Fermi-edge singularities in photoluminescence spectra of n-type modulation-doped quantum wells with a lateral periodic potential

We demonstrate that a many-body effect between electrons and a finite-mass hole can be modulated externally by lateral periodic potentials in a n-type modulation-doped ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}-\mathrm{G}\mathrm{a}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum-well structure. A peculiar asymmetric peak is observed in the photoluminescence spectra 2.5 meV below the Fermi energy when a weak lateral periodic potential is applied, whereas no significant feature is observed without any lateral potential. The asymmetric peak is shown to be due to the recombination of the electrons at the Fermi surface and a hole, by investigating the oscillations of the energy positions and the intensity of the emission spectrum as a function of the magnetic field.