Chern Invariants of Topological Continua; a Self-Consistent Nonlocal Hydrodynamic Model

Abstract

The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this principle works well for periodic photonic topological insulators, difficulties arise in the case of continuous systems with no intrinsic periodicity, due to the absence of a finite Brillouin zone, which may lead to an ill-behaved response for diverging wavenumbers. This problem has been solved previously by introducing an ad hoc material model including a spatial cutoff wavenumber. However, this method introduces other difficulties, such as an unphysical response at large wavenumbers, and the need to interpolate the interfaced materials permittivity functions. In this work, we show that the inclusion of realistic spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wavenumbers, forming a complete, self-consistent model. This model clarifies the subtle and rich topological wave physics of continuous media.

References in corpus (22)

• Topological Insulators
• Topological Photonics
• Photonic Floquet Topological Insulators
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• 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
• Nonlocal optical response in metallic nanostructures
• Topological Polaritons
• Plasmon Weyl Degeneracies in Magnetized Plasma
• Topological magnetoplasmon
• Bulk-edge correspondence for topological photonic continua
• Experimental observation of topological exciton-polaritons in transition metal dichalcogenide monolayers
• Berry phase, Berry Connection, and Chern Number for a Continuum Bianisotropic Material from a Classical Electromagnetics Perspective
• Anomalous bulk-edge correspondence in continuous media
• Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Unidirectional and diffractionless surface plasmon-polaritons on three-dimensional nonreciprocal plasmonic platforms
• The effects of three-dimensional defects on one-way surface plasmon propagation for photonic topological insulators comprised of continuous media
• Robust surface plasmon polaritons on gyrotropic interfaces
• Dissipation-induced topological transitions in continuous Weyl materials
• Indium Antimonide, constraints on practicality as a magneto-optical platform for topological surface plasmon polaritons
• Notes on photonic topological insulators and scattering-protected edge states - a brief introduction

Cited by in corpus (6)

• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Long-lived qubit entanglement by surface plasmon polaritons in a Weyl semimetal
• The Uniqueness Theorem for Nonlocal Hydrodynamic Media
• Unidirectional Curved Surface Plasmon Polariton in a Radially Magnetized System
• Topological edge states of continuous Hamiltonians
• Effective Medium Perspective on Topological Transitions in Metamaterials