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Using first-principles density functional theoretical analysis, we predictcoexisting ferroelectric and semi-metallic states in two-dimensional monolayerof h-NbN subjected to electric field and in-plane strain ($\epsilon$). Atstrains close to $\epsilon$=4.85%, where its out-of-plane spontaneouspolarization changes sign without inverting the structure, we demonstrate ahysteretic response of its structure and polarization to electric field, anduncover a three-state (P=$\pm$P$_o$Po, 0) switching during which h-NbN passesthrough Dirac semi-metallic states. With first-principles evidence for acombination of electronic and phononic ferroelectricity, we present a simplemodel that captures the energetics of coupled electronic and structuralpolarization, and show that electronic ferroelectricity arises in a materialwhich is highly polarizable (small bandgap) and exhibits a largeelectron-phonon coupling leading to anomalous dynamical charges. These insightswill guide search for electronic ferroelectrics, and our results on 2D h-NbNwill stimulate development of piezo-field effect transistors and devices basedon the multi-level logic.

Prediction of Coupled Electronic and Phononic Ferroelectricity in Strained 2D h-NbN: First-principles Theoretical Analysis