Abstract
The quantum Hall (QH) effect1 is observed in two-dimensional electronic systems (2DES’s) subjected to a strong, uniform, transverse external magnetic field. Experi mentally, such systems are realized as inversion layers that form at the interfaces of heterostructures (e.g., GaAs/Al x Ga1−xAs) in the presence of an electric field (gate voltage) perpendicular to the structures. To develop an idea of the orders of magnitude involved in QH systems, we recall that sample sizes are typically of a few tenths of a mm times a few mm, whereas the charge carrier densities, n = n electron - n hole, are of the order of 1011/cm2, and the magnetic fields, B c , range from about 0.1 T up to 30 T. Moreover, experiments are performed at very low temperatures, T, typically between 10 mK and 100 mK. An important quantity characterizing QH systems is the filling factor v. denoting by Φ o = h/e = 4.14 · 10−11 Tcm2 the magnetic flux quantum and by B c,⊥ the component of the magnetic field B c perpendicular to a 2DES, the filling factor is defined by v = nΦo/B c,⊥.
Keywords
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K. von Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45, 494 (1980)
D.C. Tsui, H.L. Stormer, and A.C. Gossard, Phys. Rev. B 48, 1559 (1982)
for a review, see, e.g., R.E. Prange and S.M. Gervin, eds., The Quantum Hall Effect,
Second Edition, Graduate Texts in Contemporary Physics (Springer, New York, 1990).
B.L. Al’tshuler and P.A. Lee, Physics Today 41 (12), 36 (1988)
R.A. Webb and S. Washburn, ibid. 41 (12), 46 (1988).
R. Mottahedeh et al. ,Solid State Commun. 72, 1065 (1989)
D. Yoshioka, J. Phys. Soc. Jpn. 62, 839 (1993).
J. Fröhlich and U.M. Studer, Commun. Math. Phys. 148, 553 (1992)
J. Fröhlich and U.M. Studer, Rev. Mod. Phys.65, 733 (1993).
J. Fröhlich, U.M. Studer, and E. Thiran, “Gauge symmetry, integral lattices, and theclassification of quantum Hall fluids”, preprint, KUL-TF-93/33.
J. Fröhlich and E. Thiran, “Integral quadratic forms, Kac-Moody algebras, and fractionalquantum Hall effect: an ADE - O classification”, preprint, ETH-TH/93-22.
B.I. Halperin, Phys. Rev. B 25, 2185 (1982)
M. Büttiker, ibid. 38, 9375 (1988)
C.W.J. Beenakker, Phys. Rev. Lett. 64, 216 (1990)
A.H. MacDonald, ibid. 64, 220 (1990)
X.G. Wen, ibid. 64, 2206 (1990); Phys. Rev. B 41, 12838 (1990)
J. Fröhlich and T. Kerler, Nucl. Phys. B 354, 369 (1991)
M. Stone, Ann. Phys. (N.Y.) 207, 38 (1991)
R.C. Ashoori et al ,Phys. Rev. B 45, 3894 (1992)
K. von Klitzing, Physica B 184, 1 (1993).
P. Goddard and D. Olive, Int. J. Mod. Phys. A 1, 303 (1986).
R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983); Phys. Rev. B 27, 3383 (1983).
D.C. Tsui, Physica B 164, 59 (1990), and references therein
H.W. Jiang et al ,Phys. Rev. B 44, 8107 (1991)
H.L. Stormer, Physica B 177, 401 (1992), and references therein.
R.L. Willett et al ,Phys. Rev. Lett. 59, 1776 (1987)
J.P. Eisenstein et al, ibid. 61, 997 (1988); Surf. Sci. 229, 31 (1990).
R.G. Clark et al ,Phys. Rev. Lett. 60, 1747 (1988)
S.W. Hwang et al. ,Surf. Sci. 263, 72 (1992).
J.H. Conway, F.R.S. Sloane, and N.J.A. Sloane, Proc. R. Soc. Lond. A 418, 17 (1988), and references therein.
R. Slansky, Phys. Reports 79, 1 (1981).
F.D.M. Haldane, Phys. Rev. Lett. 51, 605 (1983); B.I. Halperin, ibid. 52, 1583 (1984).
J.K. Jain and V.J. Goldman, Phys. Rev. B 45, 1255 (1992).
J.K. Jain, Phys. Rev. Lett. 63, 199 (1989); Phys. Rev. B 41, 7653 (1990).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media New York
About this chapter
Cite this chapter
Fröhlich, J., Studer, U.M., Thiran, E. (1994). An ADE-O Classification of Minimal Incompressible Quantum Hall Fluids. In: Fannes, M., Maes, C., Verbeure, A. (eds) On Three Levels. NATO ASI Series, vol 324. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2460-1_23
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2460-1_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6047-6
Online ISBN: 978-1-4615-2460-1
eBook Packages: Springer Book Archive