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Il Nuovo Cimento D

, Volume 1, Issue 2, pp 155–168 | Cite as

Crystal electrons in magnetic fields: Second-order perturbation for general periodic potentials

  • A. Rauh
  • H. J. Schellnhuber
Article

Summary

The diamagnetic band structure is derived up to second order in the periodic potential. This is done for arbitrary crystal potentials and rational magnetic fields. Our perturbative treatment should give the correct energy spectrum in the Landau regime including the condition for magnetic breakdown. We also present an exact effective Hamiltonian which is reduced to 2 space dimensions for a general crystal potential.

Keywords

Landau Level Periodic Potential Translation Operator Crystal Electron Magnetic Breakdown 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Riassunto

Si deduce la struttura di banda diamagnetica fino al second'ordine nel potenziale periodico. Ciò è fatto per potenziali di cristallo arbitrari e campi magnetici razionali. Il nostro procedimento perturbativo dovrebbe dare il corretto spettro di energia nel regime di Landau che include la condizione di caduta magnetica. Si presenta anche un'hamiltoniana efficace esatta che è ridotta a due dimensioni spaziali per un potenziale cristallino generale.

Резюме

Определяется диамагнитная зонная структура с точностью до второго порядка по периодическому потенциалу. Вычисления проводятся для произвольных кристаллических потенциалов и рациональных магнитных полей. Наш пертурбационный подход должен давать правильный энергетический спектр В режиме Ландау, включая условие для магнитного нарушения. Мы также приводим точный эффективный Гамильтониан, который сводится к двум пространственным измерениям для общего кристаллического потенциала.

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References

  1. (1).
    H. J. Schellnhuber: Thesis, University of Regensburg (1980).Google Scholar
  2. (2).
    H. J. Schellnhuber andG. M. Obermair:Phys. Rev. Lett.,45, 276 (1980).MathSciNetCrossRefADSGoogle Scholar
  3. (3).
    G. M. Obermair andH. J. Schellnhuber:Phys. Rev. B,23, 5185 (1981).CrossRefADSGoogle Scholar
  4. (4).
    H. J. Schellnhuber, G. M. Obermair andA. Rauh:Phys. Rev. B,23, 5191 (1981).CrossRefADSGoogle Scholar
  5. (5).
    R. Peierls:Z. Phys.,80, 763 (1933).MATHCrossRefADSGoogle Scholar
  6. (6).
    L. Onsager:Philos. Mag.,43, 1006 (1952).Google Scholar
  7. (7).
    M. Guira, R. Marcon andP. Marietti:Nuovo Cimento B,29, 49 (1975).ADSGoogle Scholar
  8. (8).
    A. Rauh andH. J. Schellnhuber:Phys. Status Solidi B,106, 53 (1981).Google Scholar
  9. (9).
    A. B. Pippard:Proc. R. Soc. London Ser. A,270, 1 (1962).MATHADSCrossRefGoogle Scholar
  10. (10).
    J. Zak:Phys. Rev. Sect. A,136, 1647 (1964).MATHMathSciNetADSGoogle Scholar
  11. (11).
    F. Bentosela:Nuovo Cimento B,16, 115 (1973).ADSGoogle Scholar
  12. (12).
    G. H. Wannier:J. Math. Phys. (N. Y.),21, 2844 (1980).CrossRefADSGoogle Scholar
  13. (13).
    H. J. Fischbeck:Phys. Status Solidi,3, 1082 (1963).MATHGoogle Scholar
  14. (14).
    E. Brown:Phys. Rev. Sect. A,133, 1038 (1964).ADSGoogle Scholar
  15. (15).
    H. J. Fischbeck:Phys. Status Solidi,38, 11 (1970).Google Scholar
  16. (16).
    A. Rauh:Phys. Status Solidi B,69, K9 (1975).ADSGoogle Scholar
  17. (17).
    W. Opechowski andW. G. Tam:Physica (The Hague),42, 529 (1969).MathSciNetCrossRefADSGoogle Scholar
  18. (18).
    H. W. Neumann andA. Rauh:Phys. Status Solidi B,96, 233 (1979).ADSGoogle Scholar
  19. (19).
    A. Rauh, S. R. Salinas andL. C. de Menezes:Phys. Rev. B,17, 591 (1978).MathSciNetCrossRefADSGoogle Scholar

Copyright information

© Società Italiana di Fisica 1982

Authors and Affiliations

  • A. Rauh
    • 1
  • H. J. Schellnhuber
    • 2
  1. 1.Fachbereich Physik der UniversitätOldenburgBRD
  2. 2.Fakultät für Physik der UniversitätRegensburgBRD

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