Neutral and charged excitons in a quantum tube

The optical transition energies of neutral and charged excitons in a quantum tube are calculated as a function of the Aharonov-Bohm magnetic flux Φ. The oscillation amplitude of the ground state energy of the electron-hole relative motion is shown to be larger in a quantum tube than a quantum ring with strong confinement in the axis direction. We find a double maxima structure in the optical transition energy for a quantum tube with radius R = 0.5 in units of the effective Bohr radius because of the difference in the Φ dependencies between the single electron energy and the relative-motion energy of a charged exciton state.