  The electronic structure evolutions of few-layer black phosphorus (BP) under
pressure shows a wealth of phenomena, such as the nonmonotonic change of direct
gap at the {\Gamma} point, the layer-number dependence, and the distinct
responses to normal and hydrostatic pressures. A full and unified understanding
to these rich phenomena remains lacking. Here, we provide a unified
understanding from the competition between interlayer quasi-bonding (QB)
interactions and intralayer chemical bonding interactions. The former decreases
while the latter increases the band gap under pressure and the origin can be
correlated to different combinations of inter- and intra-layer antibonding or
bonding interactions at the band edges. More interestingly, the interlayer QB
interactions are a coexistence of two categories of interactions, namely, the
coexistence of interactions between bands of the same occupancy
(occupied-occupied and empty-empty interactions) and of different occupancies
(occupied-empty interaction); and, the overall effect is a four-level
interaction, which explains the anomalous interlayer-antibonding feature of the
conduction band edge of bilayer BP. Our current study lay the foundation for
the electronic structure tuning of two-dimensional (2D) BP, and, our analysis
method for multi-energy-level interactions can be applied to other 2D
semiconductor homo- and hetero-structures that have occupied-empty interlayer
interactions.
