Topological classification of Chern-type insulators with the photonic Green function

Abstract

The Chern topological numbers of a material system are traditionally written in terms of the Berry curvature which depends explicitly on the material band structure and on the Bloch eigenwaves. Here, we demonstrate that it is possible to calculate the gap Chern numbers of a photonic platform without having any detailed knowledge of its band structure, relying simply on the system photonic Green function. It is shown that the gap Chern number is given by an integral of the photonic Green function along a line of the complex frequency plane parallel to the imaginary axis. Our theory applies to arbitrary frequency dispersive fully three-dimensional photonic crystals, as well as to the case of electromagnetic continua with no intrinsic periodicity.

under review since 16 Jan

References in corpus (10)

• Topological Photonics
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Analogs of quantum Hall effect edge states in photonic crystals
• Bulk-edge correspondence for topological photonic continua
• PTD Symmetry Protected Scattering Anomaly in Optics
• Fluctuation-induced forces on an atom near a photonic topological material
• Topological Angular Momentum and Radiative Heat Transport in Closed Orbits
• Topological number and Fermion Green's function of Strongly Interacting Topological Superconductors
• Negative spontaneous emission by a moving two-level atom
• Link between the photonic and electronic topological phases in artificial graphene

Cited by in corpus (13)

• Topological theory of non-Hermitian photonic systems
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Topological origin of electromagnetic energy sinks
• Hidden Time-Reversal Symmetry in Dissipative Reciprocal Systems
• Quantized Angular Momentum in Topological Optical Systems
• Indifferent electromagnetic modes: bound states and topology
• Link between the photonic and electronic topological phases in artificial graphene
• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Asymmetric Cherenkov Emission in a Topological Plasmonic Waveguide
• Momentum-Space Topological Effects of Nonreciprocity
• Geometry and Topological photonics
• Spontaneous Rotational Symmetry Breaking in a Kramers Two-Level System
• Topologically induced transparency in a two-phase metamaterial