Theoretical Studies Of Quantum Dots And Effect Of Magnetic Fields And An Impurity

Quantum dots (QDs) are low-dimensional quantum structure ofsemiconductor. Research on them is one of the hot topics in condensed-matterphysics in recent years, thus a great lot of researches in theory and experimenthave been carried out. The aim of this paper is that the schrodinger equations ofQDs subjected to an external magnetic field and affected by an impurity aresolved, and studies effect of factors, e.g. the magnetic field and the impurity, onthe properties of QDs. This thesis consists of seven chapters.In chapter 1, properties and applications of QDs, as well as their theoryresearch methods are briefly introduced.In chapter 2, theory of a 2-dimensional N-electron QD subjected to themagnetic field and affected by the impurity is improved. The theory points are asfollows: adopting adjustable harmonic oscillation product-functions as basisfunctions, selecting proper basis functions from them, and making use of phononrepresentation and transform of Talmi-Moshinsky coefficients, the schrodingerequation of the QD is solved directly, and the qualitative exact eigensolutions (theeigenstates and eigenenergies) are obtained.In chapter 3, symmetry constraint is discussed. Inherence relation amongsymmetry constraint, electronic structure and magic angular momentum is theemphasis.In chapter 4, a 2-dimensional 3-electron QD is studied. Firstly, influence ofthe magnetic field and the impurity on energy spectra of low-lying states of theQD is researched, respectively. Secondly, the ground states are investigated. Theprimary result is ( L0 ,S0) phase diagrams of the ground states. The diagramsindicate clearly synthesized effect of the magnetic field and the impurity on theground states. Moreover, the dependences of the size, the geometric feature, andthe optical absorption of the ground state QD on the magnetic field and theimpurity are obtained. Finally, in the cases of parabolic potential and square wellpotential a number of spin-diagrams are given.In chapter 5, it is investigated for the application that a 2-electron QD is usedas a highly sensitive switch. Based on singlet-triplet transition of the QD andsymmetry constraint, and making use of Coulomb blockade, if the relatedparameters are skillfully adjusted, pass in and out of an electron is controlled bythe QD.In chapter 6, the effect of the magnetic field and the impurity on energyspectra of low-lying states of excitons is studied. An exciton( X ), a positiveexciton( X +), and a negative exciton( X ?) are adopted as examples, thereby theeffect of the magnetic field and the impurity is studied.Chapter 7 is summary of the whole paper.