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    Fine structure of Berry curvature and nonquantized valley Chern numbers in valley photonic crystals

    Wei Dai1,*, Taiki Yoda1,*, Yuto Moritake1,2, and Masaya Notomi1,3,†

    • *These authors contributed equally to this work.
    • †Contact author: notomi@phys.sci.isct.ac.jp; masaya.notomi@ntt.com

    Phys. Rev. B 113, 195412 – Published 14 May, 2026

    DOI: https://doi.org/10.1103/1sq1-3168

    Abstract

    Valley photonics has emerged as a promising platform in topological photonic systems, yet the topological nature of valley-dependent phenomena remains unsettled. Theoretically, intervalley scattering may occur with structural imperfections, and global Chern numbers vanish due to time-reversal symmetry. As a result, valley-dependent topology is locally defined around K(K′) points in the half-Brillouin zone (HBZ). While half-integer valley Chern numbers have been widely assumed, their quantization and topological validity remain controversial. Here, we systematically investigate a continuous spectrum of valley photonic crystal designs by evaluating their Berry curvatures, valley Chern numbers, and angular momenta. We show that valley Chern numbers are generically unquantized and instead form a continuous spectrum varying with structural parameters. We further reveal previously unexplored fine structures in the Berry curvature distribution in momentum space. The unquantized valley Chern numbers are attributed to inter- and intravalley cancellation of Berry curvature, highlighting the absence of a protecting mechanism for quantization. Our results call for a reassessment of valley-dependent topology and provide a more rigorous framework for interpreting valley-related photonic phenomena.

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