Current distribution in Hall bars and breakdown of the quantum Hall effect

A numerical study is made of current distribution in small Hall bars with disorder. It is observed , in particular, that in the Hall-plateau regime the Hall current tends to concentrate near the sample edges while it diminishes on average in the sample interior as a consequence of localization. Also reported is another numerical experiment on a related, but rather independent topic, the breakdown of the quantum Hall effect. It is pointed out that the competition of the Hall field with disorder in the sample interior, an intra subband process, can account for both the magnitude and magnetic-field dependence ∝ B 3/2 of the critical breakdown fields observed experimentally. 1. Introduction The current distribution in a Hall sample is a subject of interest pertaining to the foundation of the quantum Hall effect (QHE). In spite of various studies, both experimental [1] and theoretical [2-6], it is still a focus of attention and controversy whether the Hall current flows in the sample interior or along the sample edges. In this paper we first report on a numerical study of current distribution in small Hall samples with disorder and verify some theoretical observations [7]. In particular, we demonstrate an important physics of redistribution of the Hall current via disorder. A by-product of the numerical analysis is a hint as to a rather independent subject, the breakdown of the quantum Hall effect [8-13]. We report on a numerical analysis [14] to verify that the competition of the Hall field with disorder in the sample interior, an intra subband process, can account for both the magnitude and magnetic-field dependence ∝ B 3/2 of the critical breakdown fields E cr observed in a series of experiments by Kawaji et al. [11-13].