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
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.
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.
E. J. Johnson and H. Y. Fan, Phys. Rev. 139, A 1991 (1965).
A. Baldereschi and N. O. Lipari, Phys. Rev. Lett 25, 373 (1970) and Phys. Rev. B3, 439 (1971).
Altarelli and N. O. Lipari, Phys. Rev. B7, 3798 (1973) and ibid. Altarelli and N. O. Lipari, Phys. Rev. B8, 4046 (E) (1973).
L. Swierkowski, Phys. Rev. 10, 3311 (1974).
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.
L. Swierkowski, Il Nuovo Cimento B29, 340 (1975).
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.
W. Ekardt, Solid State Comm. 16, 233 (1975), and ibid. in print.
N. O. Lipari and M. Altarelli, Solid State Comm. 13, 1791 (1973) and M. Altarelli and N. O. Lipari, Phys. Rev. B9, 1733 (1974).
G. L. Bir, G. E. Pikus, L. G. Suslina, and D. L. Fedorov, Sov. Phys. Solid State 12, 926 (1970).
M. M. Denisov and V. P. Makarov, phys. stat. sol. b56, 9 (1973).
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
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 = μ0e4/2h2∈0 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.
J. M. Luttinger, Phys. Rev. 102, 1030 (1956).
E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
A. K. Bhattacharjee and S. Rodriguez, Phys. Rev. B6, 3836 (1972).
D. Bimberg, K. Cho, and W. Kottler, proc. of the Int. Colleque on “Physics in High Magnetic Fields”, Grenoble 1974, p. 211.
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.
W. Schairer, D. Bimberg, W. Kottler, K. Cho and M. Schmidt, Phys. Rev. B13, 3452 (1976).
W. Rühle and D. Bimberg, Phys. Rev. B12, 2382 (1975).
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.
L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); F. A. Jenkins and E. Segré, ibid., Phys. Rev. 55, p. 52.
D. Cabib, E. Fabri, and G. Fiorio, Il Nuovo Cimento 10B, 185 (1972).
P. Lawaetz, Phys. Rev. B4, 3460 (1971).
E. P. Pokatilov and M. M. Rusanov, Sov. Phys. Solid State 10, 2458 (1969).
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).
D. M. Larsen, J. Phys. Chem. Solids 29, 271 (1968).
N. Lee, D. M. Larsen and B. Lax, J. Phys. Chem. Solids 34, 1059 (1973).
L. D. Landau and E. M. Lifschitz, Quantenmechanik, p. 132, Akademie-Verlag, Berlin (1966).
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.
D. Bimberg K. Hess, N. O. Lipari, J. U. Fischbach, and M. Altarelli, Physica B.
D. Bimberg, K. Cho, and N. O. Lipari, to be published.
Y. Yafet, R. W. Keyes and E. N. Adams, J. Phys. Chem. Solids 1, 137 (1956).
R. F. Wallis and H. J. Bowlden, J. Phys. Chem. Solids 7, 78 (1958).
W. S. Boyle and R. E. Howard, J. Phys. Chem. Solids 19, 181 (1961).
R. J. Elliott and R. Loudon, J. Phys. Chem. Solids 8, 382 (1958).
H. Hasegawa and R. E. Howard, J. Phys. Chem. Solids 21, 179 (1961).
A. G. Zhilich, Sov. Phys. Solid State 13, 2425 (1972).
G. J. Rees, J. Phys. C4, 2822 (1971), ibid. G. J. Rees, J. Phys. C5, 539 (1972).
M. H. Johnson and B. A. Lippmann, Phys. Rev. 76, 828 (1949).
J. C. Hensel and K. Suzuki, Phys. Rev. Letters 22, 838 (1969).
E. J. Johnson, Phys. Rev. Lett. 19, 352 (1967).
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.
L. M. Roth, B. Lax and S. Zwerdling, Phys., Rev. 114, 90 (1959).
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.
S. Zwerdling, B. Lax, L. M. Roth and K. Button, Phys. Rev. 114, 80 (1959).
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).
D. D. Sell, S. E. Stokowski, R. Dingle and J. V. DiLorenzo, Phys. Rev. B7, 4568 (1973).
J. U. Fischbach, W. Rühle D. Bimberg and E. Bauser, Solid State Commun. 18, 1255 (1976).
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).
E. M. Gershenzon, G. N. Goltsman and N. G. Ptitsina, Sov. Phys.-JETP 37, 299 (1973).
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).
W. Dreybrodt, K. Cho, S. Suga, and F. Willmann, to be published.
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.
