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Induced Representations of Space Groups in Phonon Spectroscopy of Crystals

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Site Symmetry in Crystals

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 108))

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Abstract

The use of the site-symmetry approach in lattice dynamics allows one to make a quick group-theoretical analysis of the phonon symmetry not only at the Brillouin-zone center but in the entire Brillouin zone. To demonstrate the efficiency of this method for crystals with many atoms in the unit cell we have considered the symmetry of crystalline, high-temperature superconductor phonon states. Bearing in mind the considerable current theoretical and experimental interest in the study of semiconductor superlattices we consider selection rules due to phonon symmetry and optical spectra for the semiconductor superlattices (GaAs)m(AlAs)n and (Si)m(Ge)n.

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References

  1. H. Poulet, J.P. Mathieu: Spectres de vibration et symétrie des cristaux (Gordon and Breach, Paris 1970)

    Google Scholar 

  2. D.L. Rousseau, R.P. Bauman, S.P.S. Porto: J. Raman Spectrosc. 10,253 (1981)

    Article  ADS  Google Scholar 

  3. G.N. Zhizhin, B.N. Mavrin, V.F. Shabanov: Opticheskiye kolebatel’nyye spectry kristallov (Optical Phonon Spectra of Crystals (Nauka, Moscow 1984) [in Russian]

    Google Scholar 

  4. O.V. Kovalev: Fiz. Tverd. Tela 17, 1700 (1975) [English transl.: Sov. Phys.-Solid State 17, 1106 (1975)

    Google Scholar 

  5. B. Jusserand, M. Cardona: Raman spectroscopy of vibrations in superlattices, in Light Scattering in Solids V: Superlattices and Other Micro-structures, ed. by M. Cardona, G. Güntherodt, Topics Appll. Phys., Vol. 66 (Springer, Berlin, Heidelberg 1989) pp. 49–152

    Google Scholar 

  6. J. Sapriel, B. Djafari Rouhani: Surf. Sci. Rep. 10, 189 (1989)

    Article  Google Scholar 

  7. J. Sapriel, J.C. Michel, J.C. Toledano, R. Vacher, J. Kervarec, A. Regreny: Phys. Rev. B 28, 2007 (1983)

    Article  ADS  Google Scholar 

  8. Yu.E. Kitaev, R.A. Evarestov: Fiz. Tverd. Tela 30, 2970 (1988) [English transl.: Sov. Phys.Solid—State 30, 1712 (1989)]

    Google Scholar 

  9. B.H. Bairamov, R.A. Evarestov, I.P. Ipatova, Yu.E. Kitaev, A.Yu. Maslov, M. Delaney, T.A. Gant, M.V. Klein, D. Levi, J. Klem, H. Morkoc: Superlattices Microstruct. 6, 227 (1989)

    Article  ADS  Google Scholar 

  10. B.H. Bairamov, T.A. Gant, M. Delaney, Yu.E. Kitaev, M.V. Klein, D. Levi, H. Morkoc, R.A. Evarestov: Zh. Eksp. Teor. Fiz. 95, 2200 (1989) [English transl.: Sov. Phys.—JETP 68, 1271 (1989)]

    Google Scholar 

  11. M.I. Alonso, M. Cardona, G. Kanellis: Solid State Commun. 69, 479 (1989); Corrigendum, ibid 70 (7), i (1989)

    Article  ADS  Google Scholar 

  12. A.P. Cracknell, B.L. Davies, S.G. Miller, W.F. Love: Kronecker Product Tables, Vols. 2, 3: Wave Vector Selection Rules and Reductions of Kronecker Products for Irreducible Representations of Space Groups (Plenum, New York 1979)

    Google Scholar 

  13. C. Thomsen, M. Cardona: Raman scattering in high-Tc superconductors, in Physical Properties of High-T c superconductors, ed. by D.M. Ginsberg (World-Scientific, Singapore 1989) p. 409–507

    Google Scholar 

  14. J.D. Jorgensen, H.-B. Schutter, D.G. Hinks, D.W. Capone, K. Zhang, M.B. Brodsky: Phys. Rev. Lett. 58, 1024 (1987)

    Article  ADS  Google Scholar 

  15. J.B. Torrance, Y. Tokura, S. La Placa, T.C. Huang, R.J. Savoy, A.I. Nazzal: Solid State Commun. 66, 703 (1988)

    Article  ADS  Google Scholar 

  16. J.-K. Liang, Y.I. Zhang, J.Q. Huang, S.S. Xie, G.C. Che, X.R. Chen, Y.M. Ni, D.N. Zhen, S.L. Jia: Physica C 156, 616 (1988)

    Article  ADS  Google Scholar 

  17. M. Onoda, M. Sato: Solid State Commun. 67, 799 (1988)

    Article  ADS  Google Scholar 

  18. Yu.E. Kitaev, R.A. Evarestov: Fiz. Tverd. Tela 31 (6), 76 (1989) [English transl.: Sov. Phys.—Solid State 31, 958 (1989)]

