Below you will find the complete set of materials constituting my PhD thesis, "Correlations in semiconductor quantum dots". The thesis is comprised of a series of eight papers, and all of them are provided here for download.
In this Thesis we present a theoretical study of correlation effects in strongly interacting electronic and electron-hole systems confined in semiconductor quantum dots. We 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 we 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 we identify the properties of our systems due to correlations and formulate predictions of how these properties could be observed experimentally. We confront these predictions with results of recent photoluminescence and transport measurements.
First we 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 we analyse the evolution of the ground state of this system as a function of the magnetic field. In the phase diagram of the system we 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.
We 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 we consider electron-hole systems. We 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 we 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. We 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.
Thesis contents
Download the full text in a single file
(PDF, 3969 kB)
| Abstract | i | |||
| Sommaire | iii | |||
| Acknowledgements | v | |||
| List of Acronyms | x | |||
| List of Figures | xvi | |||
| Plan of the Thesis and Statement of Originality | 1 | |||
| Download the preliminaries as a single file (PDF, 209 kB) | ||||
| 1 | Introduction | 8 | ||
| 1.1 | Elementary properties of quantum dots | 8 | ||
| 1.2 | Quantum-dot density of states | 10 | ||
| 1.3 | Fabrication of quantum dots | 15 | ||
| 1.3.1 | Gated quantum-dot devices | 16 | ||
| 1.3.2 | Self-assembled quantum dots | 22 | ||
| 1.3.3 | Quantum rings | 30 | ||
| 1.4 | Spectroscopy | 33 | ||
| 1.4.1 | Photoluminescence experiment | 33 | ||
| 1.4.2 | Tunneling experiment | 35 | ||
| 1.5 | Electronic correlations in QDs: overview of the field and scientific contributions of this thesis |
41 | ||
| Download the first chapter as a single file (PDF, 1324 kB) | ||||
| 2 | Single-particle states in typical quantum-dot confinements | 48 | ||
| 2.1 | Parabolic lateral confinement | 49 | ||
| 2.2 | Confinement of the quantum disk | 57 | ||
| 2.2.1 | Quantum disk in the absence of the magnetic field | 58 | ||
| 2.2.2 | Quantum disk in finite magnetic fields | 61 | ||
| 2.3 | Confinement of the quantum ring | 68 | ||
| Download the second chapter as a single file (PDF, 766 kB) | ||||
| 3 | Methods of analysis of confined many-particle systems | 72 | ||
| 3.1 | The problem of many interacting particles in a QD confinement | 73 | ||
| 3.1.1 | The many-particle Hamiltonian | 73 | ||
| 3.1.2 | Coulomb matrix elements in the harmonic-oscillator basis | 75 | ||
| 3.2 | The Hartree-Fock method | 81 | ||
| 3.3 | The exact diagonalisation approach | 84 | ||
| 3.3.1 | Notation and choice of basis | 85 | ||
| 3.3.2 | Exact diagonalisation method optimised for parabolic lateral confinements | 89 | ||
| 3.3.3 | Creation of the Hamiltonian matrix | 95 | ||
| 3.3.4 | Diagonalisation of large and sparse matrices | 102 | ||
| 3.4 | Other methods accounting for electronic correlations | 118 | ||
| 3.4.1 | Spin density functional theory | 120 | ||
| 3.4.2 | Monte Carlo methods | 125 | ||
| Download the third chapter as a single file (PDF, 618 kB) | ||||
| 4 | Electronic correlations as a function of the confinement energy | 132 | ||
| Download the fourth chapter as a single file (PDF, 361 kB) | ||||
| 5 | Electronic correlations as a function of the magnetic field | 140 | ||
| 5.1 | Collapse of the ν=2 phase of the quantum Hall droplet | 141 | ||
| 5.2 | Pairing of spin excitations in high magnetic fields | 152 | ||
| Download the fifth chapter as a single file (PDF, 589 kB) | ||||
| 6 | Correlations in a coupled quantum-dot molecule | 158 | ||
| 6.1 | Single-particle states of the QD molecule | 159 | ||
| 6.2 | Entangled states of an electron-hole complex in the QD molecule | 172 | ||
| Download the sixth chapter as a single file (PDF, 647 kB) | ||||
| 7 | Negatively charged exciton on a quantum ring | 176 | ||
| Download the seventh chapter as a single file (PDF, 186 kB) | ||||
| 8 | Conclusions | 182 | ||
| Download the conclusions as a single file (PDF, 118 kB) | ||||