Electron-hole separation studies near the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn/></mml:math>quantum Hall state in modulation-doped GaAs/(Al,Ga)As single heterojunctions in high magnetic fields

Abstract

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 $\ensuremath{\sim}60 \mathrm{T}$ and at temperatures in the 0.4--2.1 K range. At low fields $(\ensuremath{\nu}&gt;2),$ 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 $(\ensuremath{\nu}&gt;2)$ with increasing field. At $\ensuremath{\nu}{=2}^{\ensuremath{-}},$ an second strong exciton transition appears at a lower energy primarily in ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization due to a spin $\ensuremath{\uparrow}$ electron recombining with a valence-band hole. It rapidly gains intensity between $2&gt;\ensuremath{\nu}&gt;1,$ but disappears at $\ensuremath{\nu}{=1}^{+}.$ At $\ensuremath{\nu}{=1}^{\ensuremath{-}}$ another redshifted transition emerges that has been described as a recombination of an electron in an initial ``free hole state.'' Its intensity in ${\ensuremath{\sigma}}^{\ensuremath{-}}$ polarization increases and reaches a maximum between $1&gt;\ensuremath{\nu}&gt;1/3.$ Such behavior becomes more pronounced as the carrier density increases. The redshift at $\ensuremath{\nu}=1$ 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.