Integer quantum Hall transitions on tight-binding lattices

We investigate the integer quantum Hall transition in the lowest Landau band of two-dimensional tight-binding lattices for non-interacting electrons affected by a perpendicular magnetic field. Specifically, we consider both simple square lattices, where Landau levels are broadened by random potentials, and random Voronoi-Delaunay lattices in which (topological) disorder is introduced by bonds between randomly positioned sites. Based on a recursive Green function approach, we calculate the smallest positive Lyapunov exponent describing the long-range behavior of the wave function intensities along a quasi-one-dimensional lattice stripe. In both systems, we observe that the critical exponent of the localization length takes a value of ν≈2.60. Our critical estimates, thus, coincide with those based on the semi-classical Chalker-Coddington (CC) network model, see e.g. [1]. They do not agree with the reduced critical exponent, ν≈2.37, found by Gruzberg et al. in a recently proposed geometrically disordered CC model [2].

[1] K. Slevin and T. Ohtsuki, Phys. Rev. B 80, 041304 (2009)
[2] I. A. Gruzberg et al., Phys. Rev. B 95, 125414 (2017)