.

Topological wave transport has become an important area of research in photonic and phononic systems, providing new insights into wave propagation and enabling promising technological applications. Although photons and phonons share common features in periodic media, they are fundamentally different in nature and are most often investigated separately. In this work, we present an analog of the quantum valley-Hall effect for both electromagnetic and elastic waves within a single platform. By breaking normal mirror symmetry in a graphene-like lattice, valley-polarized bandgaps are opened in both photonic and phononic band structures. Numerical simulations reveal nontrivial Berry curvature distributions and opposite valley Chern numbers, leading to the emergence of robust interface states at domain walls between topologically distinct crystals in both photonic and phononic domains. The topological nature and robustness of these edge modes are demonstrated through transmission calculations and spatial Fourier and Laplace spectral analyses, which allow a clear distinction between topological and trivial modes. This work establishes a unified platform enabling valley-Hall topology for both photonics and phononics and opens new perspectives for integrated multimodal and hybrid light-sound devices.

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• Berry curvature
• Phononics
• Photonics
• Topological metamaterials
• Valley degrees of freedom
• Elemental semiconductors
• Phononic crystals
• Photonic crystals