Advertisement

Point impurities remove degeneracy of the Landau levels in a two-dimensional electron gas

  • A. M. Dyugaev
  • P. D. Grigoriev
  • Yu. N. Ovchinnikov
Condensed Matter

Abstract

The density of states of a two-dimensional electron gas in a magnetic field has been studied taking into account the scattering on point impurities. It is demonstrated that allowance for the electron-impurity interaction completely removes degeneracy of the Landau levels even for a small volume density of these point defects. The density of states is calculated in a self-consistent approximation taking into account all diagrams without intersections of the impurity lines. The electron density of states ρ is determined by the contribution from a cut of the one-particle Green’s function rather than from a pole. In a wide range of the electron energies ω (measured from each Landau level), the value of ρ(ω) is inversely proportional to the energy |ω| and proportional to the impurity concentration. The obtained results are applicable to various two-dimensional electron systems such as inversion layers, heterostructures, and electrons on the surface of liquid helium.

PACS numbers

73.20.At 71.70.Di 73.20.Hb 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. B. Shikin and Yu. P. Monarkha, Two-Dimensional Charged Systems in Helium (Nauka, Moscow, 1989).Google Scholar
  2. 2.
    The Quantum Hall Effect, Ed. by R. Prange and S. M. Girvin (Springer, New York, 1987; Mir, Moscow, 1989).Google Scholar
  3. 3.
    E. M. Baskin, L. N. Magarill, and M. V. Éntin, Zh. Éksp. Teor. Fiz. 75, 723 (1978) [Sov. Phys. JETP 48, 365 (1978)].Google Scholar
  4. 4.
    A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics (Fizmatgiz, Moscow, 1962; Prentice Hall, Englewood Cliffs, N.J., 1963).Google Scholar
  5. 5.
    Yu. A. Bychkov, Zh. Éksp. Teor. Fiz. 39, 1401 (1960) [Sov. Phys. JETP 12, 971 (1960)].Google Scholar
  6. 6.
    Tsunea Ando, J. Phys. Soc. Jpn. 36, 1521 (1974); J. Phys. Soc. Jpn. 37, 622 (1974).Google Scholar
  7. 7.
    L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 3rd ed. (Nauka, Moscow, 1974; Pergamon, New York, 1977).Google Scholar
  8. 8.
    F. Wegner, Z. Phys. B 51, 279 (1983).CrossRefGoogle Scholar
  9. 9.
    E. Brezin, D. I. Gross, and C. Itzykson, Nucl. Phys. B 235, 24 (1984).ADSMathSciNetGoogle Scholar
  10. 10.
    W. Apel, J. Phys. C 20, L577 (1987).CrossRefADSGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • A. M. Dyugaev
    • 1
    • 2
  • P. D. Grigoriev
    • 1
    • 3
  • Yu. N. Ovchinnikov
    • 1
    • 2
  1. 1.Landau Institute of Theoretical PhysicsRussian Academy of SciencesChernogolovka, Moscow regionRussia
  2. 2.Max Planck Institute for the Physics of Complex SystemsDresdenGermany
  3. 3.High Magnetic Field LaboratoryMPI-FRF and CNRS, BP166GrenobleFrance

Personalised recommendations