One- and two-dimensional quantum transport in thin gold wires

We report on magnetoresistance (MR) measurements of thin gold wires of various widths, w between 50 nm and 50 μm prepared by electron-beam lithography. The MR is measured at temperatures between $T=1.5\mathrm{}$ and 25 K using a ${}^4\mathrm{He}$-bath cryostat where magnetic fields up to $B=5\mathrm{}\mathrm{T}$ can be applied perpendicular to the film plane. Varying the widths of the gold wires we find the “strength” of the MR being proportional to $w^{-1}$ consistent with one-dimensional (1D) behavior and constant for wires of larger widths indicating 2D behavior. This allows analyzing the MR data of the various gold wires using detailed theoretical calculations concerning 1D and 2D quantum transport. We obtain the phase coherence length and its temperature dependence, which is almost independent of whether the gold wires show 1D or 2D quantum transport behavior. This additionally confirms the analysis of the MR data and exhibits that the phase coherence length displays intrinsic scattering properties.