Theory of Charge Transport through Vibrating Molecules

In this Thesis we study several aspects of charge transport through single molecule junctions. Focusing on the interaction of the electrons with vibrations we devise toy-models which capture the consequences of many-body interactions for transport properties of the junction. We begin with the study of heating, cooling and stability of the molecular bridge. First, the dynamics of the vibrational mode is followed using the master equation. Using this approximate technique, we identify the regimes in which the electronic current is pumping energy into the vibrational mode, or alternatively, absorbing energy from it. An important conclusion of this study is that at large currents, the pumping of energy into vibrations may result in uncontrolled heating, making the structure unstable; Alternatively, at small biases, extraction of energy from vibrations is possible, resulting in a cooling behavior. We extend the model to include a dissipative environment, such as the vibrating backbone of the molecule or the solvent, and demonstrate that dissipation may alleviate structural instability. From the comparison of the behavior of a strongly anharmonic mode (two-level system) with a fully harmonic mode a surprising conclusion is reached: the cooling/heating analysis in both cases produces qualitatively similar results. Finally, we confirm the microscopic equivalent of the Second Law, the charge and energy Fluctuation Theorem, at the level of second order markovian master equation. In order to study exactly the vibration assisted electron transport through a donor-acceptor junction we develop a numerical scheme based on the influence functional path integral (INFPI) and quasi-adiabatic path integral (QUAPI) methods. With this tool, the results obtained with the perturbative kinetic master equation are confirmed validating the approximations used there. We further extend the model to include direct electronic tunneling. Encouraged by the similarity of transport behavior in harmonic and strongly anharmonic junctions, we compare the non-equilibrium Anderson-Holstein model of electron interacting with a harmonic mode to its variant, in which the infinite ladder of the harmonic mode is truncated. In this case, interestingly, the two models show significant differences: strong vibrational anharmonicity does not allow for the Franck-Condon blockade or current hysteresis effects found in the harmonic model. Instead, it introduces a novel many-body off-resonance blockade. We conclude with the study of electronic decoherence due to the interaction with vibrations. To this end, we consider three cases of electronic transport through a molecular junction: fully coherent (rigid molecule), fully dephased and purely inelastic. We demonstrate that the three cases produce characteristic energy profiles and may be distinguished from one another via the measurement of the thermopower.Ph.D