Electron screening and strength of long-range Coulomb interactions in black phosphorene: From bulk to nanoribbon

Experimental observations of anisotropic tightly bound excitons in black phosphorene, and correlated phenomena such as room-temperature magnetically active edges in phosphorene nanoribbons (PNRs), sparked discussions on the controversial screening of the Coulomb interaction in phosphorene-based materials. In this way, we investigate the first-principles electronic screening of the long-range Coulomb interaction in black phosphorene from bulk to nanoribbon by employing ab initio calculations in conjunction with the constrained random-phase approximation. The bands near the Fermi energy (EF) are predominantly pz orbital characters, and due to the puckering, they are not well separated from the other bands with s, pₓ, and especially py characters. This proximity in energy levels increases the contribution of pₓ/py4pt0ex→4pt0expz transitions to the polarization function and significantly alters the Coulomb parameters. In semiconducting systems, the on-site Coulomb interaction values (Hubbard U) range from 4.1 to 6.5 eV and depend on the correlated subspace, electronic structure, nanoribbon's width, and edge passivation. We find an anisotropic behavior of long-range Coulomb interaction along the zigzag and armchair directions in black phosphorene at the static limit. Our long-range interaction has revealed a nonconventional screening in semiconducting nanoribbons. We have discovered that screening actually enhances the electron-hole interaction for separations larger than a critical distance rc, which is contrary to what was previously seen in conventional semiconductors. This unique ``antiscreening'' region helps to explain the large experimentally extrapolated exciton binding energies of PNRs. In unpassivated zigzag nanoribbons, due to a metallic screening channel stemming from quasi-flat-edge bands at EF, we find U/Wb>1 (the bandwidth Wb) and large gradient of intersite Coulomb interactions, making them correlated materials. We have investigated the instability of the paramagnetic state of bare zigzag PNRs toward ferromagnetism using a Stoner model based on the calculated Hubbard U parameters.