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Properties describing the dynamics of crystal electrons for the case of a non-local potential

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Zeitschrift für Physik A Hadrons and nuclei

Abstract

Thek-p formalism ist generalized to allow for non-local one-electron Hamiltonains, too. The one-electron energiesE nk are found to be continuous functions ofk and to be analytic provided different bands do not touch. In addition, af-sum rule is derived and it is shown that the expectation value of the velocity operator coincides with the usual definition of group velocity. Explicit expressions for the non-diagonal elements of the velocity operator and of the effective mass tensor are given.

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References

  1. Hedin, L. D.: Quantum Chemistry Group, Technical Report (Uppsala), No. 84, (1962) unpublished; — Phys. Rev.139 A, 796 (1965); — Arkiv Fysik30, 231 (1965).

  2. Brinkman, W., Goodman, B.: Phys. Rev.149, 597 (1966).

    Article  ADS  Google Scholar 

  3. Bross, H.: Z. Physik215, 485 (1968).

    Article  ADS  Google Scholar 

  4. Bross, H., Weilacher, H.: Z. Physik225, 325 (1972).

    Article  ADS  Google Scholar 

  5. Bross, H., Stöhr, H.: In: Herman, F., Dalton, N. W., Köhler, T.: Computational solid state physics, p. 143. New York-London: Plenum Press 1972.

    Chapter  Google Scholar 

  6. Kane, E. O.: In: Semiconductors and semimetals (ed. R. K. Willardson and A. C. Beer), vol. 1, Physics of III-V compounds. New York-London: Academic Press 1966.

    Google Scholar 

  7. Cardona, M., Pollak, F. H.: Phys. Ref.142, 539 (1960).

    Google Scholar 

  8. See for example: Jones, H.: Theory of brillouin zones and electronic states in crystals. Amsterdam: North-Holland Publishing Co. 1962.

    MATH  Google Scholar 

  9. Streitwolf, H. W.: Phys. stat. sol.4, K 105 (1955).

    Article  ADS  Google Scholar 

  10. Blount, E. J.: Solid State Phys.13, 305 (1962).

    MathSciNet  Google Scholar 

  11. Adams, E. N.: Phys. Rev.85, 411 (1957).

    Google Scholar 

  12. Stolz, H.: Ann. Phys. (Lpzg.) (7),7, 353 (1961).

    Article  ADS  Google Scholar 

  13. Fuchs, K.: Proc. Roy. Soc. (London), Ser. A176, 214 (1940).

    Article  ADS  MathSciNet  Google Scholar 

  14. Peierls, R.: Z. Physik53, 255 (1929).

    Article  ADS  Google Scholar 

  15. Bross, H., Bohn, G.: Phys. stat. sol.20, 277 (1967).

    Article  ADS  Google Scholar 

  16. Stöhr, H.: Dissertation, München 1971.

  17. Stöhr, H., Bross, H.: Phys. stat. sol.54, 227 (1972).

    Article  ADS  Google Scholar 

  18. Bross, H.: Z. Naturforsch.15 a, 869 (1960).

    ADS  Google Scholar 

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Authors and Affiliations

  1. Sektion Physik der Universität München, Federal Republic of Germany

    H. Bross & H. Weilacher

Authors
  1. H. Bross
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  2. H. Weilacher
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Additional information

The authors gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft sponsoring these investigations by a „Sachbeihilfe”. They are grateful to Dr. H. Stöhr for discussions, and making it possible to test for formalism in the case of Cu. Finally they are indebted to the Leibniz-Rechenzentrum where the numerical calculations were performed.

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Bross, H., Weilacher, H. Properties describing the dynamics of crystal electrons for the case of a non-local potential. Z. Physik 262, 95–104 (1973). https://doi.org/10.1007/BF01399720

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