Time-dependent electronic transport and relaxation in nanoscale conductors

At the nanoscale, multifaceted time-dependent transport effects of charge carriers can occur. In general, these transport effects are the result of nonequilibrium conditions which tend towards the equilibrium state. The nature of the nonequilibrium conditions as well as the underlying system affect the transport of the charge carriers.
    In this thesis, we study the pair-amplitude dynamics in a superconductor-quantum dot hybrid and the propagation and relaxation of photoexcited electrons in a Fe/Au heterostructure as specific examples of nanoscale time-dependent transport.
    The pair-amplitude dynamics is studied in a single-level quantum dot which is coupled strongly to two superconducting leads. In addition, the dot is tunnel coupled to a normal conductor. The coupling to the superconductors induces superconducting correlations in form of a pair amplitude on the quantum dot. We describe the pair-amplitude dynamics with a real-time diagrammatics approach where all noninteracting degrees of freedom of the leads are integrated out. The diagrammatic method yields a master equation that describes the time evolution of the quantum dot in terms of its reduced density matrix.
    We consider two different nonequilibrium scenarios. First, a quench which starts rich pair-amplitude dynamics consisting of an oscillation arising from resonantly tunneling Cooper pairs and an exponential decay due to dissipative tunneling events between the dot and the normal conducting lead. Second, the system is externally driven to overcome the relaxation. We discuss the response of the pair amplitude in the adiabatic and in the the fast-driving limit. For both scenarios, we can excite oscillations of the pair amplitude with a large amplitude.
    To study the propagation and relaxation of photoexcited charge carriers in a Fe/Au heterostructure, we compute numerically the trajectories of electrons propagating from the Fe/Au interface to the Au surface. More precisely, the final energy and propagation time is determined within the framework of a Monte-Carlo simulation. Our work is motivated by recent experiments on a Fe/Au heterostructure. Here, the electrons are excited with a back-pump laser in the Fe layer, injected into the Au layer and finally measured by a probe laser on the Au surface. Due to the pump-probe method access to the ultrafast time evolution of the hot electron distribution is gained. Our results match with the experimental results on a qualitative level. With the detailed information about the relaxation and propagation dynamics in the simulation, it is then further possible to interpret the thickness dependence of the electron distribution.
    With our simulation, we are able to identify the transport regime of the electrons which is either ballistic or superdiffusive.
    In addition, we calculate the dynamics of the electron distribution in the same sample using the Boltzmann equation combined with diffusive transport. Due to the diffusive regime, the thickness dependence of the electron distribution changes significantly. Hence, thickness-dependent measurements are able to distinguish between the different transport regimes in the experiment. With both the simulation and the diffusive calculation, we get a full picture of the transport effects in the ballistic, superdiffusive and diffusive regime.


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