Environmental Screening Effects in 2D Materials: Renormalization of the Bandgap, Electronic Structure, and Optical Spectra of Few-Layer Black Phosphorus.

Few-layer black phosphorus has recently emerged as a promising 2D semiconductor, notable for its widely tunable bandgap, highly anisotropic properties, and theoretically predicted large exciton binding energies. To avoid degradation, it has become common practice to encapsulate black phosphorus devices. It is generally assumed that this encapsulation does not qualitatively affect their optical properties. Here, we show that the contrary is true. We have performed ab initio GW and GW plus Bethe-Salpeter equation (GW-BSE) calculations to determine the quasiparticle (QP) band structure and optical spectrum of one-layer (1L) through four-layer (4L) black phosphorus, with and without encapsulation between hexagonal boron nitride and sapphire. We show that black phosphorus is exceptionally sensitive to environmental screening. Encapsulation reduces the exciton binding energy in 1L by as much as 70% and completely eliminates the presence of a bound exciton in the 4L structure. The reduction in the exciton binding energies is offset by a similarly large renormalization of the QP bandgap so that the optical gap remains nearly unchanged, but the nature of the excited states and the qualitative features of the absorption spectrum change dramatically.