Microscopic mechanism of the tunable band gap in potassium-doped few-layer black phosphorus

Abstract

Tuning band gaps in two-dimensional (2D) materials is of great interest for the fundamental and practical aspects of contemporary material sciences. Recently, black phosphorus (BP) consisting of stacked layers of phosphorene was experimentally observed to show a widely tunable band gap by means of the deposition of potassium (K) atoms on the surface, thereby allowing great flexibility in the design and optimization of electronic and optoelectronic devices. Here, based on density-functional theory calculations, we demonstrates that the donated electrons from K dopants are mostly localized in the topmost BP layer and this surface charging efficiently screens the K ion potential. It is found that, as the K doping increases, the extreme surface charging and its screening of K atoms shift the conduction bands down in energy, i.e., towards a higher binding energy, because they have more charge near the surface, while it has little influence on the valence bands having more charge in the deeper layers. This result provides a different explanation for the observed tunable band gap compared to the previously proposed giant Stark effect where a vertical electric field from the positively ionized K overlayer to the negatively charged BP layers shifts the conduction band minimum ${\mathrm{\ensuremath{\Gamma}}}_{1\mathrm{c}}$ (valence band minimum ${\mathrm{\ensuremath{\Gamma}}}_{8\mathrm{v}}$) downwards (upwards). The present prediction of ${\mathrm{\ensuremath{\Gamma}}}_{1\mathrm{c}}$ and ${\mathrm{\ensuremath{\Gamma}}}_{8\mathrm{v}}$ as a function of the K doping reproduces well the widely tunable band gap, anisotropic Dirac semimetal state, and band-inverted semimetal state, as observed in an angle-resolved photoemission spectroscopy experiment. Our findings shed new light on a route for tunable band gap engineering of 2D materials through the surface doping of alkali metals.