  In this work, we use density functional theory calculations to demonstrate
how spontaneous electric polarizations can be induced \textit{via} a hybrid
improper ferroelectric mechanism in iodide perovskites, a family well-known to
display solar-optimal band gaps, to create new materials for photoferroic
applications. We first assemble three chemically distinct
($A$$A^{\prime}$)($B$$B^{\prime}$)I$_6$ double perovskites using
centrosymmetric $AB$I$_3$ perovskite iodides (where $A$ = Cs, Rb, K and $B$ =
Sn, Ge) as building units. In each superlattice, we investigate the effects of
three types of $A$- and $B$-site cation ordering schemes and three different
$B$I$_6$ octahedral rotation patterns. Out of these 27 combinations, we find
that 15 produce polar space groups and display spontaneous electric
polarizations ranging from 0.26 to 23.33 $\mu$C/cm$^2$. Furthermore, we find
that a layered $A$-site/rock salt $B$-site ordering, in the presence of an
$a^0a^0c^+$ rotation pattern, produces a chiral "vortex-like" $A$-site
displacement pattern. We then investigate the effect of epitaxial strain on one
of these systems, (CsRb)(SnGe)I$_6$, in layered and rock salt ordered
configurations. In both phases, we find strong competition between the cation
ordering schemes as well as an enhancement of the spontaneous polarization
magnitude under tensile strain. Finally, using advanced functionals, we
demonstrate that these compounds display low band gaps ranging from 0.2 to 1.3
eV. These results demonstrate that cation ordering and epitaxial strain are
powerful ways to induce and control new functionalities in
technologically-useful families of materials.
