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Wannier-mott polaritons in magnetic fields

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Book cover Festkörperprobleme 17

Part of the book series: Advances in Solid State Physics ((ASSP,volume 17))

Abstract

A review of recent theories of excitons in magnetic fields in cubic, semi-conductors is given. The valence band degeneracy and anisotropy and the exchange interaction which are taken into account in these theories create a number of typical effects (like an (mj)-dependent diamagnetism) which are verified experimentally in several materials. Consistent sets of band structure parameters are determined from a best fit of magneto-reflection results to the high field theory. A proper interpretation of the reflection experiments demands a correct line shape analysis, including the effects of an exponentially decreasing exciton free surface layer and spatial dispersion: The polariton picture has to be used. The anisotropic compression of the exciton wavefunction in high magnetic fields is directly observed via the anisotropic reduction of the exciton free surface layer. A strong increase of the oscillator strength and of the exchange interaction is another consequence of this compression. The enhanced long range part of the exchange interaction and the Magneto-Stark-Effect could explain the recently observed dependence of the transverse exciton energies on the direction of the magnetic field.

This paper was prepared during a guest term at the Fachbereich Physik, Technische Universität Berlin

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References

  1. Exellent reviews of the theoretical and some of the experimental work which was done on excitons until 1962 is given by R. S. Knox: Theory of Excitons, Suppl. 5 of Solid State Physics (H. Ehrenreich, F. Seitz, and D. Turnbull, eds.) Academic Press, New York 1963). By R. J. Elliott, Theory of Excitons I in “Polarons and Excitons” (C. G. Kuper and G. D. Whitfield, eds.) p. 269. Plenum Press, New York 1963 and by H. Haken, Theory of Excitons II in “Polarons and Excitons” (C. G. Kuper and G. D. Whitfield, eds.) p. 295. Plenum Press, New York 1963.

    Google Scholar 

  2. J. O. Dimmock reviews the situation for III–V-compounds in “Semiconductors, and Semimetals”, Vol. 3 (R. K. Willardson and A. C. Beer, eds.) p. 259. Academic Press, New York 1967.

    Google Scholar 

  3. E. J. Johnson and H. Y. Fan, Phys. Rev. 139, A 1991 (1965).

    ADS  Google Scholar 

  4. A. Baldereschi and N. O. Lipari, Phys. Rev. Lett 25, 373 (1970) and Phys. Rev. B3, 439 (1971).

    Article  ADS  Google Scholar 

  5. Altarelli and N. O. Lipari, Phys. Rev. B7, 3798 (1973) and ibid. Altarelli and N. O. Lipari, Phys. Rev. B8, 4046 (E) (1973).

    Article  ADS  Google Scholar 

  6. L. Swierkowski, Phys. Rev. 10, 3311 (1974).

    Article  ADS  Google Scholar 

  7. K. Cho, S. Suga, W. Dreybrodt and F. Willmann, Phys. Rev. B11, 1512 (1975); ibid. K. Cho, S. Suga, W. Dreybrodt, and F. Willmann, Phys. Rev. B12, 1608 (E) (1975) and K. Cho, W. Dreybrodt, P. Hiesinger, S. Suga, and F. Willmann. Proc. 12th Int. Conf. on Physics of Semiconductors (M. H. Pilkuhn, ed.) p. 945, Teubner, Stuttgart 1974.

    Article  ADS  Google Scholar 

  8. L. Swierkowski, Il Nuovo Cimento B29, 340 (1975).

    Article  ADS  Google Scholar 

  9. K. Cho, Proc. of the Int. Conf. on the application of High Magnetic Fields in Semiconductor Physics (G. Landwehr, ed.) p. 315, Würzburg University Press, Würzburg 1974.

    Google Scholar 

  10. W. Ekardt, Solid State Comm. 16, 233 (1975), and ibid. in print.

    Article  ADS  Google Scholar 

  11. N. O. Lipari and M. Altarelli, Solid State Comm. 13, 1791 (1973) and M. Altarelli and N. O. Lipari, Phys. Rev. B9, 1733 (1974).

