Mesoscopic transport in the quasi-one-dimensional wires and rings made of a two-dimensional conductor of width W and length L ≫ W was studied. The aim was to compare an impurity-free conductor containing grain boundaries with a grain-free conductor exhibiting impurity disorder. A single grain boundary was modelled as a set of the two-dimensional δ-function-like barriers positioned equidistantly on a straight line and disorder was emulated by a large number of such straight lines, intersecting the conductor with random orientation in random positions. The impurity disorder was modelled by the two-dimensional δ barriers with the randomly chosen positions and signs. The electron transmission through the wires was calculated by the scattering-matrix method, and the Landauer conductance was obtained. Moreover, the persistent current in rings threaded by magnetic flux was calculated. The flux-dependent cyclic boundary conditions were incorporated into the scattering-matrix method and a trick was introduced which permitted the study of persistent currents in rings of almost realistic size. Attention was focussed mainly upon the numerical results for when L was much larger than the electron mean-free-path; when the transport was diffusive. If the grain boundaries were weakly reflecting, systems with grain boundaries exhibited the same (mean) conductance and the same (typical) persistent current as did systems with impurities, and the results also agreed with single-particle theories which treated disorder as being a white-noise-like potential. If the grain boundaries were strongly reflecting, the rings with grain boundaries exhibited typical persistent currents which were about three times larger than the white-noise-based theory; thus resembling the experimental data of Jariwala et al. (2001). Finally, the study was extended to three-dimensional wires/rings with columnar grains. Due to the columnar shape of the grains, the resultant persistent current exceeded the white-noise-based theory by an order of magnitude; as in the experiment of Chandrasekhar et al. (1991).

Conductance and Persistent Current in Quasi-One-Dimensional Systems with Grain Boundaries: Effects of the Strongly Reflecting and Columnar Grains. J.Feilhauer, M.Moško: Physical Review B, 2011, 84[8], 085454