Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics

Abstract

The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of topological photonics, as it determines the precise physical manifestations of nontrivial topological features. Even though the bulk-edge correspondence has been extensively discussed and used in the literature, it seems that in the general photonic case with dispersive materials it has no solid mathematical foundation and is essentially a conjecture. Here, I present a rigorous demonstration of this fundamental principle by showing that the thermal fluctuation-induced light-angular momentum spectral density in a closed cavity can be expressed in terms of the photonic gap Chern number, as well as in terms of the net number of unidirectional edge states. In particular, I highlight the rather fundamental connections between topological numbers in Chern-type photonic insulators and the fluctuation-induced light-momentum

to be published in PRX

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• Topological waves in fluids with odd viscosity
• Anomalous bulk-edge correspondence in continuous media
• Topological theory of non-Hermitian photonic systems
• Anomalous Topological Active Matter
• Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics
• Photonic topological insulators a beginner's introduction
• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Exciting Pseudospin Dependent Edge States in Plasmonic Metasurfaces
• The interacting Rice-Mele model: bulk and boundaries
• Manipulating Topological Valley Modes in Plasmonic Metasurfaces
• Topological origin of electromagnetic energy sinks
• Photonic analogues of the Haldane and Kane-Mele models
• Quantized Angular Momentum in Topological Optical Systems
• Chiral Maxwell waves in continuous media from Berry monopoles
• Surface charge theorem and topological constraints for edge states: An analytical study of one-dimensional nearest-neighbor tight-binding models
• Chiral photonic topological states in Penrose quasicrystals
• Chern Invariants of Topological Continua; a Self-Consistent Nonlocal Hydrodynamic Model
• Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model
• Ill-defined Topological Phases in Dispersive Photonic Crystals
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Topological Insights from State Manipulation in a Classical Elastic System
• Geometry and Topological photonics
• Quantum dot coupled to topological insulators: The role of edge states
• Classifying topological floppy modes in the continuum
• Topologically induced transparency in a two-phase metamaterial
• Exceptional light propagation via generalized bulk-edge correspondence
• Gauge theory for topological waves in continuum fluids with odd viscosity