LAUSR

Using first-principles density functional theoretical analysis, we predict coexisting ferroelectric and semimetallic states in a two-dimensional monolayer of h-NbN subjected to an electric field and in-plane strain (ε). At strains close to ε=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 an electric field, and uncover a three-state (P=±P_{o}, 0) switching during which h-NbN passes through Dirac semimetallic 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 band gap) and exhibits a large electron-phonon coupling leading to anomalous dynamical charges. These insights will guide the search for electronic ferroelectrics, and our results on 2D h-NbN will stimulate development of piezofield effect transistors and devices based on the multilevel logic.