Weakly nonlinear quantum transport: an exactly solvable model

TL;DR

This paper presents an exactly solvable model of weakly nonlinear quantum transport in a 2D quantum wire, revealing sign changes in non-linear conductance near resonance and addressing gauge invariance corrections.

Contribution

It introduces an exactly solvable model for weakly nonlinear quantum transport and derives analytical corrections to maintain gauge invariance.

Findings

Second order non-linear conductance changes sign near resonance.

Transport properties exhibit complete reflection at resonance energy.

Analytical gauge invariance corrections are derived for finite scattering regions.

Abstract

We have studied the weakly non-linear quantum transport properties of a two-dimensional quantum wire which can be solved exactly. The non-linear transport coefficients have been calculated and interesting physical properties revealed. In particular we found that as the incoming electron energy approaches a resonant point given by energy $E=E_r$, where the transport is characterized by a complete reflection, the second order non-linear conductance changes its sign. This has interesting implications to the current-voltage characteristics. We have also investigated the establishment of the gauge invariance condition. We found that for systems with a finite scattering region, correction terms to the theoretical formalism are needed to preserve the gauge invariance. These corrections were derived analytically for this model.