Geometrical exponents in the integer quantum Hall effect

Institutt for Fysikk, Norges Teknisk-naturvitenskapelige Universitet, N-7034 Trondheim, Norway

Received: 6 December 1995
Accepted: 18 November 1996

Abstract

We point out that the extended Chalker-Coddington model in the “classical” limit, i.e. the limit of large disorder, shows crossover to the so-called “smart kinetic walks”. The reason why this limit has previously been identified with ordinary percolation is, presumably, that the localization length exponents ν coincide for the two problems. Other exponents, like the fractal dimension D, differ. This gives an opportunity to test the consistency of the semiclassical picture of the localization-delocalization transitions in the integer quantum Hall effect. We calculate numerically, using the extended Chalker-Coddington model, two exponents τ and D that characterize critical properties of the geometry of the wave function at these transitions. We find that the exponents, within our precision, are equal to those of two-dimensional percolation, as predicted by the semiclassical picture.