  By taking account of the electric-field-induced charge screening, a
self-consistent calculation within the framework of the tight-binding approach
is employed to obtain the electronic band structure of gated multilayer
phosphorene and the charge densities on the different phosphorene layers. We
find charge density and screening anomalies in single-gated multilayer
phosphorene and electron-hole bilayers in dual-gated multilayer phosphorene.
Due to the unique puckered lattice structure, both intralayer and interlayer
charge screenings are important in gated multilayer phosphorene. We find that
the electric-field tuning of the band structure of multilayer phosphorene is
distinctively different in the presence and absence of charge screening. For
instance, it is shown that the unscreened band gap of multilayer phosphorene
decreases dramatically with increasing electric-field strength. However, in the
presence of charge screening, the magnitude of this band-gap decrease is
significantly reduced and the reduction depends strongly on the number of
phosphorene layers. Our theoretical results of the band-gap tuning are in good
agreement with recent experiments.
