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11944252798
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note
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See, for instance, the nontrivial Chern numbers for the square lattice.
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17
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10744228490
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S. Melinte, M. Berciu, C. Zhou, E. Tutuc, S. J. Papadakis, C. Harrison, E. P. De Poortere, M. Wu, P. M. Chaikin, M. Shayegan, R. N. Bhatt, and R. A. Register, Phys. Rev. Lett. 92, 036802 (2004).
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Wu, M.8
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Register, R.A.12
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19
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11944259692
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private communication
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e). The amplitude of the periodic potential's largest Fourier components is estimated to be of the order of 1 K, while the scattering rate from the zero field mobility is estimated to be ℏlτ-8 K [P. Chaikin (private communication)]. This shows that disorder is large compared to the small periodic modulation, although both are small enough that one can neglect Landau level (LL) mixing.
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Chaikin, P.1
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20
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4243971222
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The Kubo formula and the Landauer formula have been found to be equivalent in the current context for longitudinal conductance, see Daniel S. Fisher and Patrick A. Lee, Phys. Rev. B 23, 6851 (1981).
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12344271673
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Various equivalent forms of Kubo formula for conductivity exist, see for example, R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); R. Kubo, M. Toda, and N. Hashitsume, Nonequilibrium Statistical Mechanics (Springer, New York, 1985), also Refs. 6 and 7. Reference 28 offers detailed derivation of different forms, and Ref. 19 proves that in a certain type of model (similar to ours), the Kubo and the Landauer formalisms are equivalent.
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Kubo, R.1
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31
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12344271673
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Springer, New York
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Various equivalent forms of Kubo formula for conductivity exist, see for example, R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957); R. Kubo, M. Toda, and N. Hashitsume, Nonequilibrium Statistical Mechanics (Springer, New York, 1985), also Refs. 6 and 7. Reference 28 offers detailed derivation of different forms, and Ref. 19 proves that in a certain type of model (similar to ours), the Kubo and the Landauer formalisms are equivalent.
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Nonequilibrium Statistical Mechanics
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Kubo, R.1
Toda, M.2
Hashitsume, N.3
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34
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11944273422
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note
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As we introduce the computational method, it will also become clear that in the Landauer formula, the conductance is not strongly dependent on the detailed dispersion relation of the leads.
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35
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11944254036
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note
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2/h), i.e., each conduction channel may contribute a maximum of one unit conductance, since in this case there is no coupling between (and therefore scattering into) other channels. Each injected electron either comes out on the other side of the sample (if electron density and magnetic field B are such that the Fermi level is inside a subband) or is completely reflected back (if Fermi level is in one of the gaps of the Hofstadter butterfly).
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37
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0034324569
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Magnus Paulsson and Sven Stafström, Phys. Rev. B 64, 035416 (2001); J. Phys.: Condens. Matter 12, 9433 (2000).
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M. Baertschy, T. N. Rescigno, W. A. Isaacs, X. Li, and C. W. McCurdy, Phys. Rev. A 63, 022712 (2001); For details of the software used see http://www.nersc.gov/xiaoye/SuperLU
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