Current conservation in two-dimensional AC-transport

TL;DR

This paper investigates current conservation in a 2D quantum wire under AC fields, revealing the need for correction terms in scattering matrix calculations and analyzing their behavior near subband energies.

Contribution

The authors derived analytical correction terms for current conservation in 2D quantum wires, extending previous models and explaining deviations observed in numerical studies.

Findings

Correction terms are necessary for accurate current conservation calculations.

Near the first subband, results match 1D cases.

Corrections diverge as energy approaches higher subbands.

Abstract

The electric current conservation in a two-dimensional quantum wire under a time dependent field is investigated. Such a conservation is obtained as the global density of states contribution to the emittance is balanced by the contribution due to the internal charge response inside the sample. However when the global partial density of states is approximately calculated using scattering matrix only, correction terms are needed to obtain precise current conservation. We have derived these corrections analytically using a specific two-dimensional system. We found that when the incident energy $E$ is near the first subband, our result reduces to the one-dimensional result. As $E$ approaches to the $n$-th subband with $n>1$, the correction term diverges. This explains the systematic deviation to precise current conservation observed in a previous numerical calculation.