Strong interaction of Fermi-edge singularity and exciton related to $N=2\mathrm{}$ subband in a modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/{\mathrm{In}}_y{\mathrm{Ga}}_{1-y}\mathrm{As}/\mathrm{GaAs}$ quantum well

We have investigated photoluminescence and photoluminescence excitation spectra from a one-side modulation-doped ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/{\mathrm{In}}_y{\mathrm{Ga}}_{1-y}\mathrm{As}/\mathrm{GaAs}$ single quantum well under a near-resonance condition between the $N=2\mathrm{}$ subband and the Fermi level of the two-dimensional electron gas. Under such conditions, strong interaction between electrons at the Fermi edge and the exciton related to the $N=2\mathrm{}$ subband can be observed. The Fermi-edge singularity (FES) is enhanced first, and then the FES and the $N=2\mathrm{}$ exciton repel each other. Finally, the $N=2\mathrm{}$ exciton is screened by excess electrons with increased excitation power. With an increase in temperature, the FES rapidly quenches, and the intensity of the $N=2\mathrm{}$ exciton transition increases accompanied by a blueshift of its peak position.