Transverse Hall Effect in the Electric Quantum Limit

Abstract

When a current density $\overrightarrow{\mathrm{J}}$ and a magnetic induction $\overrightarrow{\mathrm{B}}$ are in the plane of a layer thin enough to quantize the motion perpendicular to the plane of the layer, the Hall voltage arises from deformation of the quantized states. If the layer is asymmetric, the Hall voltage will in general contain a term in $B^2$, as well as a term in $\overrightarrow{\mathrm{J}}\times \overrightarrow{\mathrm{B}}$. Numerical results are given for $n$-type inversion layers on (100) silicon surfaces.