    Article  ADS  Google Scholar 

  12. G. L. Bir, G. E. Pikus, L. G. Suslina, and D. L. Fedorov, Sov. Phys. Solid State 12, 926 (1970).

    Google Scholar 

  13. M. M. Denisov and V. P. Makarov, phys. stat. sol. b56, 9 (1973).

    Article  ADS  Google Scholar 

  14. Reflection, luminescence, absorption and Raman experiments with 1.5 m (double pass) or 1 m spectrometers equipped with holographic gratings are possible in a free aperture of 16° at d-c-fields up to 20 Tesla as a routine now at the Hochfeld-Magnetlabor in Grenoble

    Google Scholar 

  15. γ is a dimensionless measure of the magnetic field with γ = ħωc/2 Ry, where ħωc is the cyclotron resonance energy and Ry is the exciton Rydberg defined as ħωc = ħeH/μ0c, and Ry = μ0e4/2h20 2 ≅ 13.6 eV · μ0/∈0 2. Here μ0 is the exciton reduced mass with 1/μ0 = 1/me + μ1/m0, where μ1 is the Luttinger parameter and the other symbols have their usual meaning.

    Google Scholar 

  16. J. M. Luttinger, Phys. Rev. 102, 1030 (1956).

    Article  MATH  ADS  Google Scholar 

  17. E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).

    Article  ADS  Google Scholar 

  18. A. K. Bhattacharjee and S. Rodriguez, Phys. Rev. B6, 3836 (1972).

    Article  ADS  Google Scholar 

  19. D. Bimberg, K. Cho, and W. Kottler, proc. of the Int. Colleque on “Physics in High Magnetic Fields”, Grenoble 1974, p. 211.

    Google Scholar 

  20. G. F. Koster, J. O. Dimmeck, R. G. Wheeler, H. Statz, “Properties of the thirty-two Points Groups”, M.I.T. Press, Cambridge, Mass. 1962.

    Google Scholar 

  21. W. Schairer, D. Bimberg, W. Kottler, K. Cho and M. Schmidt, Phys. Rev. B13, 3452 (1976).

    Article  ADS  Google Scholar 

  22. W. Rühle and D. Bimberg, Phys. Rev. B12, 2382 (1975).

    Article  ADS  Google Scholar 

  23. D. Bimberg P. J. Dean, and F. Mansfield, J. Luminescence 12/13, 271 (1976). P. J. Dean, D. Bimberg, and F. Mansfield, Phys. Rev. B15, April 1977 and D. Bimberg and P. J. Dean, ibid., Phys. Rev. B15, April 1977, in print.

    Article  Google Scholar 

  24. L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); F. A. Jenkins and E. Segré, ibid., Phys. Rev. 55, p. 52.

    Article  MATH  ADS  Google Scholar 

  25. D. Cabib, E. Fabri, and G. Fiorio, Il Nuovo Cimento 10B, 185 (1972).

    ADS  Google Scholar 

  26. P. Lawaetz, Phys. Rev. B4, 3460 (1971).

    Article  ADS  Google Scholar 

  27. E. P. Pokatilov and M. M. Rusanov, Sov. Phys. Solid State 10, 2458 (1969).

    Google Scholar 

  28. A. Baldereschi and F. Bassani, in Proc. 10th Int. Conf. Phys. Semic. p. 191, Atomic Energy Commission, Cambridge/Mass. (1971) and F. Bassani and A. Baldereschi, Surface Science 37, 304 (1973).

    Google Scholar 

  29. D. M. Larsen, J. Phys. Chem. Solids 29, 271 (1968).

    Article  ADS  Google Scholar 

  30. N. Lee, D. M. Larsen and B. Lax, J. Phys. Chem. Solids 34, 1059 (1973).

    Article  ADS  Google Scholar 

  31. L. D. Landau and E. M. Lifschitz, Quantenmechanik, p. 132, Akademie-Verlag, Berlin (1966).

    Google Scholar 

  32. K. Hess, D. Bimberg, N. O. Lipari, J. U. Fischbach, and M. Altarelli, Proc. 13th Int. Conf. Phys. Semic., Rome (1976) and D. Bimberg, K. Hess, N. O. Lipari, J. U. Fischbach, and M. Altarelli, Bull. Am. Phys. Soc.

