Magnetoresistance of bismuth nanowire arrays: A possible transition from one-dimensional to three-dimensional localization

This paper reports a series of magnetoresistance measurements made on arrays of bismuth nanowires with diameters ranging from 28±3 to 70±10 nm. The data were taken between 1.4 and 10 K in magnetic fields from 0 to 5 T. The magnetoresistance curves below 4.2 K show a steplike increase in magnetoresistance relative to the curves at 4.2 K, occurring at the field at which the magnetic length $L_H$ equals the wire diameter d. At low B fields where $L_H>d,$ the electron wave function is confined by the wire diameter, while at high magnetic fields for which $L_H<d,$ the carriers are in a bulklike environment. These results suggest that the steplike magnetoresistance is due to a transition between one-dimensional (1D) localization and 3D localization.