Quantum capacitance properties of the holes in planar germanium

Quantum capacitance of two-dimensional (2D) systems contains useful physical information. Here, we report a high sensitivity quantum capacitance measurement with an improved radio frequency superheterodyne bridge technique for probing the electronic characteristic of Ge/SiGe 2D hole gas (2DHG) at low temperatures and under a perpendicular magnetic field B_⊥. At low fields, a rapid decrease in quantum capacitance following $B⊥−3$ dependence is observed, indicating an abrupt change in chemical potential near the gate boundary at high frequencies; at high fields, a series of capacitance oscillations are observed due to the Landau quantization and Zeeman splitting of the Ge/SiGe 2DHG, where gate-dependent effective $g$ factor under B_⊥ is extracted. These results represent implementation of the high-precision capacitance measurement for exploring the physical properties of Ge/SiGe 2DHG.