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

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.