Theory of Photoluminescence of the $\nu =1$ Quantum Hall State: Excitons, Spin-Waves and Spin-Textures

Abstract

We study the theory of intrinsic photoluminescence of two-dimensional electron systems in the vicinity of the $\nu =1$ quantum Hall state. We focus predominantly on the recombination of a band of initial ``excitonic states'' that are the low-lying energy states of our model at $\nu =1$. It is shown that the recombination of excitonic states can account for recent observations of the polarization-resolved spectra of a high-mobility GaAs quantum well. The asymmetric broadening of the spectral line in the ${\sigma }_{-}$ polarization is explained to be the result of the ``shake-up'' of spin-waves upon radiative recombination of excitonic states. We derive line shapes for the recombination of excitonic states in the presence of long-range disorder that compare favourably with the experimental observations. We also discuss the stabilities and recombination spectra of other (``charged'') initial states of our model. An additional high-energy line observed in experiment is shown to be consistent with the recombination of a positively-charged state. The recombination spectrum of a negatively-charged initial state, predicted by our model but not observed in the present experiments, is shown to provide a direct measure of the formation energy of the smallest ``charged spin-texture'' of the $\nu =1$ state.

23 pages, 7 postscript figures included. Revtex with epsf.tex and multicol.sty. The revised version contains slightly improved numerical results and a few additional discussions of the results

References in corpus (4)

• Evidence for Skyrmions and Single Spin Flips in the Integer Quantized Hall Effect
• Evidence of Skyrmion excitations about $\nu =1$ in n-Modulation Doped Single Quantum Wells by Inter-band Optical Transmission
• Skyrmions without Sigma Models in Quantum Hall Ferromagnets
• Theory of Exciton Recombination from the Magnetically Induced Wigner Crystal

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• Ultrafast Nonlinear Optical Response of Strongly Correlated Systems: Dynamics in the Quantum Hall Effect Regime
• The absorption spectrum around nu=1: evidence for a small size Skyrmion
• Confinement of two-dimensional excitons in a non-homogeneous magnetic field
• Shake-up Processes in a Low-Density Two-Dimensional Electron Gas: Spin-Dependent Transitions to Higher Hole Landau Levels
• Charged hydrogenic problem in a magnetic field: Non-commutative translations, unitary transformations, and coherent states
• Theory of ultrafast exciton dynamics in the Quantum Hall system
• Optical control over bulk excitations in fractional quantum Hall systems
• Enhancement of the spin-gap in fully occupied two-dimensional Landau levels
• Skyrmionic excitons
• Optical excitations in compressible and incompressible two-dimensional electron liquids
• Localization of spinwaves in the quantum Hall ferromagnet
• Photoluminescence Detected Doublet Structure in the Integer and Fractional Quantum Hall Regime
• Photoluminescence spectrum of an interacting two-dimensional electron gas at ν=1
• Many-body luminescence from highly excited quantum-confined structures