Dirac hierarchy in confined Mie resonance photonic crystals

Abstract

The Dirac hierarchy (DH), comprising an eightfold bulk Dirac cone (DC), a fourfold surface DC, a twofold hinge, and a corner state, has been proposed and observed in acoustic systems recently. DH establishes a versatile platform for exploring exotic phenomena related to the hierarchy of Dirac physics and topological phases at varying dimensions. However, the investigation of DH in the context of photonic crystals is still lacking, as the electromagnetic interactions in the 3D configuration are complex and difficult to match with the tight-binding model. In this study, we first propose a photonic DH in the Mie-confined resonance framework with band chirality. DH with 2D surface states, 1D hinge states, and 0D corner states is obtained by lattice distortions. Besides, we extend the 3D framework to the disclination-introduced photonic system and prove the coexistence of robust disclination, corner, and hinge states. Our work explores the Dirac physics in photonics, offers insights to manipulate electromagnetic waves at varying dimensions, and reveals unconventional bulk-disclination correspondence in 3D photonic materials.