Origin of metallic ferroelectricity in group-V monolayer black phosphorus

Recent research has shown that monolayer black phosphorus (BP) can be metallic while sustaining spontaneous polarization. Using density-functional calculations and mean-field theory, we perform a systematic study on the origin of the metallic ferroelectricity in monolayer BP which is composed of only one element with a strong covalent bond. We find that, in contrast to ionic compounds, metallic monolayer BP exhibits lattice deformation between adjacent cells due to the covalent bond. This benefits the survival of spontaneous polarization despite the fact that the long-range Coulomb interactions between dipoles are screened by itinerant electrons. Through the orbital selective external potential method, we reveal that the strength of $s{p}^{3}$ hybridization of monolayer BP significantly impacts such lattice distortion and therefore the ferroelectricity. These findings significantly enrich our understanding of metallic polarization and provide insights to help discover novel ferroelectric materials.