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 $R_X^{\mathrm{th}}$ and the exciton transition energy $E_X^{\mathrm{th}}$. The results derived from our theory, which has no adjustable parameters, are compared with the experimental value $E_X^{\mathrm{ex}}$ and the estimated value $R_X^{\mathrm{es}}$ obtained for $S1\mathrm{}$ series (${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{G}\mathrm{a}}_{0.7}{\mathrm{Al}}_{0.3}\hspace{0.5em}\mathrm{As}$) and $S2\mathrm{}$ series (GaAs-AlAs). In the $S1\mathrm{}$ sample, where the thicknesses of the two quantum wells, which define a T wire, are identical (balanced T wire), $E_X^{\mathrm{th}}=1590\mathrm{}\hspace{0.5em}\mathrm{meV}$ compared to $E_X^{\mathrm{ex}}=1591\mathrm{}$ and $R_X^{\mathrm{th}}=15\mathrm{}\hspace{0.5em}\mathrm{meV}$ while $R_X^{\mathrm{es}}=17\mathrm{}\pm 3\mathrm{\hspace{0.5em}}\mathrm{meV}$. In the balanced $S2\mathrm{}$ sample we obtain $E_X^{\mathrm{th}}=1626\mathrm{}\hspace{0.5em}\mathrm{meV}$ compared to $E_X^{\mathrm{ex}}=1621\mathrm{}\hspace{0.5em}\mathrm{meV}$ and $R_X^{\mathrm{th}}=18\mathrm{}\hspace{0.5em}\mathrm{meV}$ while $R_X^{\mathrm{es}}=27\mathrm{}\pm 3\mathrm{\hspace{0.5em}}\mathrm{meV}$. The large width of the photoluminescence line for the samples of the $S2\mathrm{}$ 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.