    Google Scholar 

  33. D. Bimberg K. Hess, N. O. Lipari, J. U. Fischbach, and M. Altarelli, Physica B.

    Google Scholar 

  34. D. Bimberg, K. Cho, and N. O. Lipari, to be published.

    Google Scholar 

  35. Y. Yafet, R. W. Keyes and E. N. Adams, J. Phys. Chem. Solids 1, 137 (1956).

    Article  ADS  Google Scholar 

  36. R. F. Wallis and H. J. Bowlden, J. Phys. Chem. Solids 7, 78 (1958).

    Article  ADS  Google Scholar 

  37. W. S. Boyle and R. E. Howard, J. Phys. Chem. Solids 19, 181 (1961).

    Article  ADS  Google Scholar 

  38. R. J. Elliott and R. Loudon, J. Phys. Chem. Solids 8, 382 (1958).

    Article  ADS  Google Scholar 

  39. H. Hasegawa and R. E. Howard, J. Phys. Chem. Solids 21, 179 (1961).

    Article  ADS  Google Scholar 

  40. A. G. Zhilich, Sov. Phys. Solid State 13, 2425 (1972).

    Google Scholar 

  41. G. J. Rees, J. Phys. C4, 2822 (1971), ibid. G. J. Rees, J. Phys. C5, 539 (1972).

    Article  ADS  Google Scholar 

  42. M. H. Johnson and B. A. Lippmann, Phys. Rev. 76, 828 (1949).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  43. J. C. Hensel and K. Suzuki, Phys. Rev. Letters 22, 838 (1969).

    Article  ADS  Google Scholar 

  44. E. J. Johnson, Phys. Rev. Lett. 19, 352 (1967).

    Article  ADS  Google Scholar 

  45. C. R. Pidgeon and R. N. Brown, Phys. Rev. 146, 575 (1966) see also the review by R. L. Aggarwal, in Semiconductors and Semimetals Vol. 9 (R. K. Willardson and A. C. Beer, eds.) p. 151, Academic Press, New York 1972.

    Article  ADS  Google Scholar 

  46. L. M. Roth, B. Lax and S. Zwerdling, Phys., Rev. 114, 90 (1959).

    Article  ADS  Google Scholar 

  47. See. e.g. D. Bimberg and W. Schairer, Phys. Rev. Lett. 28, 442 (1972). The line assigned there as n=3 was later shown to be the n=2 line.

    Article  ADS  Google Scholar 

  48. S. Zwerdling, B. Lax, L. M. Roth and K. Button, Phys. Rev. 114, 80 (1959).

    Article  ADS  Google Scholar 

  49. See e.g. Fig. 3: S. Askenazy in New developments in semiconductors, p. 333 (P. R. Wallace, R. Harris, and M. J. Zuckermann, eds.) Nordhoff, Leyden 1970).

    Google Scholar 

  50. D. D. Sell, S. E. Stokowski, R. Dingle and J. V. DiLorenzo, Phys. Rev. B7, 4568 (1973).

    Article  ADS  Google Scholar 

  51. J. U. Fischbach, W. Rühle D. Bimberg and E. Bauser, Solid State Commun. 18, 1255 (1976).

    Article  ADS  Google Scholar 

  52. Y. Nisida and K. Muro, Suppl. of the Progress of Theor. Phys. 57, 77 (1975), and Y. Nisida, K. Muro, and U. Kawata, Infrared Physics 16, 207 (1976).

    Article  ADS  Google Scholar 

  53. E. M. Gershenzon, G. N. Goltsman and N. G. Ptitsina, Sov. Phys.-JETP 37, 299 (1973).

    ADS  Google Scholar 

  54. V. S. Vavilov, N. V. Guzeer, V. A. Zayat, V.L Kononenko, T.S. Mandel'shtam and V. N. Murzin, Sov. Phys. JETP Letters 17, 345 (1973).

    ADS  Google Scholar 

  55. W. Dreybrodt, K. Cho, S. Suga, and F. Willmann, to be published.

    Google Scholar 

  56. B. Segall and D. T. F. Marple, in “Physics and Chemistry of II–VI-Compounds (N. Aven and J. S. Prener, eds.), North Holland Company, Amsterdam 1967.