    Google Scholar 

  19. V.A. Veryazov, Yu.E. Kitaev, V.P. Smirnov, R.A. Evarestov: Electron and Phonon States in high-Tc superconductors, in Vysokotemperaturnaya sverkhprovodimost. Fundamental’nyye i prikladnyye issledovaniya. (High-Tc Superconductivity. Fundamental and Applied Studies), Vol. 1, ed. by A.A. Kiselev (Mashinostroeniye, Leningrad 1990) pp. 446–512 [in Russian]

    Google Scholar 

  20. M. Cardona, C. Thomsen, R. Liu, H.G. von Schnering, M. Hartweg, Y.F. Yan, Z.X. Zhao: Solid State Commun. 66, 1225 (1988)

    Article  ADS  Google Scholar 

  21. M. Stavola, D.M. Krol, L.F. Schneemeyer, S.A. Sunshine, R.M. Fleming, J.V. Waszczak, S.G. Kosinski: Phys. Rev. B 38, 5110 (1988)

    Article  ADS  Google Scholar 

  22. O.V. Kosogov, M.V. Belousov, V.A. Vasilyev, V.Yu. Davydov, Kim Gvan Dyo, A.A. Kopylov, V.D. Petrikov, V.V. Tretyakov: Pis’ma Zh. Eksp. Teor. Fiz. 48, 488 (1988) [English transl.: JETP Lett. 48,530 (1988)]

    ADS  Google Scholar 

  23. A.A. Bush, I.V. Gladyshev, A.A. Golub, O.Yu. Mashtakov, V.Yu. Mirovitskii, M.F. Limonov, Yu.F. Markov, A.G. Panfilov: Sverkhprovodimost, Fiz. Khim. Tekh. 2 (9), 104 (1989) [in Russian]

    Google Scholar 

  24. M. Iliev, V. Hadjiev: Physica C 157,495 (1989)

    Article  ADS  Google Scholar 

  25. I.V. Aleksandrov, A.B. Bykov, A.F. Goncharov, V.N. Denisov, B.N. Mavrin, O.K. Melnikov, V.B. Podobedov, N.I. Romanova: Pis’ma Zh. Eksp. Teor. Fiz. 49, 150 (1989). [English transl.: JETP Lett. 49, 175 (1989)]

    ADS  Google Scholar 

  26. S.K. Blower, C. Greaves: Mater. Res. Bull. 23, 765 (1988)

    Article  Google Scholar 

  27. P. Confiant, J.-C. Boivin, D. Thomas: J. Solid State Chem. 35, 192 (1980)

    Article  ADS  Google Scholar 

  28. A.A. Bush, Yu.E. Kitaev, M.A. Kulikov, M.F. Limonov, Yu.F. Markov, A.A. Novikov, V.P. Sirotinkin, Yu.V. Titov, R.A. Evarestov: Fiz. Tverd. Tela 34, 148 (1992), [English transl.: Sov. Phys.—Solid State]

    Google Scholar 

  29. M.F. Limonov, Yu.F. Markov, A.G. Panfilov, B.S. Razbirin, A.A. Bush, I.S. Dubenko: Solid State Commun. 75, 511 (1990)

    Article  ADS  Google Scholar 

  30. M.F. Limonov, Yu.F. Markov, A.G. Panfilov, B.S. Razbirin: Sverkhprovodimost, Fiz. Khim. Tekh. 4, 233 (1991) [English transl.: Supercond., Phys. Chem. Technol. 4, 198 (1991)]

    Google Scholar 

  31. R. Zallen, M.L. Slade, A.T. Ward: Phys. Rev. B 3, 4257 (1971)

    Article  ADS  Google Scholar 

  32. P. Rouqette, J. Allegre, J. Camassel, J. Pascual: Phys. Rev. B 38, 12470 (1988)

    Article  ADS  Google Scholar 

  33. I.P. Ipatova, Yu.E. Kitaev, V.G. Malyshkin, R.A. Evarestov: Fiz. Tverd. Tela 32 1565 (1990) [English transl.: Sov. Phys.-Solid State 32, 918 (1990)]

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemistry, St. Petersburg University St. Peterhoff, Universitetiskii pr. 2, 198904, St. Petersburg, Russia

    Professor Robert A. Evarestov

  2. Department of Theoretical Physics, Institute of Fine Mechanics and Optics, Sablinskaya 14, 197101, St. Petersburg, Russia

    Professor Vyacheslav P. Smirnov

Authors
  1. Professor Robert A. Evarestov
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  2. Professor Vyacheslav P. Smirnov
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© 1993 Springer-Verlag Berlin Heidelberg

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Evarestov, R.A., Smirnov, V.P. (1993). Induced Representations of Space Groups in Phonon Spectroscopy of Crystals. In: Site Symmetry in Crystals. Springer Series in Solid-State Sciences, vol 108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97442-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-97442-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-97444-1

  • Online ISBN: 978-3-642-97442-7

  • eBook Packages: Springer Book Archive

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