  Tuning band gaps in two-dimensional (2D) materials is of great interest in
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 design and optimization of electronic and optoelectronic
devices. Here, based on the density-functional theory calculations, we
demonstrates that the donated electrons from K dopants are mostly localized at
the topmost BP layer and such a 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 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
${\Gamma}_{\rm 1c}$ (valence band minimum ${\Gamma}_{\rm 8v}$) downwards
(upwards). The present prediction of ${\Gamma}_{\rm 1c}$ and ${\Gamma}_{\rm
8v}$ 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 by 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.