    Google Scholar 

  57. G. D. Mahan and J. J. Hopfield, Phys. Rev. 135, A 428 (1964).

    Article  ADS  Google Scholar 

  58. H. Venghaus et al., unpublished results.

    Google Scholar 

  59. R. Dingle, Phys. Rev. B8, 4627 (1973).

    Article  ADS  Google Scholar 

  60. N. O. Lipari, M. Altarelli and R. Dingle, Solid State Commun. 16, 1189 (1975).

    Article  ADS  Google Scholar 

  61. F. Willmann, S. Suga, W. Dreybrodt and K. Cho, Solid State Commun. 14, 783 (1974).

    Article  ADS  Google Scholar 

  62. S. B. Nam, D. C. Reynolds, and C. W. Litton, J. Luminescence 12/13 (1976).

    Google Scholar 

  63. S. B. Nam, D. C. Reynolds, C. W. Litton, R. J. Almassy, T. C. Collins, and C. M. Wolfe, Phys. Rev. B13, 761 (1976).

    Article  ADS  Google Scholar 

  64. S. B. Nam, D. C. Reynolds, C. W. Litton, T. C. Collins, P. J. Dean and R. C. Clarke, Phys. Rev. B13, 1643 (1976).

    Article  ADS  Google Scholar 

  65. D. Bimberg and J. U. Fischbach, Verhandlg. DPG VI10, 365 (1975).

    Google Scholar 

  66. J. Lagois, to be published.

    Google Scholar 

  67. J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963).

    Article  ADS  Google Scholar 

  68. J. J. Hopfield, Proc. Int. Conf. Phys. Semicon., Kyoto 1966; J. Phys. Soc. Japan 21 Supplement, 77 (1966).

    Google Scholar 

  69. A review on this work is given in chapter 11 of the book by Knox (Ref. [1]) and by V. M. Agranovich and V. L. Ginzburg, Spatial Dispersion in the Crystal Optics and the Theory of Excitons”, Interscience Publishers, London 1966.

    Google Scholar 

  70. S. I. Pekar, Sov. Phys. JETP 6, 785 (1958), and Sov. Phys. Solid State 4, 953 (1962).

    MathSciNet  ADS  Google Scholar 

  71. J. Bjellmann, M. Grossmann and S. Nikitine, in Polaritons (E. Burstein and F. de Martini, eds.), Pergamon, New York 1974.

    Google Scholar 

  72. F. Evangelisti, A. Frova and J. U. Fischbach, Phys. Rev. Lett. 29, 1001 (1972). F. Evangelisti, J. U. Fischbach, and A. Frova, Phys. Rev. B9, 1516 (1974); F. Evangelisti, A. Frova, and J. U. Fischbach, Surface Science 37, 841 (1973).

    Article  ADS  Google Scholar 

  73. D. Bimberg and M. Rosenzweig, unpublished results.

    Google Scholar 

  74. K. Lösch and D. Bimberg, Verhandlg. DPG (VI) 12, 47 (1977).

    Google Scholar 

  75. E. O. Kane, Phys. Rev. B11, 3850 (1975).

    Article  ADS  Google Scholar 

  76. M. Altarelli and N. O. Lipari. Proc. of the Int. Conf. Phys. Semic. Rome 1976. p. 811.

    Google Scholar 

  77. D. Bimberg and W. Rühle, Proc. XII Int. Conf. on the Physicis of Semiconductors, Stuttgart 1974, p. 561 (ed by M. H. Pilkuhn).

    Google Scholar 

  78. R. A. Stradling, Proc. of the Int. Conf. on the “Application of High Magnetic in Semiconductor Physics”, Würzburg 1972 (ed. by G. Landwehr), p. 434.

