Conductance and persistent current in quasi-one-dimensional systems with grain boundaries: Effects of the strongly reflecting and columnar grains

Abstract

We study mesoscopic transport in the quasi-one-dimensional wires and rings made of a two-dimensional conductor of width $W$ and length $L\ensuremath{\gg}W$. Our aim is to compare an impurity-free conductor with grain boundaries with a grain-free conductor with impurity disorder. A single grain boundary is modeled as a set of the two-dimensional $\ensuremath{\delta}$-function-like barriers positioned equidistantly on a straight line and disorder is emulated by a large number of such straight lines, intersecting the conductor with random orientation in random positions. The impurity disorder is modeled by the two-dimensional $\ensuremath{\delta}$ barriers with the randomly chosen positions and signs. The electron transmission through the wires is calculated by the scattering-matrix method, and the Landauer conductance is obtained. Moreover, we calculate the persistent current in the rings threaded by magnetic flux: We incorporate into the scattering-matrix method the flux-dependent cyclic boundary conditions and we introduce a trick allowing us to study the persistent currents in rings of almost realistic size. We mainly focus on the numerical results for $L$ much larger than the electron mean-free path, when the transport is diffusive. If the grain boundaries are weakly reflecting, the systems with grain boundaries show the same (mean) conductance and the same (typical) persistent current as the systems with impurities, and the results also agree with the single-particle theories treating disorder as a white-noise-like potential. If the grain boundaries are strongly reflecting, the rings with the grain boundaries show the typical persistent currents about three times larger than the white-noise-based theory, thus resembling the experimental data of Jariwala et al. [Phys. Rev. Lett. 86, 1594 (2001)]. Finally, we extend our study to the three-dimensional wires/rings with columnar grains. Due to the columnar shape of the grains, the resulting persistent current exceeds the white-noise-based theory by one order of magnitude, similarly as in the experiment of Chandrasekhar et al. [Phys. Rev. Lett. 67, 3578 (1991)].