Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics

TL;DR

This paper investigates apparent violations of the bulk-edge correspondence in topological photonic materials, revealing that physical effects like attenuation and nonlocality prevent true violations despite formal mathematical inconsistencies.

Contribution

It demonstrates that physical effects such as attenuation and nonlocality induce practical violations of the bulk-edge correspondence in topological electromagnetics.

Findings

Bulk-edge correspondence can be formally restored by spatial dispersion.

Attenuation of highly confined modes prevents true topological protection.

Practical violations occur even in ideal, lossless materials due to physical effects.

Abstract

In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for uniform topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging wavenumbers. Considering a nonreciprocal plasma as a model system, we show that the inclusion of spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wavenumbers. Most importantly, however, our findings show that, for the considered cases, the correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Our work helps clarifying the subtle and rich topological wave physics of continuous media.