Quantum dot studies with path integral Monte Carlo.

The purpose of this thesis is to investigate the properties of semiconductor quantum dots by applying a quantum Monte Carlo technique. In the quantum mechanical regime such systems exhibit a range of fascinating and potentially useful phenomena. It is found that path integral Monte Carlo is generally a powerful technique for evaluating finite temperature properties of quantum many-body systems. The method is outlined for the treatment of a single-particle system. The generalisation to N particles is explained while the appropriate symmetry of the wave functions is incorporated for identical particles. Inherent numerical problems which arise for fermions are considered. An efficient new method is introduced which significantly reduces the statistical errors for large numbers of fermions. The Monte Carlo procedure is adapted to allow the calculation of magnetic field dependent quantities. The question of the existence of a molecular analogue to a Wigner crystal in a quantum dot is investigated. The phase diagram for the six-electron system studied exhibits an ordered phase in the regime of weak electrostatic confinement and low temperature. The melting temperature of this phase is found to be enhanced by the presence of a perpendicularly applied magnetic field. The dimensionality of quantum dots is considered. The two-electron ground state undergoes a transition as the crossover between three and two dimensions is effected.