Research On Energy Levels And Far-Infrared Spectroscopy Of Quantum Rings In A Magnetic Field

Since the middle of the last century, with the development of the low-dimensional semiconductor device fabrication technology, quantum rings have attracted considerable interests because of its unique physical properties and potential applications.Among many theoretical models for electronic states in a quantum ring, the eccentric circular parabolic potential model and the careful sidestep potential model are widely adopted. However, the eccentric circular parabolic potential is difficult to give an appropriate center-potential-barrier height of the quantum ring. The careful sidestep potential model has too many variables to control. We put forward a new potential model: U(r)=C₀ {1+C₁e^-C₃(r-R)[(r-R)²-C₂]}. This model not only can describe the fabrication course of a InGaAs nanoscopic semiconductor ring but also can overcome the shortcomings of the two former models. According to this model we study the electronic states of a two-dimensional quantum ring in a perpendicular magnetic field. We use the exact diagonalization method and replace theδfuction by a Lorentzian function. The functions of the states are expanded in terms of the two-dimensional isotropic harmonic oscillator wave functions. We also have done some theoretical calculations and analyses for FIR spectroscopy.In this paper, we study the effect of magnetic field on the quantum energy levels in a quantum ring. The results show that with increasing magnetic field, the ground state changes from angular momentum m =0 to one with higher and higher negative m . The ground state transition takes place from a zero angular momentum ( m =0) state to one with m =?1 at B = 7.5T.We investigate the right and left circularly polarized far-infrared spectroscopy. We find that with increasing magnetic field strength, in the low-energy rigion there are four possible transitions, which satisfy the selection rule, and the ground state may be changed. At the same time the FIR absorption is split into two large groups of peaks: the low- energy peaks and the high-energy peaks. The low-energy peaks correspond to transitions involving only n =0 ground state and areΔn =0 transitions, whereas the high-energy peaks involve n =0 and 1 levels and areΔn =1 transitions. Our results have a good agreement with experimental ones.The width of potential well in our potential model is narrower than that in the eccentric parabolic potential model, but the center barrier in our model is slightly higher and the potential approach to the one in a realistic quantum ring with increasing radial coordinate r . Our potential model is more suitable for the study of the problems with a high magnetic field, a high-energy level and multi-electronic systems.