Doping of semiconductors by impurity atoms enabled their widespread technological application in microelectronics and optoelectronics. However, doping has proven elusive for strongly confined colloidal semiconductor nanocrystals because of the synthetic challenge of how to introduce single impurities, as well as a lack of fundamental understanding of this heavily doped limit under strong quantum confinement. We developed a method to dope semiconductor nanocrystals with metal impurities, enabling control of the band gap and Fermi energy. A combination of optical measurements, scanning tunneling spectroscopy, and theory revealed the emergence of a confined impurity band and band-tailing. Our method yields n- and p-doped semiconductor nanocrystals, which have potential applications in solar cells, thin-film transistors, and optoelectronic devices.

Current nonequilibrium Monte Carlo methods suffer from a dynamical sign problem that makes simulating real-time dynamics for long times exponentially hard. We propose a new 'Inchworm Algorithm', based on iteratively reusing information obtained in previous steps to extend the propagation to longer times. The algorithm largely overcomes the dynamical sign problem, changing the scaling from exponential to quadratic. We use the method to solve the Anderson impurity model in the Kondo and mixed valence regimes, obtaining results both for quenches and for spin dynamics in the presence of an oscillatory magnetic field.

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Memory effects play a key role in the dynamics of strongly correlated systems driven out of equilibrium. In the present study, we explore the nature of memory in the nonequilibrium Anderson impurity model. The Nakajima-Zwanzig-Mori formalism is used to derive an exact generalized quantum master equation for the reduced density matrix of the interacting quantum dot, which includes a non-Markovian memory kernel. A real-time path integral formulation is developed, in which all diagrams are stochastically sampled in order to numerically evaluate the memory kernel. We explore the effects of temperature down to the Kondo regime, as well as the role of source-drain bias voltage and band width on the memory. Typically, the memory decays on timescales significantly shorter than the dynamics of the reduced density matrix itself, yet under certain conditions it develops a smaller long tail. In addition we address the conditions required for the existence, uniqueness and stability of a steady-state.

The interplay between interference effects and electron-electron interactions in electron transport through an interacting double quantum dot system is investigated using a hierarchical quantum master equation approach which becomes exact if carried to infinite order and converges well if the temperature is not too low. Decoherence due to electron-electron interactions is found to give rise to pronounced negative differential resistance, enhanced broadening of structures in current-voltage characteristics, and an inversion of the electronic population. Dependence on gate voltage is shown to be a useful method of distinguishing decoherence-induced phenomena from effects induced by other mechanisms such as the presence of a blocking state. Comparison of results obtained by the hierarchical quantum master equation approach to those obtained from the Born-Markov approximation to the Nakajima-Zwanzig equation and from the noncrossing approximation to the nonequilibrium Green's function reveals the importance of an interdot coupling that originates from the energy dependence of the conduction bands in the leads and the need for a systematic perturbative expansion.