  The polarization and piezoelectric response of the BiTe$X$ ($X$=Cl, Br, and
I) layered tellurohalides are computed from first principles. The results
confirm a mixed ionic-covalent character of the bonding, and demonstrate that
the internal structure within each triple layer is only weakly affected by the
external stress, while the changes in the charge distribution with stress
produce a substantial negative piezoelectric response. This suggests a new
mechanism for negative piezoelectric response that should remain robust even in
ultra-thin film form in this class of materials.
