Using numerical simulations, we observe phase locking, Arnold tongues, and Devil's staircases for vortex lattices driven at varying angles with respect to an underlying superconducting periodic pinning array. This rich structure should be observable in transport measurements. The transverse V (I) curves have a Devil's staircase structure, with plateaus occurring near the driving angles along symmetry directions of the pinning array. Each of the plateaus corresponds to a different dynamical phase with a distinctive vortex structure and flow pattern.

We study stochastic transport of fluxons in superconductors by alternating current (AC) rectification. Our simulated system provides a fluxon pump, "lens", or fluxon "rectifier" because the applied electrical AC is transformed into a net DC motion of fluxons. Thermal fluctuations and the asymmetry of the ratchet channel walls induce this "diode" effect, which can have important applications in devices, like SQUID magnetometers, and for fluxon optics, including convex and concave fluxon lenses. Certain features are unique to this novel two-dimensional (2D) geometric pump, and different from the previously studied 1D ratchets.Comment: Phys. Rev. Lett. 83, in press (1999); 4 pages, 5 .gif figures; figures also available at http://www-personal.engin.umich.edu/~nori/ratche

Using Langevin simulations, we examine driven colloids interacting with quenched disorder. For weak substrates the colloids form an ordered state and depin elastically. For increasing substrate strength, we find a sharp crossover to inhomogeneous depinning and a substantial increase in the depinning force, analogous to the peak effect in superconductors. The velocity versus driving force curve shows criticality at depinning, with a change in scaling exponent occurring at the order to disorder crossover. Upon application of a sudden pulse of driving force, pronounced transients appear in the disordered regime which are due to the formation of long-lived colloidal flow channels.

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.

We study vortex states and dynamics in two-dimensional ͑2D͒ superconductors with periodic pinning at fractional submatching fields using numerical simulations. For square pinning arrays we show that ordered vortex states form at 1/1,1/2, and 1/4 filling fractions while only partially ordered states form at other filling fractions, such as 1/3 and 1/5, in agreement with recent imaging experiments. For triangular pinning arrays we observe matching effects at filling fractions of 1/1, 6/7, 2/3, 1/3, 1/4, 1/6, and 1/7. For both square and triangular pinning arrays we also find that, for certain submatching fillings, vortex configurations depend on pinning strength. For weak pinning, ordering in which a portion of the vortices are positioned between pinning sites can occur. Depinning of the vortices at the matching fields, where the vortices are ordered, is elastic while at the incommensurate fields the motion is plastic. At the incommensurate fields, as the applied driving force is increased, there can be a transition to elastic flow where the vortices move along the pinning sites in 1D channels and a reordering transition to a triangular or distorted triangular lattice occurs. We also discuss the current-voltage curves and how they relate to the vortex ordering at commensurate and incommensurate fields.

We present results from an extensive series of simulations and analytical work on driven vortex lattices interacting with periodic arrays of pinning sites. An extremely rich variety of dynamical plastic flow phases, very distinct from those observed in random arrays, are found as a function of an applied driving force. Signatures of the transitions between these different dynamical phases appear as very pronounced jumps and dips in striking voltage-current V(I) curves that exhibit hysteresis, reentrant behavior, and negative differential conductivity. By monitoring the moving vortex lattice, we show that these features coincide with pronounced changes in the microscopic structure and transport behavior of the driven lattice. For the case when the number of vortices is greater than the number of pinning sites, the plastic flow regimes include a one-dimensional ͑1D͒ interstitial flow of vortices between the rows of pinned vortices, a disordered flow regime where 2D pin-to-pin and winding interstitial motion of vortices occurs, and a 1D incommensurate flow regime where vortex motion is confined along the pinning rows. In the last case, flux-line channels with an incommensurate number of vortices contain mobile flux discommensurations or ''flux solitons,'' and commensurate channels remain pinned. At high driving forces, the 1D incommensurate paths of moving vortices persist with the entire vortex lattice flowing. In this regime, the incommensurate channels move at a higher velocity than the commensurate ones, causing incommensurate and commensurate rows of moving vortices to slide past one another. Thus there is no recrystallization at large driving forces. Moreover, these phases cannot be described by elastic theories. Different system parameters produce other phases, including an ordered channel flow regime, where a small number of vortices are pinned and the rest of the lattice flows through the interstitial regions, and a vacancy flow regime, which occurs when the number of vortices is less than the number of pinning sites. We also find a striking reentrant disordered-motion regime in which the vortex lattice undergoes a series of order-disorder transitions that display unusual hysteresis properties. By varying a wide range of values for the microscopic pinning parameters, including pinning strength, radius, density, and the degree of ordering, as well as varying the commensurability of the vortex lattice with its pinning substrate, we obtain a series of interesting dynamic phase diagrams that outline the onset of the different dynamical phases. We show that many of these phases and the phase boundaries can be well understood in terms of analytical arguments.

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Using a particle-based simulation model, we show that quenched disorder creates a drive-dependent skyrmion Hall effect as measured by the change in the ratio =R V V of the skyrmion velocity perpendicular (V ⊥ ) and parallel (V ) to an external drive. R is zero at depinning and increases linearly with increasing drive, in agreement with recent experimental observations. At sufficiently high drives where the skyrmions enter a free flow regime, R saturates to the disorder-free limit. This behavior is robust for a wide range of disorder strengths and intrinsic Hall angle values, and occurs whenever plastic flow is present. For systems with small intrinsic Hall angles, we find that the Hall angle increases linearly with external drive, as also observed in experiment. In the weak pinning regime where the skyrmion lattice depins elastically, R is nonlinear and the net direction of the skyrmion lattice motion can rotate as a function of external drive. We show that the changes in the skyrmion Hall effect correlate with changes in the power spectrum of the skyrmion velocity noise fluctuations. The plastic flow regime is associated with f 1 noise, while in the regime in which R has saturated, the noise is white with a weak narrow band signal, and the noise power drops by several orders of magnitude. At low drives, the velocity noise in the perpendicular and parallel directions is of the same order of magnitude, while at intermediate drives the perpendicular noise fluctuations are much larger.