We report analytic results on quantum capacitance (Cq) measurements and their optical tuning in a dual-gated device with potassium-doped multi-layered black phosphorous (BP) as the channel material. The two-dimensional (2D) layered BP is highly anisotropic with a semi-Dirac dispersion marked by linear and quadratic contributions. The Cq calculations mirror this asymmetric arrangement. A further increase in the asymmetry and consequently Cq is predicted by photon-dressing the BP dispersion. To achieve this and tune Cq in a field-effect transistor (FET), we suggest a configuration wherein a pair of electrostatic (top) and optical (back) gates clamp a BP channel. The back gate shines an optical pulse to rearrange the dispersion of the 2D BP. Analytic calculations are done with Floquet Hamiltonians in the off-resonant regime. The value of such Cq calculations, in addition to its role in adjusting the current drive of an FET, is discussed in the context of metal-insulator and topological phase transitions and enhancements to the thermoelectric figure of merit.

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