Abstract
The energy spectrum of a two-dimensional electron gas placed in a transversal magnetic field B consists of quantized Landau levels. In the absence of disorder, the degeneracy of each Landau level is N=B A/φ0, where A is the area of the sample and φ0=h/e is the magnetic flux quantum. With disorder, localized states appear at the top and bottom of the broadened Landau level, whereas states in the centre of the Landau level (the critical region) remain delocalized. This single-electron theory adequately explains most aspects of the integer quantum Hall effect1. One unnoticed issue is the location of the new states that appear in the Landau level with increasing B. Here, we show that they appear predominantly inside the critical region. This situation leads to a ‘spectral ordering’ of the localized states, which explains the stripes observed in measurements of the local inverse compressibility2,3, of two-terminal conductance4 and of Hall and longitudinal resistances5 without the need to invoke interactions as done in previous work6,7,8.
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Acknowledgements
We thank B. Jouault and X.-G. Zhang for many stimulating discussions and insightful opinions. This research was carried out at the Center for Nanophase Materials Sciences, sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, US Department of Energy. M.B. acknowledges support from the Sloan Foundation, CIfAR Nanoelectronics and NSERC.
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Zhou, C., Berciu, M. Spectral weight transfer in the integer quantum Hall effect and its consequences. Nature Phys 4, 24–27 (2008). https://doi.org/10.1038/nphys786
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DOI: https://doi.org/10.1038/nphys786
