Weakly Nonlinear AC Response: Theory and Application

TL;DR

This paper develops a comprehensive theoretical framework for analyzing weakly nonlinear AC electrical responses in quantum transport, emphasizing electron interactions and providing measurable predictions.

Contribution

It introduces a microscopic formalism that unifies linear and weakly nonlinear response theories, maintaining fundamental physical principles.

Findings

Derived dynamic conductance for weakly nonlinear regimes

Predicted nonlinear-nonequilibrium charge distribution

Established a measurable scaling relation for nonlinear capacitance

Abstract

We report a microscopic and general theoretical formalism for electrical response which is appropriate for both DC and AC weakly nonlinear quantum transport. The formalism emphasizes the electron-electron interaction and maintains current conservation and gauge invariance. It makes a formal connection between linear response and scattering matrix theory at the weakly nonlinear level. We derive the dynamic conductance and predict the nonlinear-nonequilibrium charge distribution. The definition of a nonlinear capacitance leads to a remarkable scaling relation which can be measured to give microscopic information about a conductor.