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Edge-state critical behavior of the integer quantum Hall transition

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Abstract

The integer quantum Hall effect features a paradigmatic quantum phase transition. Despite decades of work, experimental, numerical, and analytical studies have yet to agree on a unified understanding of the critical behavior. Based on a numerical Green function approach, we consider the quantum Hall transition in a microscopic model of non-interacting disordered electrons on a simple square lattice. In a strip geometry, topologically induced edge states extend along the system rim and undergo localization–delocalization transitions as function of energy. We investigate the boundary critical behavior in the lowest Landau band and compare it with a recent tight-binding approach to the bulk critical behavior [Phys. Rev. B 99, 121301(R) (2019)] as well as other recent studies of the quantum Hall transition with both open and periodic boundary conditions.

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Notes

  1. We consider fits as reasonable when the mean squared deviation approximates the data’s standard deviation. Unless noted otherwise, the given uncertainties of the critical estimates represent statistical standard deviations with respect to individual fits.

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Acknowledgements

This work was supported by the NSF under Grant Nos. DMR-1506152 and DMR-1828489.

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Authors and Affiliations

  1. Department of Physics, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Martin Puschmann & Thomas Vojta

  2. Institute of Physics, Chemnitz University of Technology, 09107, Chemnitz, Germany

    Philipp Cain & Michael Schreiber

Authors
  1. Martin Puschmann
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  2. Philipp Cain
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  3. Michael Schreiber
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  4. Thomas Vojta
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Contributions

M. P. and T. V. conceived the presented idea. M. P. performed the simulations, analyzed the data, and took the lead in writing the manuscript. All authors discussed the results and provided critical feedback to the analysis and the manuscript.

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Correspondence to Thomas Vojta.

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Puschmann, M., Cain, P., Schreiber, M. et al. Edge-state critical behavior of the integer quantum Hall transition. Eur. Phys. J. Spec. Top. 230, 1003–1007 (2021). https://doi.org/10.1140/epjs/s11734-021-00064-6

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