Boundary critical behavior of the integer quantum Hall transition

We recently performed a high-accuracy study of the integer quantum Hall transition for a microscopic model of non-interacting disordered electrons: Based on a recursive Green function approach, we investigated the electronic wave functions in the lowest Landau band of a tight-binding model on a simple square lattice. To determine the bulk critical behavior, we employed lattices with the topology of an infinite cylinder [1].
Here, we consider quasi-one-dimensional lattices with the topology of an infinite strip, i.e., open boundary conditions. Edge states can expand along the entire rim of the system. They can undergo a boundary localization-delocalization transition. We investigate its critical behavior in the lowest Landau band and compare it with previous works. Additionally, we study the localization-delocalization transitions in the lowest Landau band of two-dimensional topologically disordered random Voronoi-Delaunay lattices [2].
[1] M. Puschmann et al., arXiv:1805.09958
[2] M. Puschmann et al., Eur. Phys. J. B 88, 314