Geometrical effects on the Hall resistance in ballistic microstructures

Abstract

We calculate the Hall resistance of four-probe junctions with unusual geometries similar to those used in recent experiments. We find a variety of behavior, including quenching at low magnetic fields and a negative Hall resistance at low fields. Our results are in excellent agreement with the experiments and are explained naturally through the concept of collimation of the electrons in the leads. In particular, we find that a gradually changing width is necessary on all four leads in order to produce good quenching, and that a negative Hall resistance in a widened cross structure requires both a region of gradual widening to provide collimation and a region of rapid widening to reflect the collimated beam.