Full Counting Statistics Of A Single Quantum Dot With Effective Nuclear-spin Magnetic Field

The controlled manipulation of the localized electron spins in semiconductor QDs is crit-ical for quantum information processing with confined electron spins. Recently, the hyperfineinteraction between localized electron and nuclear spins in the QDs has attracted much attenti-on since it is the dominant mechanism of electron spin relaxation in QDs at low temperature.Due to the random configuration of nuclear spins, the quantum transport properties of electro-ns through the QD system can be strongly affected by the orientation and magnitude of theeffective nuclear magnetic field. On the other hand, it has been theoretically and experiment-ally demonstrated that the full counting statistics (FCS) properties can allow one to identifythe intrinsic properties of the QD system and access the information of electron correlationbeyond what is obtainable from the differential conductance or the average current. Consequ-ently, the FCS of electron transport through the QD system can not only provide a deeperinsight into the nature of quantum transport mechanism, but also propose a new way to obtainthe information on the orientation and magnitude of effective nuclear-spin magnetic field. Inthe thesis,Firstly, we present the FCS formalism based on an effective particle number resolvedquantum master equation, and outline the procedure to calculate the first three current cumul-ants based on a spinless single-level QD system.Secondly, we study theoretically the full counting statistics of electron transport througha quantum dot weakly coupled to two ferromagnetic leads, in which an effective nuclear-spinmagnetic field originating from the configuration of nuclear spins is considered. It is demonst-rated that the orientation and magnitude of the effective nuclear magnetic field has no influen-ceon the average current; whereas that has a significant impact on the shot noise and skewness,especially for a relatively large spin polarizations of the two ferromagnetic electrodes and themagnitude of the effective nuclear magnetic field being smaller than the QD-electrode coup- ling. These characteristics can be used to detect the orientation and magnitude of the effectivenuclear magnetic field in the single QD, and provide some theoretical basis for further study-ing the decoherence mechanisms in the QD.Finally, we summarize the thesis.