Electronic Green's functions in a T-shaped multi-quantum dot system

TL;DR

This paper develops a comprehensive method to calculate electronic Green's functions in T-shaped multi-quantum dot systems, accounting for Coulomb interactions and tunneling, with implications for quantum computing applications.

Contribution

It introduces a generalized set of equations for Green's functions in multi-quantum dot systems, including finite Coulomb interactions and interdot tunneling, beyond traditional approximations.

Findings

Important corrections in Green's functions due to Coulomb interactions.

Method applicable to Coulomb blockade regime.

Potential use in quantum dot qubit systems.

Abstract

We developed a set of equations to calculate the electronic Green's functions in a T-shaped multi-quantum dot system using the equation of motion method. We model the system using a generalized Anderson Hamiltonian which accounts for {\em finite} intradot on-site Coulomb interaction in all component dots as well as for the interdot electron tunneling between adjacent quantum dots. Our results are obtained within and beyond the Hartree-Fock approximation and provide a path to evaluate all the electronic correlations in the multi-quantum dot system in the Coulomb blockade regime. Both approximations provide information on the physical effects related to the finite intradot on-site Coulomb interaction. As a particular example for our generalized results, we considered the simplest T-shaped system consisting of two dots and proved that our approximation introduces important corrections in the detector and side dots Green's functions, and implicitly in the evaluation of the system's transport properties. The multi-quantum dot T-shaped setup may be of interest for the practical realization of qubit states in quantum dots systems.