  A strategy for obtaining low band gap oxide ferroelectrics based on charge
imbalance is described and illustrated by first principles studies of the
hypothetical compound Bi$_6$Ti$_4$O$_{17}$, which is an alternate stacking of
the ferroelectric Bi$_4$Ti$_3$O$_{12}$. We find that this compound is
ferroelectric, similar to Bi$_4$Ti$_3$O$_{12}$ although with a reduced
polarization. Importantly, calculations of the electronic structure with the
recently developed functional of Tran and Blaha yield a much reduced band gap
of 1.83 eV for this material compared to Bi$_4$Ti$_3$O$_{12}$. Therefore,
Bi$_6$Ti$_4$O$_{17}$ is predicted to be a low band gap ferroelectric material.
