Quantum Confined State Properties And Qubit Scheme In Semiconductor Nanorings

Low-dimensional nanostructures, also known as confined quantum nanostruc-tures, have shown abundant quantum properties because of their low dimension and fi-nite size. In recent years, semiconductor nanorings have attracted much interests of theresearchers in nanostructures. The confined quantum state properties in semiconduc-tor nanorings have been deeply studied in this thesis. Our study mainly involves threesubjects, i.e., Two-electron states and their entanglement in a double-barrier nanoring,a charge qubit scheme in a double-barrier nanoring, and Rotating Wigner Molecules infew-electron nanorings.We have studied two-electron states and their entanglements in a two-dimensionaldouble-barrier nanoring under the in?uence of in-plane electric fields. It is found thatthe electronic states, the order of the energy levels and the entanglements are stronglydependent on the ring's structure and fields. The symmetries of the wave functionsdetermine whether crossings or anticrossings of energy levels can occur. It is clearlyshown that the entanglements can be designed by choosing the barrier height and theangle between the two barriers, and controlled by applying electric fields. It may behelpful for understanding the entanglements of fermions in nanostructures and usefulfor future studying in solid-state quantum computation.Solid state systems seem to be good candidates for quantum computing imple-mentations. We present a scheme for charge qubit implementation in a double-barriernanoring. The structure and field effects on the validity of the qubit are also studied. Inour scheme, the logical states of the qubit are encoded in the spatial wavefunctions ofthe two lowest energy states of the system. The Aharonov-Bohm phase introduced bymagnetic ?ux, instead of tunable tunnelings in the typical charge qubit schemes, alongwith electric fields can be used for implementing the quantum gate operations. Theoperation time is much shorter than the decoherence time of the system. Our resultsalso indicate that smoothly switched external fields during the quantum operations helpto avoid the errors caused by the transition to higher-lying states. These works clar-ify the wave function evolutions and quantum operation mechanism in double-barrier nanorings, and provide the physical substances for the research and design of quantumdevices in nanorings.We present trial wavefunctions in few-electron quantum rings to describe the spin-dependent rotating Wigner molecule states. This kind of many-body function is con-structed from the single-particle orbits which contain two variational parameters todescribe the characters of states in ringlike geometry. They give accurate energies andoverlappings compared with the results of exact diagonalization in both field-free andmagnetic field conditions. The size of the ring affects the electronic states and deter-mines the applicability of the functions. By examining the entanglement entropies, it isdemonstrated that the functions can correctly describe and illustrate the quantum cor-relations between electrons in RWMs, especially the AB oscillations as well as the spinand size dependence of the entropies. Such trial functional will be useful in clarifyingthe quantum behaviors of a few electrons in nanostructures.