Electrochemical capacitance of a leaky nano-capacitor

TL;DR

This paper presents a comprehensive quantum-theoretical analysis of electrochemical capacitance in leaky nanoscale capacitors, deriving new formulas for linear and nonlinear capacitance, and exploring the quantum-classical crossover.

Contribution

It introduces novel analytic expressions for both linear and nonlinear capacitance in leaky quantum capacitors, extending understanding beyond semiclassical models.

Findings

Quantum formula improves semiclassical analysis in tunneling regime

Nonlinear capacitance exhibits interesting behavior in leaky capacitors

Theory enables study of quantum to classical crossover as distance varies

Abstract

We report a detailed theoretical investigation on electrochemical capacitance of a nanoscale capacitor where there is a DC coupling between the two conductors. For this ``leaky'' quantum capacitor, we have derived general analytic expressions of the linear and second order nonlinear electrochemical capacitance within a first principles quantum theory in the discrete potential approximation. Linear and nonlinear capacitance coefficients are also derived in a self-consistent manner without the latter approximation and the self-consistent analysis is suitable for numerical calculations. At linear order, the full quantum formula improves the semiclassical analysis in the tunneling regime. At nonlinear order which has not been studied before for leaky capacitors, the nonlinear capacitance and nonlinear nonequilibrium charge show interesting behavior. Our theory allows the investigation of crossover of capacitance from a full quantum to classical regimes as the distance between the two conductors is changed.