  Using first-principles density functional theoretical analysis, we predict
coexisting ferroelectric and semi-metallic states in two-dimensional monolayer
of h-NbN subjected to electric field and in-plane strain ($\epsilon$). At
strains close to $\epsilon$=4.85%, where its out-of-plane spontaneous
polarization changes sign without inverting the structure, we demonstrate a
hysteretic response of its structure and polarization to electric field, and
uncover a three-state (P=$\pm$P$_o$Po, 0) switching during which h-NbN passes
through Dirac semi-metallic states. With first-principles evidence for a
combination of electronic and phononic ferroelectricity, we present a simple
model that captures the energetics of coupled electronic and structural
polarization, and show that electronic ferroelectricity arises in a material
which is highly polarizable (small bandgap) and exhibits a large
electron-phonon coupling leading to anomalous dynamical charges. These insights
will guide search for electronic ferroelectrics, and our results on 2D h-NbN
will stimulate development of piezo-field effect transistors and devices based
on the multi-level logic.
