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In this work, we present an analytical study on the surface plasmonpolaritons in a two dimensional parity anomaly Chern insulator. The connectionsbetween the topology in the bulk implied by the BHZ model and the dispersionrelations of the surface plasmons have been revealed. Anisotropy has beenconsidered during the calculations of the dispersion relations which allowsdifferent permittivities perpendicular to the conductive plane. Two surfaceplasmon modes each contains two branches of dispersion relations have beenfound. The topologically non-trivial case gives quite different Hallconductivities compared with the trivial one, which leads to significantmodifications of the dispersion curves or even the absence of particular branchof the surface plasmons. Our investigations pave a possible way for thedetection of the parity anomaly in a two-dimensional Chern insulator viaplasmonic responses.

Plasmonic detection of the parity anomaly in a two-dimensional Chern insulator