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Linearly Polarized Emission of Quantum Wells Subject to an In-plane Magnetic Field N. S. Averkiev, A. V. Koudinov and Yu. G. Kusrayev A.F. Ioffe Physico-Technical Institute, St.-Petersburg, Russia D. Wolverson University of Bath, Bath, United Kingdom G. Karczewski and T. Wojtowicz Institute of Physics, Warsaw, Poland Supported by INTAS

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Geometry of the PL polarization measurements z x y We measure the degree of polarization as we rotate the sample by angle about its normal z QW

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Examples of the in-plane rotation angular scans of linear polarization in QWs cos(0 ) cos(2 ) cos(4 ) B≠0

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…if the true symmetry of the QW states is: In-plane rotation of the sample: what one may expect... cos(0 ), cos(4 ) cos(0 ), cos(2 ), cos(4 ) QW

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Spin-flip Raman scattering: out-of-plane rotation dependence of the spectra

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B = B x iB y, – the value of the in-plane deformation multiplied by the respective constant of the deformation potential, – the energy separation between the heavy and the light holes, g 1 – the hole g-factor for the bulk material; the principal axis of the deformation is taken for the x axis. Theory I: the valence band Hamiltonian Calculation results in the following polarization as a function of angle ( ): – 0th harmonic – “built-in” polarization – 2nd harmonic – 4th harmonic

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Theory II: random directions of the in-plane distortions There are two serious contradictions between the above theory (with a uniform in-plane distortion) and the experimental observations: 1.The theory predicts the relationship which is however not obeyed ( ); 2.The theory predicts while the experiment shows that sometimes. One has to introduce the directional scatter of the in-plane distortions: Then, the re-calculated values of the harmonics will include the parameters of the distribution function f( ):

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Comparison with experiment I: Zero magnetic field, “built-in” polarization Symmetry: 180-deg periodicity (2 nd angular harmonic) Origin: mixing hh + lh by the in-plane distortion Term responsible for:

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Comparison with experiment II: Magnetic field applied, polarization A 2 B 2 Symmetry: 180-deg periodicity (2 nd angular harmonic) Origin: splitting of hh and e by the magnetic field Term responsible for:

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Comparison with experiment III: Magnetic field applied, polarization A 0 B 2 Symmetry: rotation invariant Origin: mixing hh + lh by the magnetic field Term responsible for:

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Comparison with experiment IV: Amplitudes of harmonics vs magnetic field – quadratic in B as long as

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Conclusions 1.The magnetic field, angular and spectral dependences of the PL polarization along with the data on the spin-flip Raman scattering were used for construction and verification of a theoretical model. 2.We have carefully analyzed the contributions of different symmetry to the linear polarization of the PL of QWs, as well as the physical mechanisms underlying them. 3.We find that the valence band states in the QWs have a reduced symmetry in the QW plane, and the principal axes of the in-plane distortions show a scatter in direction. 4.We suggest an interpretation of the 4th angular harmonic of the linear polarization.

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