Lattice Green's function approach to the solution of the spectrum of an array of quantum dots and its linear conductance

TL;DR

This paper develops a Green's function method to analyze the electronic spectrum and conductance of quantum dot arrays, providing exact solutions for perfect and defective configurations, and setting the stage for including interactions.

Contribution

It introduces a lattice Green's function approach to compute the spectrum and conductance of quantum dot arrays with and without defects, advancing theoretical tools for nanoscale transport analysis.

Findings

Exact Green's functions derived for perfect and defective arrays

Expressions for linear conductance in different configurations

Illustrative calculations for three-atom quantum dots

Abstract

In this paper we derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an attached adatom are derived. The expressions for the linear conductance for the perfect array as well as for the array with a defect are presented. The calculations are illustrated for a dot made of three atoms. The results derived here are also the starting point to include the effect of electron-electron and electron-phonon interactions on the transport properties of quantum dot arrays. Different derivations of the exact lattice Green's functions are discussed.