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Volumn 59, Issue 12, 1999, Pages 8144-8151

Quantum hall–insulator transitions in lattice models with strong disorder

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EID: 4243399913     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.8144     Document Type: Article
Times cited : (47)

References (49)
  • 1
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    • 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 scopus 로고    scopus 로고
    • 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
    • 85037876518 scopus 로고    scopus 로고
    • For a review, see
    • For a review, see
  • 5
    • 85037913312 scopus 로고    scopus 로고
    • 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.
    • 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.
  • 7
    • 4243615171 scopus 로고
    • 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.
    • (1994) Phys. Rev. B , vol.50 , pp. 8039
    • Kravchenko, S.V.1
  • 31
    • 85037912443 scopus 로고    scopus 로고
    • To be defined below. See also Refs. 30 and 31
    • To be defined below. See also Refs. 30 and 31.
  • 36
    • 0001761463 scopus 로고
    • 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);
    • (1990) Phys. Rev. B , vol.42 , pp. 10 610
    • Imai, N.1    Ishikawa, K.2    Matsuyama, T.3    Tanaka, I.4
  • 38
    • 0000176356 scopus 로고    scopus 로고
    • 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.
    • (1996) Phys. Lett. A , vol.210 , pp. 321
    • Ishikawa, K.1
  • 39
    • 0001560031 scopus 로고
    • See also A. H. MacDonald, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer (Plenum, New York, 1991).
    • 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).
    • (1983) Phys. Rev. B , vol.28 , pp. 6713
    • MacDonald, A.H.1
  • 41
    • 85037906106 scopus 로고    scopus 로고
    • 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.
    • 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.
  • 44
    • 85037912189 scopus 로고    scopus 로고
    • The situation however may be different when the carriers are holes instead of electrons; further investigation is underway.
    • The situation however may be different when the carriers are holes instead of electrons; further investigation is underway.
  • 47
    • 0028392886 scopus 로고
    • 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.
    • (1994) Surf. Sci. , vol.305 , pp. 438
    • Huckestein, B.1    Bhatt, R.N.2
  • 48
    • 85037904296 scopus 로고    scopus 로고
    • We thank S. L. Sondhi for extensive discussions on the following points.
    • We thank S. L. Sondhi for extensive discussions on the following points.
  • 49
    • 85037898148 scopus 로고    scopus 로고
    • 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.
    • 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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