Quantum Behaviors Of Interacting Electronic States In Quantum Dot Structures

The investigation on interacting electronic states in nanostructures can serve as abridge between few-body to many-body physics, and it is also the basis of controllingand utilizing quantum behaviors of the system in future quantum devices. In this thesis,we study the quantum behaviors of ground and low-lying excited states in few-electronquantum dots in magnetic fields. We investigate the characters of the few-electronstates in the transition from the electronic liquid to crystal states and mainly focus on thespin correlations, entanglements between electrons and the vortex structures in differentstates. The effects of the interaction between electrons on the vortex structures arestudied in detail. And the methods of controlling the entanglements between electronsin double-barrier nanorings by electric fields are also discussed.We employ the model Hamiltonian and the method of exact diagonalization tostudy the quantum behaviors of four- and five-electron quantum dots in magnetic fieldswith negligible Zeeman effect. It is found that the spin degree of freedom brings newcharacters to the liquid-crystal transition of the states. Without the Zeeman splitting,different spin states gradually form a narrow band within the process of crystalliza-tion due to the decreasing differences in exchange interactions of the states. With thechange of the magnetic field, the angular momentum transitions of the ground statesand the lowest states with different spins have corresponding rules. The spin corre-lations reveal the magnetic couplings between electrons and it is found that there areregular oscillations of the couplings in strong fields. The characters of entanglement en-tropies in liquid and crystal states are different due to their different angular momentumcomponents.The vortex structures of few-electron states in quantum dots are investigated byconditional single-particle wavefunctions. We present the methods of analyzing thevortex structures with the spin degree of freedom. By adjusting the interaction range,we can study the behaviors of different vortices and then reveal their different effectson reducing the interactions between electrons. It is found that the separated vorticeswhich have no use in reducing the short-range interactions may result in the absences of certain electronic states in the angular momentum transitions.Based on the unrestricted Hartree-Fock orbits, we construct the trial wavefunc-tions for the rotating Wigner crystals of electrons in quantum dots with spin degree offreedom. Comparing with the results of exact diagonalization, it can be demonstratedthat the trial functions satisfy the rules of angular momentum transitions and spin cor-relations of crystal states in magnetic fields.We also study the entanglements between two electrons in double-barrier nanor-ings to reveal the characters of entanglements between indistinguishable particles innanostructures. We analyze the symmetries of wavefunctions and present the methodsof controlling the entanglements by electric fields. The far-infrared spectroscopies ofthe system may provide the information of the energy level structures and be useful inthe experiments of controlling the entanglements.