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We report analytic results on quantum capacitance (C$_{q}$) measurements andtheir optical tuning in dual-gated device with potassium-doped multi-layeredblack phosphorous (BP) as the channel material. The two-dimensional (2D)layered BP is highly anisotropic with a semi-Dirac dispersion marked by linearand quadratic contributions. The C$_{q}$ calculations mirror this asymmetricarrangement. A further increase to the asymmetry and consequently C$_{q}$ ispredicted by photon-dressing the BP dispersion. To achieve this and tuneC$_{q}$ in a field-effect transistor (FET), we suggest a configuration whereina pair of electrostatic (top) and optical (back) gates clamp a BP channel. Theback gate shines an optical pulse to rearrange the dispersion of the 2D BP.Analytic calculations are done with Floquet Hamiltonians in the off-resonantregime. The value of such C$_{q}$ calculations, in addition, to its role inadjusting the current drive of an FET is discussed in context ofmetal-insulator and topological phase transitions and enhancements to thethermoelectric figure of merit.

Anisotropy-driven quantum capacitance in multi-layered black phosphorus