Exciton Rydberg in T-shaped quantum wires

We have calculated the electronic structure of the two series of T-shaped wires experimentally studied by T. Someya et al. [Phys. Rev. Lett. 76, 2965 (1996)]. The finite depth of the wells and the cubic symmetry of the valence band are explicitly taken into account. We obtain the theoretical value of the exciton Rydberg RXᵗʰ and the exciton transition energy EXᵗʰ. The results derived from our theory, which has no adjustable parameters, are compared with the experimental value EXᵉˣ and the estimated value RXᵉˢ obtained for $S1$ series (GaAs-Ga0.7Al0.3 As) and $S2$ series (GaAs-AlAs). In the $S1$ sample, where the thicknesses of the two quantum wells, which define a T wire, are identical (balanced T wire), EXᵗʰ=1590 meV compared to EXᵉˣ=1591 and RXᵗʰ=15 meV while RXᵉˢ=17±3 meV. In the balanced $S2$ sample we obtain EXᵗʰ=1626 meV compared to EXᵉˣ=1621 meV and RXᵗʰ=18 meV while RXᵉˢ=27±3 meV. The large width of the photoluminescence line for the samples of the $S2$ series and the discrepancy between the experimental and calculated values suggest that the luminescence is due to excitons bound to interfaces. The values of the exciton Rydberg deduced from the experiments is therefore overestimated.