  The influence of carrier type on superconductivity has been an important
issue for understanding both conventional and unconventional superconductors
[1-7]. For elements that superconduct, it is known that hole-carriers govern
the superconductivity for transition and main group metals [8-10]. The role of
hole-carriers in elements that are not normally conducting but can be converted
to superconductors, however, remains unclear due to the lack of experimental
data. Here we report the first in-situ high pressure Hall effect measurements
on single crystal black phosphorus, measured up to ~ 50 GPa, and find a
correlation between the Hall coefficient and the superconducting transition
temperature (TC). Our results reveal that hole-carriers play a vital role in
developing superconductivity and enhancing TC. Importantly, we also find a
Lifshitz transition in the high-pressure cubic phase at ~17.2GPa, which
uncovers the origin of a puzzling valley in the superconducting TC-pressure
phase diagram. These results offer insight into the role of hole-carriers in
developing superconductivity in simple semiconducting solids under pressure.
