Theory of charge transport in molecular junctions: from Coulomb blockade to coherent tunneling

We study charge transport through molecular junctions in the presence of electron-electron interaction using the nonequilibrium Green's function techniques and the renormalized perturbation theory. In the perturbation treatment, the zeroth-order Hamiltonian of the molecular junction is composed of independent single-impurity Anderson's models, which act as the channels where charges come through or occupy, and the interactions between different channels are treated as the perturbation. Using this scheme, the effects of molecule-lead, electron-electron, and hopping interactions are included nonperturbatively, and the charge transport processes can thus be studied in the intermediate parameter range from the Coulomb blockade to the coherent tunneling regimes. The concept of quasi-particles is introduced to describe the kinetic process of charge transport, and then the electric current can be studied and calculated. As a test study, the Hubbard model is used as the molecular Hamiltonian to simulate dimeric and trimeric molecular junctions. Various nonlinear current-voltage characteristics, including Coulomb blockade, negative differential resistance, rectification, and current hysteresis, are shown in the calculations, and the mechanisms are elucidated.