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 (8)

• 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
• Nonlocal optical response in metallic nanostructures
• Topological Polaritons
• Bulk-edge correspondence for topological photonic continua
• Dissipation-induced topological transitions in continuous Weyl materials
• Indium Antimonide, constraints on practicality as a magneto-optical platform for topological surface plasmon polaritons

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