Electron-hole separation studies near the nu=1 quantum Hall state in modulation-doped GaAs/(Al,Ga)As single heterojunctions in high magnetic fields

Magnetophotoluminescence (MPL) studies as a function of carrier concentration are reported for a series of very high mobility n-type modulation-doped GaAs/(Al,Ga)As single heterojunctions. The measurements were made in high magnetic fields to similar to 60 T and at temperatures in the 0.4-2.1 K range. At low fields (nu >2), the MPL recombination is dominated a free carrierlike excitonic transition as an energy close to the free exciton in bulk GaAs. The energy and intensity of this excitation undergoes Shubnikov-de Haas-type oscillations at even integer filling factors (nu> 2) with increasing field. At nu= 2(-), an second strong exciton transition appears at a lower energy primarily in sigma (-) polarization due to a spin up arrow electron recombining with a valence-band hole. It rapidly gains intensity between 2> nu> 1, but disappears at nu= 1(+). At nu= 1(-) another redshifted transition emerges that has been described as a recombination of an electron in an initial ``free hole state.{''} Its intensity in sigma (-) polarization increases and reaches a maximum between 1> nu >1/3. Such behavior becomes more pronounced as the carrier density increases. The redshift at nu= 1 has been correlated with recent theoretical models describing the theory of photoluminescence of two-dimensional electron systems. It has been used to determine the electron-hole separation as a function of carrier concentration.