Research On Exciton Binding Energy In A Triangular Quantum Wire In The Presence Of Perpendicular Magnetic Field

In this paper, a variational perturbation approach is presented to investigate the state of electron, hole and exciton in a triangular quantum wire in the presence of a perpendicular magnetic field. We calculate the exciton diamagnetic shifts as a function of the size of triangular quantum wire and magnetic field with effective potential model; we also compare our theoretical results with the experimental date. In this thesis, we obtain the following conclusions:First, we present a variational perturbation approach to research a finite triangular quantum wire subjected to a perpendicular magnetic field. Introduce a cylindrical quantum wire in calculate process, and evaluate the sectional radius of cylindrical quantum wire, which makes the confinement potential difference between triangular quantum wire and cylindrical quantum wire could be dealt with perturbation to the Hamiltonian of the cylindrical quantum wire. Then, we use variational perturbation approach to study the ground energy of electron (hole) and its wave function, and calculate the exciton diamagnetic shifts in triangular quantum wire. This approach is not only simple in calculation, but also makes calculating results close to exact value if we take into account more order of the approximate.Second, we have a research on electron, hole and exciton in a triangular quantum wire for the magnetic field perpendicular to the quantum wire, and get the calculating results indicating: the ground energy of electron (hole) increases with the increasing of the magnetic field in quantum wire, but the ground energy of electron increases with the magnetic field is more obvious than for the hole. The curve of ground energy for electron (hole) increases with the magnetic field in triangular quantum wire with different height (width) are approaching each other. In the same magnetic field, the ground-state electron (hole) energy drops slowly with the increasing of the height (width) in quantum wires of different height (width); The exciton diamagnetic shifts increase with the magnetic field, in which there is a critical point, The exciton diamagnetic shifts become larger with the height (width) in quantum wire increasing, and the critical point shift to low magnetic field. According to comparison with the Ref [59], we find that our theoretical results are much closer to the experimental dates.