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-cr ystalline (001) molybdenum and tungsten nanostructures at 4.2 K. In such na nostructures 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 bound aries of the device. An applied magnetic field changes the electronic traje ctories and therefore modifies the surface scattering. In particular, in na nowires we have observed a strong reduction (respectively, increase) of the resistance when the magnetic field is directed parallel (respectively, per pendicular) to the current. When the mean free path of electrons is of the order of or larger than the lateral sample dimensions, the nanostructures e xhibit 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 domi nated electron transport in a moderate magnetic field, resulting in a re-en trance effect in the ballistic properties of cross-type nanostructures.