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Two-dimensional materials and their heterostructures have emerged as a newclass of materials for not only fundamental physics but also for electronic andoptoelectronic applications. Black phosphorus (BP) is a relatively new additionto this class of materials. Its strong in plane anisotropy makes BP a uniquematerial to make conceptually new type of electronic devices. However, theglobal density of states (DOS) of BP in device geometry has not been measuredexperimentally. Here we report the quantum capacitance measurements togetherwith conductance measurements on a hBN protected few layer BP ($\sim$ 6 layer)in a dual gated field effect transistor (FET) geometry. The measured DOS fromour quantum capacitance is compared with the density functional theory (DFT).Our results reveal that the transport gap for quantum capacitance is smallerthan that in conductance measurements due to the presence of localized statesnear the band edge. The presence of localized states is confirmed by thevariable range hopping seen in our temperature-dependence conductivity. A largeasymmetry is observed between the electron and hole side. The asymmetric natureis attributed to the anisotropic band dispersion of BP. Our measurementsestablish the uniqueness of quantum capacitance in probing the localized statesnear the band edge, hitherto not seen in the conductance measurements.

Probing 2D Black Phosphorus by Quantum Capacitance Measurements