  Two-dimensional materials and their heterostructures have emerged as a new
class of materials for not only fundamental physics but also for electronic and
optoelectronic applications. Black phosphorus (BP) is a relatively new addition
to this class of materials. Its strong in plane anisotropy makes BP a unique
material to make conceptually new type of electronic devices. However, the
global density of states (DOS) of BP in device geometry has not been measured
experimentally. Here we report the quantum capacitance measurements together
with conductance measurements on a hBN protected few layer BP ($\sim$ 6 layer)
in a dual gated field effect transistor (FET) geometry. The measured DOS from
our quantum capacitance is compared with the density functional theory (DFT).
Our results reveal that the transport gap for quantum capacitance is smaller
than that in conductance measurements due to the presence of localized states
near the band edge. The presence of localized states is confirmed by the
variable range hopping seen in our temperature-dependence conductivity. A large
asymmetry is observed between the electron and hole side. The asymmetric nature
is attributed to the anisotropic band dispersion of BP. Our measurements
establish the uniqueness of quantum capacitance in probing the localized states
near the band edge, hitherto not seen in the conductance measurements.
