Correlations in semiconductor quantum dots

Abstract

In this Thesis, I present a theoretical study of correlation effects in strongly interacting electronic and electron-hole systems confined in semiconductor quantum dots. I focus on three systems: N electrons in a two-dimensional parabolic confinement in the absence and in the presence of a magnetic field, an electron-hole pair confined in a vertically coupled double-quantum-dot molecule, and a charged exciton in a quantum-ring confinement in a magnetic field. To analyse these systems I use the exact diagonalisation technique in the effective-mass approximation. This approach consists of three steps: construction of a basis set of particle configurations, writing the Hamiltonian in this basis in a matrix form, and numerical diagonalisation of this matrix. Each of these steps is described in detail in the text. Using the exact diagonalisation technique I identify the properties of the systems due to correlations and formulate predictions of how these properties could be observed experimentally. I confront these predictions with results of recent photoluminescence and transport measurements. First I treat the system of N electrons in a parabolic confinement in the absence of magnetic field and demonstrate how its properties, such as magnetic moments, can be engineered as a function of the system parameters and the size of the Hilbert space. Next I analyse the evolution of the ground state of this system as a function of the magnetic field. In the phase diagram of the system I identify the spin-singlet nu = 2 phase and discuss how correlations influence its phase boundaries both as a function of the magnetic field and the number of electrons. I also demonstrate that in higher magnetic fields electronic correlations lead to the appearance of spin-depolarised phases, whose stability regions separate the weakly correlated phases with higher spin. Further on, I consider electron-hole systems. I show that the Coulomb interaction leads to entanglement of the states of an electron and a hole confined in a pair of vertically coupled quantum dots. Finally I consider the system of two electrons and one hole (a negatively charged exciton) confined in a quantum ring and in the presence of the magnetic field. I show that the energy of a single electron in the ring geometry exhibits the Aharonov-Bohm oscillations as a function of the magnetic field. In the case of the negatively charged exciton these oscillations are nearly absent due to correlations among particles, and as a result the photoluminescence spectra of the charged complex are dominated by the energy of the final-state electron. The Aharonov-Bohm oscillations of the energy of a single electron are thus observed directly in the optical spectra.