Fine Structures of Berry Curvature and Unquantized Valley Chern Numbers in Valley Photonic Crystals

TL;DR

This paper investigates the topological properties of valley photonic crystals, revealing that valley Chern numbers are generally unquantized and uncovering detailed structures in Berry curvature distribution.

Contribution

It provides a systematic analysis showing valley Chern numbers are unquantized and introduces detailed insights into Berry curvature structures in valley photonics.

Findings

Valley Chern numbers are unquantized and vary with structural parameters.

Unexplored fine structures in Berry curvature distribution are revealed.

Inter- and intra-valley Berry curvature cancellation explains unquantization.

Abstract

Valley photonics has emerged as a promising platform in topological photonic systems, yet the topological nature of valley-dependent phenomena remains unsettled. Theoretically, inter-valley 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 unquan-tized 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 intra-valley 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.