Spineffekter i cirkelsymmetriska kvantpunkter

In semiconductor quantum dots, the motion of the electrons is restricted to a finite region of a two-dimensional semiconductor-semiconductor or semiconductor-insulator interface. Technologically, these systems provide interesting possibilities, for example, for future data processing applications where spin effects are utilized. Perhaps the most ambitious proposal is a spin-based quantum computer that utilizes tunable exchange interaction. Experimentalists have managed to get singlet-triplet transitions by tuning the confinement potential voltage in asymmetric quantum dots. Theoretically, some circularly symmetric quantum dots have a spin structure similar to the flux-penetrated ferromagnetic Heisenberg model, whereas other circular systems have a spin structure similar to the antiferromagnetic Heisenberg model. In this Master's Thesis, semiconductor quantum dots with different circularly symmetric confinement potentials were studied numerically in a wide range of magnetic field values. In addition to parabolic dots and rings, systems with other kinds of circularly symmetric confinement potentials were also studied. The emphasis of the study was on spin effects and differences between the systems. The studies were restricted to two-, four-, and six-electron systems. The calculations were done using the exact diagonalization (ED) and the variational quantum Monte Carlo (VMC) methods. The ED calculations were done with Landau-level mixing included, and the VMC calculations using single-configuration trial wave functions of the Slater-Jastrow type. The VMC method gave ground state energy values at most about two percent higher than the ED method, and mostly the agreement was considerably better. However, the VMC method failed almost completely to give the right spin ground states of the considered systems. The most important result of this Master's Thesis was the observation of an interesting spin phase structure in a parabolic quantum dot with a tunable perturbation. The phase diagram consisted of several distinct regions with spin structures similar to that predicted by the flux-penetrated ferromagnetic or antiferromagnetic Heisenberg model. The phase transitions were described using properties of the Laughlin and Halperin wave functions. A coupled dot-ring system had a clearly different spin structure than the dots and rings considered