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.
تحميل البحث