Optical properties of remotely doped AlAs/GaAs coupled quantum wire arrays. II. Fermi-edge singularities

We perform low-temperature optical experiments on remotely doped lateral superlattices epitaxially grown on vicinal GaAs substrates. This quantum wire system provides a degenerate electron gas of density $n_s\simeq 8\times {10}^{11}\hspace{0.5em}{\mathrm{cm}}^{-2}$ subjected to a tunable one-dimensional periodic potential of amplitude $\simeq 20\hspace{0.5em}\mathrm{meV}$ and period $\simeq 30\hspace{0.5em}\mathrm{nm},$ i.e., at the scale of its Fermi energy ${(E}_F\simeq 25\hspace{0.5em}\mathrm{meV})$ and Fermi wavelength $\left({\lambda }_F\simeq 30\hspace{0.5em}\mathrm{nm}\right).\mathrm{}$ The enhancement of Fermi-edge singularities in tilted lateral superlattices [T. Mélin and F. Laruelle, Phys. Rev. Lett. 76, 4219 (1996)] is examined in the framework of the Fano resonance scheme that we recently proposed for two-dimensional systems in presence of alloy disorder [T. Mélin and F. Laruelle, Phys. Rev. Lett. 85, 852 (2000)]. Including periodic intersubband couplings as extrinsic scatterings in the Fano model, we obtain a nice agreement with experimental data. This thus rules out possible many-body scenarios for the enhancement of Fermi-edge singularities in lateral superlattices, where multiple Coulomb diffusions of Fermi-sea electrons by charged photocreated valence holes would be boosted by the reduced dimensionality.