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arXiv · 2606.11777

Berry-phase-based Topological Charge in Quasicrystals and their Observable Features in Photonic System

Ziyi Chen·Jinyu Zou·Jinhua Gao·Gang xu
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Abstract

Topological charges based on Berry phase play the fundamental role in the topological physics. However, such topological charges remain unexplored in quasicrystals, impeding the systematic understanding of topological states in such quasiperiodic systems. In this work, by deriving all the allowed topological charges according to group representation theory and the corresponding low-energy effective Hamiltonians, we establish a universal framework for Berry-phase-based topological charges in two-dimensional quasicrystals. Taking the $C_{8v}$ quasicrystal as an example, we demonstrate and characterize a higher topological charge of $C=4$, which is inaccessible in conventional periodic systems. Applying our framework to photonic quasicrystals, we uncover that the circling of photon momentum around the charge gives a $C$ times winding of the electromagnetic field distribution pattern. Such observable feature provides a direct experimental method to probe the topological charges. Our work paves the way for exploring topological charges in quasiperiodic matter, and fundamentally bridges periodic and quasiperiodic topological band theories.

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Ziyi Chen, Jinyu Zou, Jinhua Gao, Gang xu. 2026-06-10. Berry-phase-based Topological Charge in Quasicrystals and their Observable Features in Photonic System. https://arxiv.org/abs/2606.11777

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