Numerical study of current distributions in finite planar Hall samples with disorder

Abstract

A numerical study is made of current distributions in finite-width Hall bars with disorder and some theoretical observations are verified. The equilibrium current and the Hall current are substantially different in distribution. It is observed 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. The edge states themselves scarcely affect both the equilibrium and Hall currents in the plateau regime. The sample edge combines with disorder to efficiently delocalize electrons near the edge while the Hall field competes with disorder to delocalize electrons in the sample interior. A possible mechanism is suggested for the breakdown of the quantum Hall effect.