Effective action and interaction energy of coupled quantum dots

TL;DR

This paper derives the effective action for coupled quantum dots modeled as Luttinger liquids, revealing resonance conditions, interaction energy dependence, and matching experimental data with a specific interaction parameter.

Contribution

It introduces a detailed theoretical model for coupled quantum dots as Luttinger liquids, providing explicit formulas for interaction energy and resonance conditions.

Findings

Resonance conditions form a hexagon in gate voltage space.

Interaction energy and peak-splitting depend on tunneling and charging energies.

Luttinger parameter K is estimated as 0.74 from experimental data.

Abstract

We obtain the effective action of tunnel-coupled quantum dots, by modeling the system as a Luttinger liquid with multiple barriers. For a double dot system, we find that the resonance conditions for perfect conductance form a hexagon in the plane of the two gate voltages controlling the density of electrons in each dot. We also explicitly obtain the functional dependence of the interaction energy and peak-splitting on the gate voltage controlling tunneling between the dots and their charging energies. Our results are in good agreement with recent experimental results, from which we obtain the Luttinger interaction parameter $K=0.74$.