Electron and nuclear spins in semiconductor quantum dots

The electron and nuclear spin degrees of freedom in two-dimensional semiconductor quantum dots are studied as important resources for such fields as spintronics and quantum information. The coupling of electron spins to their orbital motion, via the spinorbit interaction, and to nuclear spins, via the hyperfine interaction, are important for understanding spin-dynamics in quantum dot systems. This work is concerned with both of these interactions as they relate to two-dimensional semiconductor quantum dots. We first consider the spin-orbit interaction in many-electron quantum dots, studying its role in conductance fluctuations. We further explore the creation and destruction of spin-polarized currents by chaotic quantum dots in the strong spin-orbit limit, finding that even without magnetic fields or ferromagnets (i.e., with time reversal symmetry) such systems can produce large spin-polarizations in currents passing through a small number of open channels. We use a density matrix formalism for transport through quantum dots, allowing consideration of currents entangled between different leads, which we show can have larger fluctuations than currents which are not so entangled. Second, we consider the hyperfine interaction between electrons and approximately 106 nuclei in two-electron double quantum dots. The nuclei in each dot collectively form an effective magnetic field interacting with the electron spins. We show that a procedure originally explored with the intent to polarize the nuclei can also equalize the effective magnetic fields of the nuclei in the two quantum dots or, in other parameter regimes, can iii