Comparative Study of Time-Dependent Theories applied to Charge Transport through Molecular Junctions

This thesis deals with numerical investigations of charge transport through molecular junctions, where the latter are to be understood as single molecules sandwiched between two leads, acting as active circuit elements. The model used to describe such a device is a linear chain of tight-binding sites coupled to external fermionic leads, where the mentioned sites mimic those molecular orbitals relevant to charge transport. To this end, we discuss several techniques for describing quantum systems coupled to fermionic reservoirs. Specifically, we deal with three different formalisms: quantum master equations, derived in a perturbative manner with respect to coupling to reservoirs, the hierarchical equations of motion approach and a scheme based on timedependent nonequilibrium Green's functions. These theories are all suited to describe time-dependent effects in molecular junctions and deliver the occupation-number dynamics of molecular sites as well as the time-dependent electron current through the device. Our contribution on the theoretical side is twofold. First, we treat the derivation of master equations in great detail. This allows us to achieve a good understanding of the abstract quantities involved and also to shed light on the strengths and limitations of this approach. Second, we write the final equations of the aforementioned methods in a unified notation, which allows to better grasp similarities and further ignites a comparative discussion with the goal of choosing the most suited scheme for our envisaged numerical simulations. On the numerical side, the three schemes mentioned above were implemented in computer programs. We performed a direct comparison of the methods for the single resonant level (e.g. the ground state of a molecule or a quantum dot), where we showed the limitations of the quantum master equations, due to their intrinsic perturbative nature. For this system our findings are in agreement with other works in the literature. The key point of this thesis is represented by numerical simulations performed for a rather realistic system. In effect, the set-up is given by a molecule contacted by external leads and placed in an aqueous environment, thus being subject to the fluctuations of the solvent molecules. These external fluctuations lead to incoherent effects and influence the electron transport properties. Speciffically, we deal with a double-stranded DNA heptamer. By means of classical molecular dynamics simulations followed by quantum chemistry calculations one obtains time series of on-site energies and effective inter-site couplings. We use these trajectories to compute the electric current through the molecular junction, adopting the above mentioned Green's functions method. Its outcomes are compared with the yields of the snapshot-averaged Landauer-Buttiker approach, which is often used in related studies. Among other findings, we show that for scenarios with rapidly fluctuating system parameters (e.g. in the femtosecond range)the dominant transfer mechanism is sequential transport, since on such a time scale the system is usually not able to reach the steady state.