Quantum capacitance: a microscopic derivation

TL;DR

This paper derives the concept of quantum capacitance from a microscopic many-body physics perspective, clarifying its relation to the Lindhard function and the classical geometrical capacitance.

Contribution

It provides a detailed microscopic derivation of quantum capacitance, connecting it explicitly to the Lindhard function and semi-classical approximations.

Findings

Quantum capacitance is linked to the Lindhard function.

Effective capacitance is the series combination of geometrical and quantum capacitances.

Derivation is valid in the semi-classical limit.

Abstract

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.