Edge state critical behavior of the integer quantum Hall transition

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.

6 pages, 2 figures, builds on arXiv:1805.09958, special volume of EPJST dedicated to FQMT19 conference, final version as published

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Cited by in corpus (1)

• The integer quantum Hall transition: an $S$-matrix approach to random networks