Many-particle theory for time-dependent quantum transport in nanostructures

During the recent decades, molecular electronics has established its place as one of the promising fields in the nanoscience. The possibility to manufacture and control molecular junctions where single molecules are squeezed between the conducing electrodes has opened up new possibilities to develop nanoscale devices which could be employed as building blocks for future nanoelectronic applications. The driving force for this new branch of physics has been the experimental advances but also theoretical methods have been under intensive study and many theoretical tools have been developed to understand the electron transport processes in the nanoscale systems. This thesis focuses on developing a formalism that helps to understand the role of electron-electron interactions and the physical principles behind the time-dependent electron transport in such systems. The formalism presented in this thesis is based on the theory of non-equilibrium Green functions (NEGF) and, more specifically on the real-time propagation of the embedded Kadanoff-Baym (KB) equations which are quantum-kinetic equations for the oneparticle propagator. This formalism allows for studying ultrafast dynamical processes with femtosecond (fs) time resolution and have several advantages compared to other methods. The Kadanoff-Baym formalism can be applied to both open and closed systems. It allows for non-perturbative treatment of the external driving fields, suitable preparation of the initial state, inclusion of the initial correlation effect during timepropagation and, in addition, can deal with the electronic interactions via self-energy terms which guarantee that the conservation laws are obeyed. All these properties are vital for treating open and correlated systems associated to the physical phenomena such as electron transport. In this thesis, we apply the Kadanoff-Baym formalism to study time-dependent nonequilibrium processes of simple correlated molecular-like systems connected to electron reservoirs. We have found that the electron-electron interactions can have a major impact on the time-dependent and steady-state transport properties as well as on the spectral properties of the molecular device. The Coulomb interactions, when restricted to the scattering region only, can lead to a significant renormalization of the molecular gap in non-equilibrium conditions and can change the transient current flow considerably. Furthermore, the electronic self-energies, when treated on different levels of sophistication, can lead to very different temporal properties especially under the resonance conditions. As one of the essential results, we have also found that the initial correlation effects and initial state dependence, when accounted properly, can influence considerably on the transient dynamics. As one of the other main topics regarding the time-dependent transport, we also investigated the role of the Coulomb interactions between the molecular scattering region and the electron reservoirs. Our findings suggest that these interactions can have big impact on the dynamics of the molecular junction when driven out of equilibrium with a bias voltage. We found that the Coulomb interactions between the subsystems can also lead to strong renormalization of the resonances and change the transient and steady-state properties dramatically. In the mean-field level, however, the treatment of these lead interactions can give rise to current blockade and undamped post-transient dynamics where the system does not relax towards a steady-state. These peculiar effects can be cured with inclusion of the electron correlations which provide substantial damping to the transients and account for the important image-charge effects via polarization diagrams. Our results show that the lead interactions in general and the image charge effect can modify the current–voltage characteristics prominently and that these interactions can restrain the bias dependent quasiparticle broadening under non-equilibrium conditions