The edge and bulk electron state dominated magnetotransport in multi-terminal single-crystalline refractory metal nanostructures

We have performed magnetotransport measurements in multi-terminal single-crystalline (001) molybdenum and tungsten nanostructures at 4.2 K. In such nanostructures with thicknesses of d = 90, 170, 290 and 340 nm and lead width w = 7d, the resistance is mainly due to electronic scattering by the boundaries of the device. An applied magnetic field changes the electronic trajectories and therefore modifies the surface scattering. In particular, in nanowires we have observed a strong reduction (respectively, increase) of the resistance when the magnetic field is directed parallel (respectively, perpendicular) to the current. When the mean free path of electrons is of the order of or larger than the lateral sample dimensions, the nanostructures exhibit strong geometric effects, such as longitudinal magnetic focusing and non-monotonic dependence of the bend resistance against the magnetic field. The latter is explained by crossover from the edge to the bulk state dominated electron transport in a moderate magnetic field, resulting in a re-entrance effect in the ballistic properties of cross-type nanostructures.