Nonlinear Quantum Capacitance

TL;DR

This paper investigates the nonlinear voltage dependence of electrochemical capacitance in nano-scale conductors, deriving an exact capacitance-voltage relation and proposing a quantum scanning capacitance microscopy technique.

Contribution

It provides a novel exact expression for capacitance-voltage behavior and introduces a method to infer local spectral functions in nano-scale conductors.

Findings

Derived an exact capacitance-voltage expression for parallel plate systems.

Proposed a quantum scanning capacitance microscopy technique.

Showed the potential to deduce local spectral functions from capacitance measurements.

Abstract

We analyze the nonlinear voltage dependence of elelctrochemical capacitance for nano-scale conductors. This voltage dependence is due to finite density of states of the conductors. We derive an exact expression for the electrochemical capacitance-voltage curve for a parallel plate system. The result suggests a quantum scanning capacitance microscopy at the nano-scale: by inverting the capacitance-voltage expression one is able to deduce the local spectral function of the nano-scale conductor.