G. D. Mahan and J. J. Hopfield, Phys. Rev. 135, A 428 (1964).
H. Venghaus et al., unpublished results.
R. Dingle, Phys. Rev. B8, 4627 (1973).
N. O. Lipari, M. Altarelli and R. Dingle, Solid State Commun. 16, 1189 (1975).
F. Willmann, S. Suga, W. Dreybrodt and K. Cho, Solid State Commun. 14, 783 (1974).
S. B. Nam, D. C. Reynolds, and C. W. Litton, J. Luminescence 12/13 (1976).
S. B. Nam, D. C. Reynolds, C. W. Litton, R. J. Almassy, T. C. Collins, and C. M. Wolfe, Phys. Rev. B13, 761 (1976).
S. B. Nam, D. C. Reynolds, C. W. Litton, T. C. Collins, P. J. Dean and R. C. Clarke, Phys. Rev. B13, 1643 (1976).
D. Bimberg and J. U. Fischbach, Verhandlg. DPG VI10, 365 (1975).
J. Lagois, to be published.
J. J. Hopfield and D. G. Thomas, Phys. Rev. 132, 563 (1963).
J. J. Hopfield, Proc. Int. Conf. Phys. Semicon., Kyoto 1966; J. Phys. Soc. Japan 21 Supplement, 77 (1966).
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.
S. I. Pekar, Sov. Phys. JETP 6, 785 (1958), and Sov. Phys. Solid State 4, 953 (1962).
J. Bjellmann, M. Grossmann and S. Nikitine, in Polaritons (E. Burstein and F. de Martini, eds.), Pergamon, New York 1974.
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).
D. Bimberg and M. Rosenzweig, unpublished results.
K. Lösch and D. Bimberg, Verhandlg. DPG (VI) 12, 47 (1977).
E. O. Kane, Phys. Rev. B11, 3850 (1975).
M. Altarelli and N. O. Lipari. Proc. of the Int. Conf. Phys. Semic. Rome 1976. p. 811.
D. Bimberg and W. Rühle, Proc. XII Int. Conf. on the Physicis of Semiconductors, Stuttgart 1974, p. 561 (ed by M. H. Pilkuhn).
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.
H. R. Fettermann, D. M. Larsen, G. E. Stillman, P. E. Tannenwald and J. Waldmann, Phys. Rev. Lett. 26, 975 (1971).
G. E. Stillmann, D. M. Larsen, C. M. Wolfe, and R. C. Brandt, Solid Sate, Commun. 9, 2245 (1971).
A. M. White, J. Hinchlifee, and P. J. Dean, Solid State Commun. 10, 497 (1972).
W. Schairer, D. Bimberg, W. Kottler, K. Cho, and M. Schmidt, Phys. Rev. B13, 3452 (1976).
W. Ekardt, phys. stat. sol. b68, 53 (1975) and ibid. W. Ekardt, phys. stat. sol. b68, 491 (1975).
H. Stolz and R. Zimmermann, phys. stat. sol. b53, 315 (1972).
A Baldereschi and N. O. Lipari, Phys. Rev. B8, 2697 (1973).
D. D. Sell, Phys. Rev. B6, 3750 (1972).
R. F. Kirkmann and R. A. Stradling, private communication 1976.
J. M. Chamberlain, P. E. Simmonds, R. E. Stradling, and C. C. Bradley, Proc. 11th Int. Conf. Phys. Semic. Warsaw (1972), p. 1016.
E. O. Kane, estimates the short range exchange constants to be negligible in III–V-compounds, private communication 1976.
M. Cardona, J. Phys. Chem. Solids,, 24, 1543 (1963).
F. H. Pollak, C. W. Higginbothan, and M. Cardona, Proc. 8th Int. Conf. Phys. Semic. Kyoto 1966, p. 20.
R. L. Bowers and G. D. Mahan, Phys. Rev. 185, 1073 (1969).
P. Lawaetz, Phys. Rev. B4, 3460 (1971).
P. Lawaetz, improved values, private communication to R. A. Stradling, 1974.
A. K. Walton and U. K. Mishera, Proc. Phys. Soc. 90, 1111 (1967).
Q. F. H. Vrehen, J. Phys. Chem. Solids 29, 129 (1968).
S. Narita, M. Kobayashi, and N. Koike, Proc. 9th Int. Conf. Phys. Semic. Moscow 1968, p. 347.
R. P. Seisyan, M. A. Abdullaev and V. D. Draznin, Sov. Phys. Semic. 7, 552 (1973).
I. Balslev, Phys. Rev. 177, 1173 (1969).
M. S. Skolnick, A. K. Jain, R. A. Stradling, J. Leontin, J. C. Ousset, and S. Askenazy, J. Phys. C9, 2809 (1976).
H. R. Trebin and U. Rössler, phys. stat. sol. (b)70, 717 (1975).
W. Ekardt, Solid State Commun. 15, 889 (1974).
Y. Onodera and Y. Toyozoma, J. Phys. Soc. Japan 22, 833 (1967).
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).
W. R. Heller and A. Marcus, Phys. Rev. 84, 809 (1951).
E. O. Kane, J. Phys. Chem. Solids 1, 249 (1957).
W. Staude, Phys. Letters 29A, 228 (1969) and phys. stat. sol. b43 367 (1971).
D. G. Thomas and J. J. Hopfield, Phys. Rev. 124, 657 (1961).
L. P. Gorkov and I. E. Dzyaloshinskii, Sov. Phys JETP 26, 449 (1968).
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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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