  We present a formalism for calculating the image potential for a
two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI) as
well as for a 2D topological insulator (TI). The formalism is further
generalized for including the Coulomb coupled multiple layers. Roles of broken
inversion symmetry near the surface and the dielectric environment are
investigated by using a surface-response function. The insignificant role of
SOI in 2DEG is dramatically enhanced in TI by selecting a small relative
permittivity $\epsilon_b$ for the dielectric environment. Manipulating
$\epsilon_b$ is proven to provide an efficient way to drive electrons with
opposite spins into two different integral quantum Hall states. The prediction
made in this paper is expected to be experimentally observable for a 2DTI
system, such as Bi$_2$Se$_3$, with a helical spin behavior and a dominant
linear Rashba SOI-like term in the energy dispersion.
