Two mesoscopic models of two interacting electrons

TL;DR

This paper analyzes two mesoscopic models of interacting electrons, providing exact scattering matrices and revealing how on-site interactions can filter specific electron spin states in quantum dot systems.

Contribution

It introduces exact solutions for two-electron scattering in two mesoscopic models, highlighting the filtering effect of on-site interactions on spin states.

Findings

Exact two-particle scattering matrices derived

On-site Coulomb interaction filters spin-singlet states

Models relevant for two-electron scattering experiments

Abstract

We study two simple mesoscopic models of interacting two electrons; first one consists of two quantum coherent parallel conductors with long-range Coulomb interaction in some localized region and the other is of an interacting quantum dot (QD) side-coupled to a noninteracting quantum wire. We evaluate exact two-particle scattering matrix as well as two-particle current which are relevant in a two-particle scattering experiment in these models. Finally we show that the on-site repulsive interaction in the QD filters out the spin-singlet two-electron state from the mixed two-electron input states in the side-coupled QD model.