One-dimensional excitons in long phosphorene atomic chains

Abstract

The electronic structure of phosphorene atomic chains (PACs) embedded in various dielectric environments is studied theoretically by using a configuration interaction approach beyond the conventional double-excitation scheme. While the nominal single-particle gap of the PACs is shown to roughly obey an expected scaling law of ${L}^{\ensuremath{-}2}$, where $L$ measures the length of PACs, the quasiparticle shift is found to gradually converge to a value that is insensitive to the dielectric environment as $L$ increases. In the meantime, exciton binding energies are revealed to obey a simple scaling law of $0.96/(\ensuremath{\kappa}L)\ensuremath{-}0.02$, with $\ensuremath{\kappa}$ being the effective dielectric constant. As $L$ goes to infinity, the quasiparticle and excitonic effect are both found to be greatly suppressed as if the long-range electron-electron interactions are quenched in long PACs.