  We introduce the notion of superstructure Mottness to describe the Mott and
Wigner-Mott transition in doped strongly correlated electron systems at
commensurate filling fractions away from one electron per site. We show that
superstructure Mottness emerges in an inhomogeneous electron system when the
superstructure contains an odd number of electrons per supercell. We argue that
superstructure Mottness exists even in the absence of translation symmetry
breaking by a superlattice, provided that the extended or intersite Coulomb
interaction is strong. In the latter case, superstructure Mottness offers a
unifying framework for the Mott and Wigner physics and a nonperturbative,
strong coupling description of the Wigner-Mott transition. We support our
proposal by studying a minimal single-band ionic Hubbard $t$-$U$-$V$-$\Delta$
model with nearest neighbor Coulomb repulsion $V$ and a two-sublattice ionic
potential $\Delta$. The model is mapped onto a Hubbard model with two effective
``orbitals'' representing the two sites within the supercell, the intra and
interorbital Coulomb repulsion $U$ and $U^\prime \sim V$, and a crystal field
splitting $\Delta$. Charge order on the original lattice corresponds to orbital
order. Developing a cluster Gutzwiller approximation, we study the effects and
the interplay between $V$ and $\Delta$ on the Mott and Wigner-Mott transitions
at quarter-filling. We provide the mechanism by which the superlattice
potential enhances the correlation effects and the tendency towards local
moment formation, construct and elucidate the phase diagram in the unifying
framework of superstructure Mottness.
