  All known proper ferroelectrics are unable to polarize normal to a surface or
interface if the resulting depolarization field is unscreened, but there is no
fundamental principle that enforces this behavior. In this work, we introduce
hyperferroelectrics, a new class of proper ferroelectrics which polarize even
when the depolarization field is unscreened, this condition being equivalent to
instability of a longitudinal optic mode in addition to the
transverse-optic-mode instability characteristic of proper ferroelectrics. We
use first principles calculations to show that several recently discovered
hexagonal ferroelectric semiconductors have this property, and we examine its
consequences both in the bulk and in a superlattice geometry.
