Abstract
The range of phenomena observed in electronic systems in magnetic fields is large and spectacular. Perhaps most spectacular of all are the quantum Hall effect, and fractional quantum Hall effect. This chapter will be concerned with the theoretical description of these phenomena. Many of the aspects presented are treated in greater detail in Girvin and Prange.(1)
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References
S. M. Girvin and R. E. Prange, eds, The Quantum Hall Effect, Springer-Verlag (1987).
K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).
D. C. Tsui, H. L. Störmer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).
R. B. Laughlin, Phys. Rev. B 23, 5632 (1981).
K. von Klitzing, Surface Science 113, 113 (1982).
H. L. Störmer. and D. C. Tsui, Science 220, 1241 (1983).
T. Ando, Y. Matsumoto and Y. Uemura, J. Phys. Soc. Japan 39, 279 (1975).
R. E. Prange, Phys. Rev. B 23, 4802 (1981).
R. Joynt and R. E. Prange, Phys. Rev. B 29, 3303 (1984).
W. Brenig, Z. Phys. B 50, 305 (1983).
N. Levinson and K. Dan Vrdensk Selsk. Mat. Fys. Medd. 25, No. 9 (1949).
D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
A. M. Chang, P. Berglund, D. C. Tsui, H. L. Störmer, and J. C. M. Hwang, Phys. Rev. Lett. 53, 997 (1984).
R. G. Clark, in: 18th International Conference on Physics of Semiconductors (Olof Engstrom, ed., World Scientific Vol. 1, p. 393, (1986).
R. G. Clark, R. J. Nicholas, A. Usher, C. T. Foxon, and J. J. Harris, Surface Science 170, 141 (1986).
R. G. Clark, S. R. Haynes, A. M. Suckling, J. R. Mallett, P A. Wright, J. J. Harris, and C. T. Foxon, Phys. Rev. Lett. 62, 1536 (1989).
J. P. Eisenstein, H. L. Stormer, L. Pfeiffer and K. W. West, Phys. Rev. Lett. 62, 1540 (1989).
R. B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983).
Q. Niu, D. J. Thouless, and Y. S. Wu, Phys. Rev. B 31, 3372 (1985)
R. Tao and F. D. M. Haldane, Phys. Rev. B 33, 3844 (1986)
J. R. Schrieffer, “Strange Quantum Numbers in Condensed Matter and Field Theory,” NSF-ITP-85-124 Preprint (1985).
B. I. Halperin, Helv. Phys. Acta 56, 75 (1983).
J. M. Caillol, D. Levesque, J. J. Weis, and J. P. Hansen, J. Stat. Phys. 28, 325 (1982).
R. Morf and B. I. Halperin, Phys. Rev. B 33, 2221 (1986).
S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Phys. Rev. B 33, 2481 (1986).
F. D. M. Haldane and E. H. Rezayi, Phys. Rev. Lett. 54, 237 (1985).
B. I. Halperin, Phys. Rev. Lett. 52, 1583 (1984).
G. Fano, F. Ortolani, and E. Colombo, Phys. Rev. B 34, 2670 (1986).
F. D. M. Haldane, Phys. Rev. Lett. 51, 605 (1983).
D. Arovas, J. R. Schrieffer and F. Wilczek, Phys. Rev. Lett. 53, 722 (1984)
P. BĂ©ran and R. Morf, Phys. Rev. B 43, 12654 (1991).
R. Morf, N. D’Ambrumenil, and B. I. Halperin, Phys. Rev. B 34, 3037 (1986).
R. Willett, J. P. Eisenstein, H. L. Stormer, D. C. Tsui, A. C. Gossard, and J. H. English, Phys. Rev. Lett. 59, 1776 (1987).
J. P. Eisenstein, R. Willett, H. L. Stormer, D. C. Tsui, A. C. Gossard, and J. H. English, Phys. Rev. Lett. 61, 997 (1988).
F. D. M. Haldane, in: The Quantum Hall Effect (S. M. Girvin and R. E. Prange, eds.), Springer-Verlag (1987).
N. D’Ambrumenil and A. M. Reynolds, J. Phys. C 21, 119 (1988).
A. H. MacDonald and S. M. Girvin, Phys. Rev. B 33, 4009 (1986).
S. Kivelson, C. Callin, D. P. Arovas, and J. R. Schrieffer, Phys. Rev. Lett. 56, 873 (1986).
G. Baskaran, Phys. Rev. Lett. 56, 2716 (1986).
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Sections 8.95 and 8.97), Academic Press (1980).
E. Brown, Phys. Rev. 133, 1038 (1968).
B. I. Halperin, Scientific American, April 1986 p. 40.
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d’Ambrumenil, N. (1993). Theory of the Quantum Hall Effect. In: Butcher, P., March, N.H., Tosi, M.P. (eds) Physics of Low-Dimensional Semiconductor Structures. Physics of Solids and Liquids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2415-5_6
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DOI: https://doi.org/10.1007/978-1-4899-2415-5_6
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