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

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.