Quasiparticle energies, excitons, and optical spectra of few-layer black phosphorus

We report first-principles GW–Bethe–Salpeter-equation (BSE) studies of excited-state properties of few-layer black phosphorus (BP) (phosphorene). With improved GW computational methods, we obtained converged quasiparticle band gaps and optical absorption spectra by the single-shot (G₀W₀) procedure. Moreover, we reveal fine structures of anisotropic excitons, including the series of one-dimensional like wave functions, spin singlet–triplet splitting, and electron–hole binding energy spectra by solving BSE. An effective-mass model is employed to describe these electron–hole pairs, shedding light on estimating the exciton binding energy of anisotropic two-dimensional semiconductors without expensive ab initio simulations. Finally, the anisotropic optical response of BP is explained by using optical selection rules based on the projected single-particle density of states at band edges. (paper)