Transport Properties of Multiple Quantum Dots Arranged in Parallel: Results from the Bethe Ansatz

TL;DR

This paper uses the Bethe Ansatz to exactly analyze transport properties in a double quantum dot system, revealing universal conductance behaviors, Kondo effects, and interference phenomena at zero and finite temperatures.

Contribution

It introduces an exactly solvable model for double quantum dots, enabling precise characterization of complex transport phenomena including Kondo effects and conductance interference.

Findings

Identification of RKKY Kondo effect and standard Kondo effect.

Observation of conductance zeros due to interference.

Quantitative analysis of transport features using exact solutions.

Abstract

In this paper we analyze transport through a double dot system connected to two external leads. Imagining each dot possessing a single active level, we model the system through a generalization of the Anderson model. We argue that this model is exactly solvable when certain constraints are placed upon the dot Coulomb charging energy, the dot-lead hybridization, and the value of the applied gate voltage. Using this exact solvability, we access the zero temperature linear response conductance both in and out of the presence of a Zeeman field. We are also able to study the finite temperature linear response conductance. We focus on universal behaviour and identify three primary features in the transport of the dots: i) a so-called RKKY Kondo effect; ii) a standard Kondo effect; and iii) interference phenomena leading to sharp variations in the conductance including conductance zeros. We are able to use the exact solvability of the dot model to characterize these phenomena quantitatively. While here we primarily consider a double dot system, the approach adopted applies equally well to N-dot systems.