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


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 


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  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

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