  We have calculated the Casimir-Polder interaction (CPI) of a micro-particle
with a sheet on the basis of the Klimchitskaya-Mostepanenko theory. We find the
result that for non-trivial susceptibility values of the sheet and
micro-particle, there is crossover between attractive and repulsive behavior.
The transition depends only on the impedance, involving permeability and
permittivity, apart from the ratio of the film thickness and the micro-particle
separation (D/d) and temperature. The approach to calculate CPI of a
micro-particle with a silicene sheet involves replacing the dielectric constant
of the sample by the static dielectric function obtained using the expressions
for the polarization function. The silicene is described by the low-energy
Liu-Yao-Feng-Ezawa (LYFE)Model Hamiltonian involving the Dirac matrices in the
chiral representation obeying the Clifford algebra.We find that the collective
charge excitations at zero doping, i.e., intrinsic plasmons, in this system,
are absent in the Dirac limit. The valley-spin-split intrinsic plasmons,
however, come into being in the case of the massive Dirac particles with
characteristic frequency close to 10 THz.Furthermore, there is a longitudinal
electric field induced topological insulator(TI) to spin-valley polarized metal
(SVPM) transition in silicene, which is also referred to as the topological
phase transition (TPT). The low-energy SVP carriers at TPT possess gap-less
(mass-less) and gapped (massive) energy spectra close to the two nodal points
in the Brillouin zone with maximum spin-polarization. We find that the
magnitude of the Casimir-Polder force at a given ratio of the film thickness
and the separation between the micro-particle and the film is greater at TPT
than at the topological insulator and trivial insulator phases.
