Resistance maps from local probing of a ballistic mesoscopic Hall bar

Abstract

The response of a ballistic mesoscopic Hall bar to a local potential barrier is investigated in the presence of an external magnetic field. The effect of the position of the local potential probe in the Hall cross on the Hall and bend resistance is investigated leading to two-dimensional (2D) resistance maps. The Onsager–Casimir symmetry relations and symmetry relations between resistance measurements when interchanging the current and voltage leads, is obtained numerically for such 2D resistance maps. Symmetry properties are derived for the Hall and bend resistance maps with respect to the position of the local potential barrier.