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arXiv · 1902.10050

Anomalous bulk-edge correspondence in continuous media

Clément Tauber·Pierre Delplace·Antoine Venaille
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Abstract

Topology plays an increasing role in physics beyond the realm of topological insulators in condensed mater. From geophysical fluids to active matter, acoustics or photonics, a growing family of systems presents topologically protected chiral edge modes. The number of such modes should coincide with the bulk topological invariant (e.g. Chern number) defined for a sample without boundary, in agreement with the bulk-edge correspondence. However this is not always the case when dealing with continuous media where there is no small scale cut-off. The number of edge modes actually depends on the boundary condition, even when the bulk is properly regularized, showing an apparent paradox where the bulk-edge correspondence is violated. In this paper we solve this paradox by showing that the anomaly is due to {ghost} edge modes hidden in the asymptotic part of the spectrum. We provide a general formalism based on scattering theory to detect all edge modes properly, so that the bulk-edge correspondence is restored. We illustrate this approach through the odd-viscous shallow-water model and the massive Dirac Hamiltonian, and discuss the physical consequences.

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Clément Tauber, Pierre Delplace, Antoine Venaille. 2019-02-26. Anomalous bulk-edge correspondence in continuous media. https://doi.org/10.1103/physrevresearch.2.013147

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