We study electron transport in quasi-one-dimensional metallic wires. Our aim is to compare an impurity-free wire with rough edges with a smooth wire with impurity disorder. We calculate the electron transmission through the wires by the scattering-matrix method, and we find the Landauer conductance for a large ensemble of disordered wires. We first study the impurity-free wire whose edges have roughness with a correlation length comparable with the Fermi wavelength. Simulating wires with the number of the conducting channels (N c ) as large as 34-347, we observe the roughness-mediated effects which are not observable for small N c (∼ 3-9) used in previous works. First, we observe the crossover from the quasi-ballistic transport to the diffusive one, where the ratio of the quasi-ballistic resistivity to the diffusive resistivity is ∼N c independent of the parameters of roughness. Second, we find that transport in the diffusive regime is carried by a small effective number of open channels, equal to ∼6. This number is universal-independent of N c and of the parameters of roughness. Third, we see that the inverse mean conductance rises linearly with the wire length (a sign of the diffusive regime) up to the length twice larger than the electron localization length. We develop a theory based on the weak-scattering limit and semiclassical Boltzmann equation, and we explain the first and second observations analytically. For the impurity disorder we find a standard diffusive behavior. Finally, we derive from the Boltzmann equation the semiclassical electron mean free path and we compare it with the quantum mean free path obtained from the Landauer conductance. They coincide for the impurity disorder; however, for the edge roughness they strongly differ, i.e., the diffusive transport in the wire with rough edges is not semiclassical. It becomes semiclassical only for roughness with a large correlation length. The conductance then behaves like the conductance of the wire with impurities, also showing the conductance fluctuations of the same size.

Future spintronic devices based on skyrmions will require precise control of the skyrmion motion. We show that this goal can be achieved through the use of magnetic antidot arrays. We perform micromagnetic simulations and semianalytical calculations based on the Thiele equation, where the skyrmion motion is driven by applied electric current via spin transfer torque (STT) or spin orbit torque (SOT) mechanism. For both torque mechanisms we demonstrate that an antidot array can guide the skyrmions in different directions depending on the parameters of the applied current pulse. Despite the fixed direction of the net driving current, due to the nontrivial interplay between the repulsive potential introduced by the antidots, the skyrmion Hall effect, and the nonuniform current distribution, full control of skyrmion motion in a 2D lattice can be achieved. Moreover, we demonstrate that the direction of skyrmion motion can be controlled by tuning only a single parameter of the current pulse, i.e., current magnitude.

We study mesoscopic transport in the quasi-one-dimensional wires and rings made of a two-dimensional conductor of width W and length L 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 δ-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 δ 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)].