2011
DOI: 10.1103/physrevb.84.245447
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Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition

Abstract: The conductance of a two-dimensional electron gas at the transition from one quantum Hall plateau to the next has sample-specific fluctuations as a function of magnetic field and Fermi energy. Here we identify a universal feature of these mesoscopic fluctuations in a Corbino geometry: The amplitude of the magnetoconductance oscillations has an e 2 /h resonance in the transition region, signaling a change in the topological quantum number of the insulating bulk. This resonance provides a signed scaling variable… Show more

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Cited by 43 publications
(47 citation statements)
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“…40 The regular geometry of the CC model allows one to apply numerical transfer matrix techniques. 41,42 Recent implementations of this [43][44][45][46][47][48] and other methods 49,50 agree on the value ν in the range 2.56-2.62, certainly different from ν exp . The discrepancy points to the importance of the long-range electron-electron interaction, which certainly affects the scaling near the integer QH transition [51][52][53][54][55][56][57][58] and is relevant for the interpretation of experiments.…”
Section: -30mentioning
confidence: 84%
“…40 The regular geometry of the CC model allows one to apply numerical transfer matrix techniques. 41,42 Recent implementations of this [43][44][45][46][47][48] and other methods 49,50 agree on the value ν in the range 2.56-2.62, certainly different from ν exp . The discrepancy points to the importance of the long-range electron-electron interaction, which certainly affects the scaling near the integer QH transition [51][52][53][54][55][56][57][58] and is relevant for the interpretation of experiments.…”
Section: -30mentioning
confidence: 84%
“…The critical exponent ν has been well studied both experimentally [33] and numerically. For the Chalker-Coddington model [34,35], the exponent is estimated to be ν ≈ 2.6 [36][37][38][39][40] (and see table 6). The universality of this value is supported by a study of the quantum Hall transition using a periodically driven Hamiltonian model [41].…”
Section: Discussionmentioning
confidence: 99%
“…For efficient numerical calculation, we follow the method of Fukui et al 27 We divide the 2π ×2π boundary condition space into a grid of L g × L g sites θ = (θ x , θ y ) = 2π L g (l x , l y ), l x , l y = 0, · · · , L g − 1, (15) so primitive vectorsμ are vectors in the directions of µ = x and y with length 2π/L g . For the mth eigenstate, we define a U (1) link variable…”
Section: The Chern Number Calculationmentioning
confidence: 99%