  In this work, we present an analytical study on the surface plasmon
polaritons in a two dimensional parity anomaly Chern insulator. The connections
between the topology in the bulk implied by the BHZ model and the dispersion
relations of the surface plasmons have been revealed. Anisotropy has been
considered during the calculations of the dispersion relations which allows
different permittivities perpendicular to the conductive plane. Two surface
plasmon modes each contains two branches of dispersion relations have been
found. The topologically non-trivial case gives quite different Hall
conductivities compared with the trivial one, which leads to significant
modifications of the dispersion curves or even the absence of particular branch
of the surface plasmons. Our investigations pave a possible way for the
detection of the parity anomaly in a two-dimensional Chern insulator via
plasmonic responses.
