-
1
-
-
0003414482
-
-
R. E. Prange, S. M. Girvin Springer-Verlag, New York
-
For reviews, see The Quantum Hall Effect, edited by R. E. Prange and S. M. Girvin (Springer-Verlag, New York, 1990);
-
(1990)
The Quantum Hall Effect
-
-
-
2
-
-
0003490204
-
-
A. Pinczuk Wiley, New York S. Das Sarma
-
Perspectives in Quantum Hall Effect, edited by S. Das Sarma and A. Pinczuk (Wiley, New York, 1997).
-
(1997)
Perspectives in Quantum Hall Effect
-
-
-
3
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-
85037876518
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For a review, see
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For a review, see
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5
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85037913312
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The critical energies are exactly at the centers of Landau bands only for electron-hole (Formula presented) symmetric models. In real semiconductor systems, this is only approximately true, with the (Formula presented) symmetry broken both by (i) a nonsymmetric random potential, and (ii) mixing between different Landau levels.
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The critical energies are exactly at the centers of Landau bands only for electron-hole (Formula presented) symmetric models. In real semiconductor systems, this is only approximately true, with the (Formula presented) symmetry broken both by (i) a nonsymmetric random potential, and (ii) mixing between different Landau levels.
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6
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26144433204
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-
E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).
-
(1979)
Phys. Rev. Lett.
, vol.42
, pp. 673
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-
Abrahams, E.1
Anderson, P.W.2
Licciardello, D.C.3
Ramakrishnan, T.V.4
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7
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4243615171
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There is experimental evidence [S. V. Kravchenko, et al., Phys. Rev. B 50, 8039 (1994)] that a metallic phase may be stabilized by strong electron-electron interactions at (Formula presented) We do not consider this possibility here.
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(1994)
Phys. Rev. B
, vol.50
, pp. 8039
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Kravchenko, S.V.1
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11
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-
4243859689
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-
S.-H. Song, D. Shahar, D. C. Tsui, Y. H. Xie, and D. Monroe, Phys. Rev. Lett. 78, 2200 (1997).
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 2200
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-
Shahar, D.1
Tsui, D.C.2
Xie, Y.H.3
Monroe, D.4
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26
-
-
0002682221
-
-
X. C. Xie, D. Z. Liu, B. Sundaram, and Q. Niu, Phys. Rev. B 54, 4966 (1996).
-
(1996)
Phys. Rev. B
, vol.54
, pp. 4966
-
-
Xie, X.C.1
Liu, D.Z.2
Sundaram, B.3
Niu, Q.4
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31
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85037912443
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To be defined below. See also Refs. 30 and 31
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To be defined below. See also Refs. 30 and 31.
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32
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3442880129
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D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
-
(1982)
Phys. Rev. Lett.
, vol.49
, pp. 405
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-
Thouless, D.J.1
Kohmoto, M.2
Nightingale, M.P.3
den Nijs, M.4
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36
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0001761463
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The quantization of the Chern number comes from the fact that it can be expressed as a winding number of a fiber bundle on a compact parameter space.3031 In our case the compact parameter space is spanned by the two boundary condition angles. It has been shown [N. Imai, K. Ishikawa, T. Matsuyama, and I. Tanaka, Phys. Rev. B 42, 10 610 (1990);
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(1990)
Phys. Rev. B
, vol.42
, pp. 10 610
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Imai, N.1
Ishikawa, K.2
Matsuyama, T.3
Tanaka, I.4
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38
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0000176356
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K. Ishikawa, et al., Phys. Lett. A 210, 321 (1996)] that the Hall conductance may also be expressed as the winding number of a compact momentum space in a properly formulated field theory. These authors further argued that the Hall conductance receives no finite size corrections in realistic situations.
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(1996)
Phys. Lett. A
, vol.210
, pp. 321
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Ishikawa, K.1
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39
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0001560031
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See also A. H. MacDonald, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer (Plenum, New York, 1991).
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A. H. MacDonald, Phys. Rev. B 28, 6713 (1983).See also A. H. MacDonald, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer (Plenum, New York, 1991).
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(1983)
Phys. Rev. B
, vol.28
, pp. 6713
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MacDonald, A.H.1
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41
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85037906106
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Strictly speaking in this case (and all other cases with even (Formula presented) the Chern numbers of the two central bands are not well defined, as there is no gap separating them; only the sum of their Chern numbers is well defined. However a gap may be opened by introducing a very small next neighbor hopping term to make the Chern numbers well defined.
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Strictly speaking in this case (and all other cases with even (Formula presented) the Chern numbers of the two central bands are not well defined, as there is no gap separating them; only the sum of their Chern numbers is well defined. However a gap may be opened by introducing a very small next neighbor hopping term to make the Chern numbers well defined.
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42
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85037891804
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K. Yang, D. Shahar, R. N. Bhatt, D. C. Tsui, and M. Shayegan, cond-mat/9805341 (unpublished).
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Yang, K.1
Shahar, D.2
Bhatt, R.N.3
Tsui, D.C.4
Shayegan, M.5
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43
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0001106242
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A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein, Phys. Rev. B 50, 7526 (1994).
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(1994)
Phys. Rev. B
, vol.50
, pp. 7526
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Ludwig, A.W.W.1
Fisher, M.P.A.2
Shankar, R.3
Grinstein, G.4
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44
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85037912189
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The situation however may be different when the carriers are holes instead of electrons; further investigation is underway.
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The situation however may be different when the carriers are holes instead of electrons; further investigation is underway.
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45
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0001707901
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For early experimental attempts in studying the IQHE in the presence of a periodic potential, see R. R. Gerhardts, D. Weiss, and K. v. Klitzing, Phys. Rev. Lett. 62, 1173 (1989);
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(1989)
Phys. Rev. Lett.
, vol.62
, pp. 1173
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Gerhardts, R.R.1
Weiss, D.2
v. Klitzing, K.3
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47
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0028392886
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Here we study exclusively the tight-binding lattice model. We note that people have also studied the continuum model in the presence of a weak periodic potential; see, e.g., B. Huckestein and R. N. Bhatt, Surf. Sci. 305, 438 (1994). We expect random potential to have similar effects there.
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(1994)
Surf. Sci.
, vol.305
, pp. 438
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Huckestein, B.1
Bhatt, R.N.2
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48
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85037904296
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We thank S. L. Sondhi for extensive discussions on the following points.
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We thank S. L. Sondhi for extensive discussions on the following points.
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49
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85037898148
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For the uncorrelated random onsite potential studied here (which maps onto Gaussian white noise potential with zero-correlation length in the continuum limit), no new length scale is introduced, although it would be interesting to study random potential with finite correlation length as well.
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For the uncorrelated random onsite potential studied here (which maps onto Gaussian white noise potential with zero-correlation length in the continuum limit), no new length scale is introduced, although it would be interesting to study random potential with finite correlation length as well.
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