Time-dependent transport through single molecules: nonequilibrium Greens functions and TDDFT

The nomenclature quantum transport has been coined for the phenomenon of electron motion through constrictions of transverse dimensions smaller than the electron wavelength, e.g., quantum-point contacts, quantum wires, molecules, etc. To describe transport properties on such a small scale, a quantum theory of transport is required. In this section we focus on quantum transport problems whose experimental setup is schematically displayed in Fig. 1a. A central region of mesoor nano-scopic size is coupled to two metallic electrodes which play the role of charge reservoirs. The whole system is initially in a well defined equilibrium configuration, described by a unique temperature and chemical potential (thermodynamic consistency). No current flows through the junction, the charge density of the electrodes being perfectly balanced. As originally proposed by Cini [1], we may drive the system out of equilibrium by exposing the electrons to an external timedependent potential which is local in time and space. For instance, we may switch on an electric field by putting the system between two capacitor plates far away from the system boundaries, see Fig. 1b. The dynamical formation of dipole layers screens the potential-drop along the electrodes and the total potential turns out to be uniform in the left and right bulks. Accordingly, the potential-drop is entirely limited to the central region. As the system size increases the remote parts are less disturbed by the junction and the density inside the electrodes approaches the equilibrium bulk-density. There has been considerable activity to describe transport through these systems on an ab initio level. Most approaches are based on a self-consistency procedure first proposed by Lang [2]. In this steady-state approach based on density functional theory (DFT), exchange and correlation is approximated by the static local-density potential and the charge density is obtained selfconsistently in the presence of the steady current. However, the original justification involved subtle points such as different Fermi levels deep inside the left and right electrodes and the implicit reference of non-local perturbations such as tunneling Hamiltonians within a DFT framework. (For a