Hyperferroelectrics: Proper Ferroelectrics with Persistent Polarization

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.