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 (proportional to B^{3/2}) of the critical breakdown fields observed experimentally.