Negatively charged exciton on the quantum ring

Abstract

In this paper, the energy-optical spectra and their Aharonov-Bohm oscillation of the negatively charged exciton are studied. A negatively charged exciton is composed of three charge particles, electrons and hole, the number of basic wave functions （basic vectors） which compose the state wave functions are large, so the numerical computing work is quite tedious. So far, many authors usually separate the spatial wave function into motion of mass centre and relative motion parts to save the numerical computing time. There is considerable discrepancy in the results of this method. It only suits the case when the external magnetic field is very weak. Considering the conservation of angular momentum, in case that there is no external electric field, we classity the whole set of basic vectors according to the values of their total orbital angular momentum. Then starting from Hamiltonian directly, we propose an alternative computing method to find the eigen values and eigen functions of the system. Our method can save more than 90% of computer time. There is no so called diamagnetic shift in our results. Our results fit well with the experimental data. The effects of the radii of the quantum ring, the value of dielectric constant and the effective mass of hole on the energy-optics spectra are systematically discussed.