Landauer resistivity dipole in a strong magnetic field

We consider a localized single impurity in a two-dimensional electron gas with a perpendicular magnetic field at filling factor 1. A scattering theory calculation is performed for the local electron density around the impurity in the presence of a finite transport current. It is shown that the current-induced Landauer resistivity dipole is rotated by 90° compared with the situation in the absence of a magnetic field. This behavior naturally reflects the structure of the resistivity tensor, with a finite value of (Formula presented) but vanishing longitudinal resistivity (Formula presented) due to the absence of backscattering. We briefly discuss the implications of our results on the potential distribution in the quantum Hall effect, and for scanning tunneling microscopy measurements of the local density of states.