Quantum capacitance: A microscopic derivation

We start from microscopic approach to many body physics and show the analytical steps and approximations required to arrive at the concept of quantum capacitance. These approximations are valid only in the semi-classical limit and the quantum capacitance in that case is determined by Lindhard function. The effective capacitance is the geometrical capacitance and the quantum capacitance in series, and this too is established starting from a microscopic theory.

Graphical AbstractWe prove from microscopic theory that in the semi-classical regime polarization charge and induced potential of an arbitrary quantum system are related by an effective capacitance Ceff.1Ceff=1C+1ηwhere, C   is geometric capacitance and ηη is quantum capacitance.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Several new concepts and ideas have developed in last few decades on nanoelectronics. ► They are essential for miniaturization of devices. Quantum capacitance is one such idea. ► We demonstrate that it can be derived microscopically in a certain regime including quantum and many body effects.