  We consider the resonant Casimir-Polder interaction of an excited alkali-type
atom which has a single (electric dipole) transition with a Chern insulator.
The Chern insulator has a nonzero, time reversal symmetry breaking Hall
conductance, leading to an additional contribution to the resonant
Casimir-Polder interaction which depends on the coupling between the Hall
conductance and the circular polarization state of the atomic transition. We
find that the resonant Casimir-Polder shift can be significantly enhanced for
de-excitation frequencies near values associated with the van Hove
singularities of the Chern insulator. Furthermore, we find that the resonant
Casimir-Polder force can become monotonically decaying and repulsive for a
relatively large atom-surface distance, if the atomic dipole transition is
right circularly polarized and the Chern number of the Chern insulator is $-1$
or the atomic dipole transition is left circularly polarized and the Chern
number is $1$.
