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N. S. Averkiev , A. V. Koudinov and Yu. G. Kusrayev

Linearly P olarized E mission of Q uantum W ells S ubject to an I n- p lane M agnetic F ield. N. S. Averkiev , A. V. Koudinov and Yu. G. Kusrayev A.F. Ioffe Physico-Technical Institute , S t.-Petersburg, Russia D. Wolverson University of Bath, Bath , United Kingdom

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N. S. Averkiev , A. V. Koudinov and Yu. G. Kusrayev

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  1. Linearly Polarized Emission of Quantum WellsSubject 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 03-51-5266

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

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

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

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

  6. Theory I: the valence band Hamiltonian Calculation results in the following polarization as a function of angle (): – “built-in” polarization • B = Bx iBy, •  – 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, g1 – the hole g-factor for the bulk material; the principal axis of the deformation is taken for the x axis. – 0th harmonic – 2nd harmonic – 4th harmonic

  7. 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: • 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():

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

  9. Comparison with experiment II: Magnetic field applied, polarization A2B2 Symmetry: 180-deg periodicity (2nd angular harmonic) Origin: splitting of hh and e by the magnetic field Term responsible for:

  10. Comparison with experiment III: Magnetic field applied, polarization A0B2 Symmetry: rotation invariant Origin: mixing hh+ lh by the magnetic field Term responsible for:

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

  12. Conclusions • 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. • 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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