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 intrasubband process, can account for both the magnitude and magnetic-field dependence ∝B3/2 of the critical breakdown fields observed experimentally.