  Within the ionic Hubbard model, electron correlations transmute the
single-particle gap of a band insulator into a Mott gap in the strong
correlation limit. However understanding the nature of possible phases in
between these two extreme insulating phases remains an outstanding challenge.
We find two strongly correlated insulating phases in between the above
extremes: (i) The insulating phase just before the Mott phase can be viewed as
gapping a non-Fermi liquid state of spinons through staggered ionic potential.
The quasi-particles of underlying spinons are orthogonal to physical electrons
and hence they do not couple to photoemission probes, giving rise to
"ARPES-dark" state due to which the ARPES gap will be larger than optical and
thermal gap. (ii) The correlated insulating phase just after the normal band
insulator corresponds to the ordered phase of slave Ising spins (Ising
insulator) where charge configuration is controlled by an underlying Ising
variable which indirectly couples to external magnetic field and hence gives
rise to additional temperature and field dependence in semiconducting
properties. In the absence of tunability for the Hubbard $U$, such a
temperature and field dependence can be conveniently employed to achieve
further control on the transport properties of Ising-based semiconductors. The
rare earth monochalcogenide semiconductors where the magneto-resistance is
anomalously large can be a candidate system for the ordered phase of Ising
variable where pairs of charge bosons are condensed in the background.
Combining present results with our previous dynamical mean field theory study,
we argue that the present picture holds if the ionic potential is strong enough
to survive the downward renormalization of the ionic potential caused by
Hubbard $U$.
