Addition spectrum of the conductance in 2-dimensional arrays of quantum dots

Abstract

We investigate the conductance spectrum to study systematically the relevant parameters in the Hamiltonian of a random two-dimensional network of quantum dots (QDs), represented as boxes containing one double-degenerate level and weakly coupled to two leads, L and R. The Hamiltonian of the system is defined using the extended-Hubbard model, where we include inter- and intra-dot ( U) Coulomb interactions and inter-dot hopping. These parameters, that determine the correlation between the electrons, are varied in different simulations and the effects on the addition spectrum in the conductance analysed. Exact diagonalisation is used to calculate the eigenstates of arrays containing several QDs and the conductance addition spectrum is calculated using the Beenakker approach. The systematic study shows that some of the features in the conductance spectra of multiple dots systems are predictable: the conductance peaks have a linear shift with the Coulomb inter- and intra-dot interactions, their amplitude converges as a function of the hopping parameter and the shape of the peaks depends (for low T regime) on T, determining their width. A resonance in the peak amplitude vs. U curve was observed.