Ill-defined Topological Phases in Dispersive Photonic Crystals

Abstract

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with little modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break-down and the Chern topology becomes ill-defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be non-integer notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk-materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.

References in corpus (21)

• Topological Insulators
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Photonics
• 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
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Bulk-edge correspondence for topological photonic continua
• First-principle calculation of Chern number in gyrotropic photonic crystals
• Topological theory of non-Hermitian photonic systems
• Proof of the bulk-edge correspondence through a link between topological photonics and fluctuation-electrodynamics
• Topological Angular Momentum and Radiative Heat Transport in Closed Orbits
• Topological classification of Chern-type insulators with the photonic Green function
• Topological origin of electromagnetic energy sinks
• Photonic analogues of the Haldane and Kane-Mele models
• Quantized Angular Momentum in Topological Optical Systems
• Absence of unidirectionally propagating surface plasmon-polaritons in nonreciprocal plasmonics
• Multiple Embedded Eigenstates in Nonlocal Plasmonic Nanostructures

Cited by in corpus (5)

• Roadmap on Nonlocality in Photonic Materials and Metamaterials
• Rotating Spacetime Modulation: Topological Phases and Spacetime Haldane Model
• Geometry and Topological photonics
• Frequency Domain Berry Curvature Effect on Time Refraction
• Nonreciprocal Local-Resonance Induced Complex Band Hybridization