Nonlinear transport properties of quantum dot systems

Abstract

This work deals with the theoretical investigation and description of nonlinear electronic transport through coupled quantum dot systems by means of various approaches. The essential aspects are the consideration of the Coulomb interaction between the carriers and the quantum coherence during the resonant tunneling process. Both provide temporal correlations in the tunneling current which manifest themselves in a characteristic manner in the current fluctuations. This means that for a deeper understanding of transport processes it is necessary not only to consider the average current, but also the shot noise behavior. Typical for current-voltage characteristics of coupled quantum dot systems is the emergence of peaks. Their physical origin and dependencies on the system parameters is elaborately discussed by means of a master equation model. Furthermore, scenarios of sub-Poissonian and super-Poissonian noise are systematically presented and analyzed. Therein, the interplay between the Coulomb interaction and Pauli’s exclusion principle clearly emerges. For the quantum coherent description of transport with Coulomb interaction the Hartree-Fock approximation is considered. It provides reasonable results for the average current, but due to the neglect of quantum fluctuations the noise proves to be inadequate. In order to establish the connection between sequential and coherent tunneling, the mechanism of dephasing of the coherent transport process is investigated. The main focus here is on the comparison of different approaches without Coulomb interaction. In particular, the average current through two quantum dots coupled in series turns out to be independent of the degree of quantum coherence in the transport process. For weak and strong coupling between the quantum dots this also holds for the zero-frequency shot noise. However, for intermediate coupling strengths the noise is sensitive to coherence. Dephasing by elastic scattering in the framework of scattering matrix formalism indeed leads to the loss of the coherent features in the noise, but for sufficiently strong dephasing the limit of sequential tunneling cannot be reached within this approach. In order to fully characterize the transport process in this context the modern concept of full counting statistics is utilized. Particularly the third order cumulant shows a qualitatively similar dephasing behavior as the shot noise.