  There are few known semiconductors exhibiting both strong optical response
and large dielectric polarizability. Inorganic materials with large dielectric
polarizability tend to be wide-band gap complex oxides. Semiconductors with
strong photoresponse to visible and infrared light tend to be weakly
polarizable. Interesting exceptions to these trends are halide perovskites and
phase-change chalcogenides. Here we introduce complex chalcogenides in the
Ba-Zr-S system in perovskite and Ruddlesden-Popper structures as a new family
of highly polarizable semiconductors. We report the results of impedance
spectroscopy on single crystals that establish BaZrS3 and Ba3Zr2S7 as
semiconductors with low-frequency relative dielectric constant (${\epsilon}_0$)
in the range 50 - 100, and band gap in the range 1.3 - 1.8 eV. Our electronic
structure calculations indicate the enhanced dielectric response in perovskite
BaZrS3 versus Ruddlesden-Popper Ba3Zr2S7 is primarily due to enhanced IR
mode-effective charges, and variations in phonon frequencies along $\langle 001
\rangle$; differences in the Born effective charges and the lattice stiffness
are of secondary importance. This combination of covalent bonding in crystal
structures more common to complex oxides results in a sizable Fr\"ohlich
coupling constant, which suggests that charge carriers are large polarons.
