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arXiv · 2004.01611

Edge state critical behavior of the integer quantum Hall transition

Martin Puschmann·Philipp Cain·Michael Schreiber·Thomas Vojta
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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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Martin Puschmann, Philipp Cain, Michael Schreiber, Thomas Vojta. 2020-04-03. Edge state critical behavior of the integer quantum Hall transition. https://doi.org/10.1140/epjs/s11734-021-00064-6

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