Dynamics and Fluctuations in Single-Electron Tunneling Devices

Abstract: In recent years, it has been routinely achieved to build nanoscale electronic devices, which generate current pulses carrying only a single elementary charge. Realizations of these single-electron emitters are based on time-dependently driven quantum dots, on single-electron turnstiles built from superconductor/normal-metal hybrid structures, and also on nanosystems employing Lorentzian voltage pulses or surface acoustic waves. In this thesis, we present theoretical studies of single-electron transport in nanoscale devices of this kind. A central focus, besides extending the understanding of the physics in these devices, is the development and application of complementary theoretical methods. This multi-method approach allows us to highlight the assets and limitations of different theories, to compare the accuracy of results and the necessary analytical/computational efforts, and, most importantly, to find novel and fruitful method combinations. In this thesis, we first propose a novel clocked spin-current source, which consists of a superconducting island tunnel coupled to two superconducting contacts via a ferromagnetic insulator layer. We demonstrate that this nanostructure can be operated as an emitter of a precise quantized spin current and we point out its working principle as well as its experimental feasibility. The second device we analyze is a single-electron source, which is built from an interacting quantum dot with tunnel coupling to a single contact. The single-electron emission is triggered by a slow time-dependent gate-voltage driving, and we present a comprehensive study of the noise spectrum of the emitted current signal. The noise contains information on the system's excitation spectrum and its dynamics, and it also reveals signatures of Coulomb interaction. To derive the noise spectra over a large frequency range, we extend a real-time diagrammatic perturbative method in the tunnel coupling to finite noise frequencies in the presence of the slow time-dependent drive. We then perform a harmonic decomposition of the noise spectra, present an interpretation of the noise in terms of individual fluctuation processes, and point out characteristic signatures for the interplay between Coulomb interaction and the time-dependent driving. Third, we turn to time-dependent density-functional theory, which is a numerical method, and we transfer insights from the diagrammatic calculations to this theory. This novel combination of methods allows us to develop a nonadiabatic (i.e. time-nonlocal) approximation of this theory's exchange-correlation potential. We relate properties of the exchange-correlation potential to physical time scales of the electron dynamics and we apply it to obtain numerical time evolutions of single and multiple quantum dots coupled to a shared electron reservoir. In addition, we extend this combination of methods to another nanosystem, namely an interacting quantum dot coupled to two contacts and exposed to time-dependent gate and bias voltages. The results presented in this part of the thesis constitute a significant step towards the application of time-dependent density-functional theory for the description of charge dynamics in complex single-electron tunneling devices.