Bodo Huckestein — Page 2

arXiv1995

Scaling Theory of the Integer Quantum Hall Effect

The scaling theory of the transitions between plateaus of the Hall conductivity in the integer Quantum Hall effect is reviewed. In the model of two-dimensional noninteracting electrons in strong magnetic fields the transitions are disorder-induced localization-delocalization transitions. While experimental and analytical approaches are surveyed, the main emphasis is on numerical studies, which successfully describe the experiments. The theoretical models for disordered systems are described in detail. An overview of the finite-size scaling theory and its relation to Anderson localization is given. The field-theoretical approach to the localization problem is outlined. Numerical methods for the calculation of scaling quantities, in particular the localization length, are detailed. The properties of local observables at the localization-delocalization transition are discussed in terms of multifractal measures. Finally, the results of extensive numerical investigations are compared with experimental findings.

cond-mat↗

arXiv1994

Corrections to Scaling in the Integer Quantum Hall Effect

Finite size corrections to scaling laws in the centers of Landau levels are studied systematically by numerical calculations. The corrections can account for the apparent non-universality of the localization length exponent $ν$. In the second lowest Landau level the irrelevant scaling index is $y_{\mathrm{irr}}=-0.38\pm0.04$. At the center of the lowest Landau level an additional periodic potential is found to be irrelevant with the same scaling index. These results suggest that the localization length exponent $ν$ is universal with respect to Landau level index and an additional periodic potential.

cond-mat↗