Magnetoexcitons in quantum wires with an anisotropic parabolic potential

We study theoretically exciton properties of quantum wires (QWR’s) with an anisotropic two-dimensional parabolic potential in a magnetic field. First, the analytical solution for the single-particle states of the QWR’s in the magnetic field is obtained. Then, the energy states are analyzed numerically including the Coulomb interaction between an electron-hole pair. The results show that the experimental results on magnetophotoluminescence (magneto-PL) of GaAs QWR’s [Y. Nagamune, Y. Arakawa, S. Tsukamoto, M. Nishioka, S. Sasaki, and N. Miura, Phys. Rev. Lett. 69, 2963 (1992)] can be well explained by this model, demonstrating the importance of the exciton effect to understand the magneto-PL properties of QWR’s. On the other hand, the diamagnetic energy shift can be understood even without considering the Coulomb interaction, because the change of the exciton binding energy due to the magnetic field is relatively small compared to the total energy shift.