Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires $(\overline{x}=0.0018)$ in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius $R$ is smaller than $16.6\mathrm{nm}$, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four ${\sigma }^{\pm }$ and two $\pi$ polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of $\pi$ and ${\sigma }^{\pm }$ polarized Zeeman components is reversed for thin quantum wires $(R<2.3\mathrm{nm})$ due to the quantum confinement effect.

• Received 30 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.205113