Transmission probability through small interacting systems: application to a series of quantum dots

TL;DR

This paper investigates the transmission probability in small interacting quantum dot systems using a Kubo-based theory, focusing on the effects of Kondo phenomena and inter-dot correlations in different parameter regimes.

Contribution

It applies a previously developed transmission probability theory to a series of quantum dots modeled by the N-impurity Anderson model, including calculations with U^2 order self-energy and vertex corrections.

Findings

Transmission probability features depend on the ratio of inter-dot transfer to level broadening.

Kondo effect dominates in the t<Γ regime, affecting transmission.

Inter-dot correlations are significant in the t>Γ regime.

Abstract

We apply a theory for the transmission probability of small interacting systems, which was formulated based on the Kubo formalism in our previous study, to a series of quantum dots described by the N-impurity Anderson model. In this report, we present the transmission pobability for the system of N=2 calculated using the order $U^2$ self-energy and vertex corrections. Particularly, we examine the features in the two typical parameter regions, $t<\Gamma$ and $t>\Gamma$, where the Kondo effect or the inter-dot correlation dominates. Here, $t$ is the inter-dot transfer and $\Gamma$ is the level broadening caused by the coupling with the noninteracting leads.