    Google Scholar 

  79. H. R. Fettermann, D. M. Larsen, G. E. Stillman, P. E. Tannenwald and J. Waldmann, Phys. Rev. Lett. 26, 975 (1971).

    Article  ADS  Google Scholar 

  80. G. E. Stillmann, D. M. Larsen, C. M. Wolfe, and R. C. Brandt, Solid Sate, Commun. 9, 2245 (1971).

    Article  ADS  Google Scholar 

  81. A. M. White, J. Hinchlifee, and P. J. Dean, Solid State Commun. 10, 497 (1972).

    Article  ADS  Google Scholar 

  82. W. Schairer, D. Bimberg, W. Kottler, K. Cho, and M. Schmidt, Phys. Rev. B13, 3452 (1976).

    Article  ADS  Google Scholar 

  83. W. Ekardt, phys. stat. sol. b68, 53 (1975) and ibid. W. Ekardt, phys. stat. sol. b68, 491 (1975).

    Article  ADS  Google Scholar 

  84. H. Stolz and R. Zimmermann, phys. stat. sol. b53, 315 (1972).

    Article  ADS  Google Scholar 

  85. A Baldereschi and N. O. Lipari, Phys. Rev. B8, 2697 (1973).

    Article  ADS  Google Scholar 

  86. D. D. Sell, Phys. Rev. B6, 3750 (1972).

    Article  ADS  Google Scholar 

  87. R. F. Kirkmann and R. A. Stradling, private communication 1976.

    Google Scholar 

  88. J. M. Chamberlain, P. E. Simmonds, R. E. Stradling, and C. C. Bradley, Proc. 11th Int. Conf. Phys. Semic. Warsaw (1972), p. 1016.

    Google Scholar 

  89. E. O. Kane, estimates the short range exchange constants to be negligible in III–V-compounds, private communication 1976.

    Google Scholar 

  90. M. Cardona, J. Phys. Chem. Solids,, 24, 1543 (1963).

    Article  ADS  Google Scholar 

  91. F. H. Pollak, C. W. Higginbothan, and M. Cardona, Proc. 8th Int. Conf. Phys. Semic. Kyoto 1966, p. 20.

    Google Scholar 

  92. R. L. Bowers and G. D. Mahan, Phys. Rev. 185, 1073 (1969).

    Article  ADS  Google Scholar 

  93. P. Lawaetz, Phys. Rev. B4, 3460 (1971).

    Article  ADS  Google Scholar 

  94. P. Lawaetz, improved values, private communication to R. A. Stradling, 1974.

    Google Scholar 

  95. A. K. Walton and U. K. Mishera, Proc. Phys. Soc. 90, 1111 (1967).

    Article  ADS  Google Scholar 

  96. Q. F. H. Vrehen, J. Phys. Chem. Solids 29, 129 (1968).

    Article  ADS  Google Scholar 

  97. S. Narita, M. Kobayashi, and N. Koike, Proc. 9th Int. Conf. Phys. Semic. Moscow 1968, p. 347.

    Google Scholar 

  98. R. P. Seisyan, M. A. Abdullaev and V. D. Draznin, Sov. Phys. Semic. 7, 552 (1973).

    Google Scholar 

  99. I. Balslev, Phys. Rev. 177, 1173 (1969).

    Article  ADS  Google Scholar 

  100. M. S. Skolnick, A. K. Jain, R. A. Stradling, J. Leontin, J. C. Ousset, and S. Askenazy, J. Phys. C9, 2809 (1976).

    Article  ADS  Google Scholar 

  101. H. R. Trebin and U. Rössler, phys. stat. sol. (b)70, 717 (1975).

    Article  ADS  Google Scholar 

  102. W. Ekardt, Solid State Commun. 15, 889 (1974).

    Article  ADS  Google Scholar 

  103. Y. Onodera and Y. Toyozoma, J. Phys. Soc. Japan 22, 833 (1967).

    Article  ADS  Google Scholar 

  104. M. Suffczynski, L. Swierkowski and W. Wardzynski, J. Phys. C8, L 52 (1952); M. Suffczynski, J. Phys. C8, L. 400 (1975); M. Suffczynski and C. Swierkowski, Optics Commun. 17, 184 (1976).

    Google Scholar 

  105. W. R. Heller and A. Marcus, Phys. Rev. 84, 809 (1951).

    Article  MATH  ADS  Google Scholar 

  106. E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).

    Article  ADS  Google Scholar 

  107. W. Staude, Phys. Letters 29A, 228 (1969) and phys. stat. sol. b43 367 (1971).

    ADS  Google Scholar 

  108. D. G. Thomas and J. J. Hopfield, Phys. Rev. 124, 657 (1961).

    Article  ADS  Google Scholar 

  109. L. P. Gorkov and I. E. Dzyaloshinskii, Sov. Phys JETP 26, 449 (1968).

    ADS  Google Scholar 

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Bimberg, D. (1977). Wannier-mott polaritons in magnetic fields. In: Treusch, J. (eds) Festkörperprobleme 17. Advances in Solid State Physics, vol 17. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0107763

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