Abstract
A recent development in understanding the problem of electron localization in two-dimensional systems in strong magnetic fields is reviewed mainly from a theoretical point of view with emphasis on the relation to the quantum Hall effect. It is shown that all the states are localized exponentially except those just at the center of the Landau level in sufficiently strong magnetic fields. The energy of extended states is shifted to the higher energy side with decreasing magnetic field. There is a scaling relation between the diagonal and off-diagonal components of the conductivity tensor.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
T. Ando, A.B. Fowler and F. Stern: Rev. Mod. Phys. 54, 437 (1982).
K. von Klitzing, G. Dorda and M. Pepper: Phys. Rev. Lett.45, 494 (1980).
S. Kawaji and J. Wakabayashi: In Physics in High Magnetic Fields, ed. S. Chikazumi and N. Miura (Springer, Berlin, 1981), p.284.
T. Ando, Y. Matsumoto and Y. Uemura: J. Phys. Soc. Jpn. 32, 859 (1972).
R.B. Laughlin: Phys. Rev. B 23, 5632 (1981).
Q. Niu, D.J. Thouless and Y.-S. Wu: Phys. Rev. B 28, 3372 (1985).
D.C. Licciardello and D.J. Thouless: J. Phys. C 8, 4157 (1975)
D.C. Licciardello and D.J. Thouless: J. Phys. C 11, 925 (1978).
E. Abrahams, P.W. Anderson, D.C. Licciardello and T.V. Ramakrishnan: Phys. Rev. Lett. 42, 673 (1979).
H. Aoki and T. Ando: Solid State Commun. 38, 1079 (1981).
T. Ando: J. Phys. Soc. Jpn. 52, 1893 (1983)
T. Ando: J. Phys. Soc. Jpn. 53, 3101 (1983)
T. Ando: J. Phys. Soc. Jpn. 53, 3126 (1983).
T. Ando and H. Aoki: J. Phys. Soc. Jpn. 54, 2238 (1985).
L. Schweitzer, B. Kramer and A. MacKinnon: J. Phys. C 17, 4111 (1984).
T. Ando, Y. Matsumoto, Y. Uemura, M. Kobayashi and K.F. Komatsubara: J. Phys. Soc. Jpn. 32, 859 (1972).
S. Kawaji and J. Wakabayashi: Surf. Sci. 58, 238 (1976).
H. Levine, S.B. Libby and A.M.M. Pruisken, Phys. Rev. Lett. 51, 1915 (1983); Nucl. Phys. B 240, 30; 49; 71 (1984).
T. Ando: Surf. Sci. 170, 243 (1986).
T. Ando: J. Phys. Soc. Jpn. 55, No.9 (1986).
H. Aoki and T. Ando, Surf. Sci. 170, 249 (1986).
S. Kawaji: Prog. Theor. Phys. Suppl. 94, 178 (1986).
H.P. Wei, A.M. Chang, D.C. Tsui, A.M.M. Pruisken and M. Razeghi: Surf. Sci. 170, 238 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ando, T. (1987). Localization in Landau Levels of 2D Systems and the Quantum Hall Effect. In: Landwehr, G. (eds) High Magnetic Fields in Semiconductor Physics. Springer Series in Solid-State Sciences, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83114-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-83114-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-83116-4
Online ISBN: 978-3-642-83114-0
eBook Packages: Springer Book Archive