Section Chern number for a 3D photonic crystal and the bulk-edge correspondence

Abstract

We have characterized the robust propagation modes of electromagnetic waves in helical structures by the section Chern number that is defined for a two-dimensional (2D) section of the three- dimensional (3D) Brillouin zone. The Weyl point in the photonic bands is associated with a dis- continuous jump of the section Chern number. A spatially localized Gaussian basis set is used to calculate the section Chern numbers where we have implemented the divergence-free condition on each basis function in 3D. The validity of the bulk-edge correspondence in a 3D photonic crystal is discussed in relation to the broken inversion symmetry.

References in corpus (21)

• Maximally-localized generalized Wannier functions for composite energy bands
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Photonics
• Photonic Floquet Topological Insulators
• Maximally localized Wannier functions: Theory and applications
• Weyl Semimetal in a Topological Insulator Multilayer
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Imaging topological edge states in silicon photonics
• Topological nodal semimetals
• Scheme to Achieve Silicon Topological Photonics
• Robust optical delay lines via topological protection
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Analogs of quantum Hall effect edge states in photonic crystals
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Experimental observation of Weyl points
• Weyl points and line nodes in gapless gyroid photonic crystals
• Exponential localization of Wannier functions in insulators
• Photonic analog of graphene model and its extension -- Dirac cone, symmetry, and edge states --
• Triviality of Bloch and Bloch-Dirac bundles
• Superconductivity and Abelian Chiral Anomalies

Cited by in corpus (8)

• A brief review of topological photonics in one, two, and three dimensions
• Multi Weyl Points and the Sign Change of Their Topological Charges in Woodpile Photonic Crystals
• First-principle calculation of Chern number in gyrotropic photonic crystals
• Electromagnetic Scattering Laws in Weyl Systems
• Cubic 3D Chern photonic insulators with orientable large Chern vectors
• Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals
• Optical Properties of Chiral Three-Dimensional Photonic Crystals made from Semiconductors
• Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure