Abstract:
Using computer simulations, we demonstrate a new type of commensurability that occurs for vortices moving longitudinally through periodic pinning arrays in the presence of an additional transverse driving force. As a function of vortex density, there is a series of broad maxima in the transverse critical depinning force that do not fall at the matching fields where the number of vortices equals an integer multiple of the number of pinning sites. The commensurability effects are associated with dynamical states in which evenly spaced structures consisting of one or more moving rows of vortices form between rows of pinning sites. Remarkably, the critical transverse depinning force can be more than an order of magnitude larger than the longitudinal depinning force.

Abstract:
Quantized vortices stunningly illustrate the coherent nature of a superfluid Bose condensate of alkali atoms. Introducing an optical lattice depletes this coherence. Consequently, novel vortex physics may emerge in an experiment on a harmonically trapped gas in the presence of a rotating optical lattice. The most dramatic effects would occur in proximity to the Mott state, an interaction dominated insulator with a fixed integer number of particles per site. We model such a rotating gas, showing that the lattice-induced spatial profile of the superfluid density drives a gross rearrangement of vortices. For example, instead of the uniform vortex lattices commonly seen in experiments, we find parameters for which the vortices all sit at a fixed distance from the center of the trap, forming a ring. Similarly, they can coalesce at the center, forming a giant vortex. We find that the properties of this system are hysteretic, even far from the Mott state. We explain this hysteresis in terms of vortex pinning, commensurability between vortex density and pinning site density, and energy barriers against changing the number of vortices. Finally, we model time-of-flight expansion, demonstrating the experimental observability of our predictions.

Abstract:
We present results from extensive simulations of driven vortex lattices interacting with periodic arrays of pinning sites. Changing an applied driving force produces a rich variety of novel dynamical plastic flow phases which are very distinct from those observed in systems with random pinning arrays. Signatures of the transition between these different dynamical phases include sudden jumps in the current-voltage curves as well as marked changes in the vortex trajectories and the vortex lattice order. Several dynamical phase diagrams are obtained as a function of commensurability, pinning strength, and spatial order of the pinning sites.

Abstract:
We use numerical simulations to examine vortex states and dynamics in periodic funnel geometries where a drive is applied in the easy flow direction. We show that this system exhibits a number of different commensurability effects when the vortex configurations match to both the periodicity of the array and the geometry of the funnels. The vortex configurations in this system are generally different from those observed for single isolated triangular superconducting samples due to the coupling of vortices in adjacent funnels. At certain matching fields, peaks in the critical current are absent due to the particular vortex configurations that occur at these fields. We find that the overall depinning force increases with increasing vortex density as a result of the enhanced vortex-vortex interactions caused by a crowding effect at the funnel tips. When a system becomes less mobile as a result of increased particle interactions, it is said to exhibit a jamming behavior. Under an applied drive we observe a series of elastic and plastic vortex flow phases which produce pronounced features such as jumps or dips in the transport curves. In all of the flow phases, only one vortex can pass through the funnel tip at a time due to the vortex-vortex repulsion forces. As a consequence of this constraint, we observe the remarkable result that the sum of the vortex velocities at a fixed drive remains nearly constant with increasing magnetic field B rather than increasing linearly. This result is similar to the behavior of sand in an hourglass. We also show how noise fluctuations can be used to distinguish the different flow phases. Our results should be readily generalizable to other systems of particles flowing in periodic funnel geometries, such as colloids or Wigner crystals.

Abstract:
recent results obtained by the author for the dynamical phase diagrams for vortices in clean films, driven by an uniform force, and interacting with periodic pinning resulting from a columnar defect lattice are discussed. using numerical simulations of a simple model and other considerations, the dynamical phase diagrams are obtained as a function of the driving force magnitude and direction, the temperature, and the vortex density. the following dynamical phases and dynamical phase transitions are found. moving vortex lattices at low temperatures, with spatial order that can be commensurate or incommensurate with the periodic pinning, moving vortex liquids and moving smectics. dynamical melting of moving vortex lattices into moving vortex liquids takes place and transverse pinning of moving commensurate vortex lattices and smectics occurs. it is found that the dynamical phase diagrams in the theoretical limit of infinite driving force magnitudes play a central role in determining the whole dynamical phase diagram: each dynamical phase originates from an infinite-drive limit phase with the same spatial symmetry that evolves continuously into finite-drive regions of the dynamical phase diagram. it is argued that this conclusion also applies for a large class of periodic pinning potentials.

Abstract:
Recent results obtained by the author for the dynamical phase diagrams for vortices in clean films, driven by an uniform force, and interacting with periodic pinning resulting from a columnar defect lattice are discussed. Using numerical simulations of a simple model and other considerations, the dynamical phase diagrams are obtained as a function of the driving force magnitude and direction, the temperature, and the vortex density. The following dynamical phases and dynamical phase transitions are found. Moving vortex lattices at low temperatures, with spatial order that can be commensurate or incommensurate with the periodic pinning, moving vortex liquids and moving smectics. Dynamical melting of moving vortex lattices into moving vortex liquids takes place and transverse pinning of moving commensurate vortex lattices and smectics occurs. It is found that the dynamical phase diagrams in the theoretical limit of infinite driving force magnitudes play a central role in determining the whole dynamical phase diagram: each dynamical phase originates from an infinite-drive limit phase with the same spatial symmetry that evolves continuously into finite-drive regions of the dynamical phase diagram. It is argued that this conclusion also applies for a large class of periodic pinning potentials.

Abstract:
We use a simple model to study the long time fluctuations induced by random pinning on the motion of driven non--interacting vortices. We find that vortex motion seen from the co--moving frame is diffusive and anisotropic, with velocity dependent diffusion constants. Longitudinal and transverse diffusion constants cross at a characteristic velocity where diffusion is isotropic. The diffusion front is elongated in the direction of the drive at low velocities and elongated in the transverse direction at large velocities. We find that the mobility in the driven direction is always larger than the transverse mobility, and becomes isotropic only in the large velocity limit.

Abstract:
We analyze the competition between thermal fluctuations and pinning of vortices in bulk type II superconductors subject to point-like disorder and derive an expression for the temperature dependence of the pinning length L_c(T) which separates different types of single vortex wandering. Given a disorder potential with a basic scale \xi and a correlator K_0(u) \sim K_0 (u/xi)^{-\beta} ln^alpha (u/xi) we determine the dependence of L_c(T) on the correlator range: correlators with \beta > 2 (short-range) and \beta <2 (long-range) lead to the known results L_c(T) \sim L_c(0) exp[C T^3] and L_c(T) \sim L_c(0) (C T)^{(4+beta)/(2-beta)}, respectively. Using functional renormalization group we show that for \beta =2 the result takes the interpolating form L_c(T) \sim L_c(0) exp[C T^{3/(2+alpha)}]. Pinning of vortices in bulk type II superconductors involves a long-range correlator with \beta=2, \alpha=1 on intermediate scales \xi

Abstract:
We numerically investigate magnetization, pinning, ordering, and dynamics of vortices interacting with pinning arrangements which have a density gradient. We focus on conformal crystal structures obtained by conformally transforming a spatially uniform periodic array, as well as non-conformal gradient structures and structures with quasiperiodic order. The conformal structures feature a density gradient and local ordering. Using magnetization simulations we find that conformal pinning arrays exhibit enhanced pinning compared to non-conformal gradient arrays as well as compared to random, periodic, and quasiperiodic arrays, for a broad range of fields. The effectiveness of conformal arrays arises from the continuum of length scales introduced into the arrays by the conformal transformation, allowing for a broad range of local commensuration effects. At higher vortex fillings above the range of conformal effectiveness, we show that a non-conformal rectangular gradient array exhibits strong pinning due to a novel commensuration effect and vortex ordering. Using transport simulations where vortices are driven along the gradient and at an angle to the gradient, we confirm the effectiveness of conformal pinning at increasing the critical current. For a rotated drive, the gradient arrays produce a strong vortex guidance effect in the direction perpendicular to the gradient.

Abstract:
We study the vortex dynamics and vortex pinning effect in Bose-Einstein condensate in a rotating double-well trap potential and co-rotating optical lattice. We show that, in agreement with the experiment, the vortex number do not diverge when the rotational frequency $\Omega \rightarrow 1$ if the trap potential is of anisotropic double-well type. The critical rotational frequency as obtained from numerical simulations agrees very well with the value $\sqrt l/l$ for $l=4$ which supports the conjecture that surface modes with angular momentum $l=4$ are excited when the rotating condensate is trapped in double-well potential. The vortex lattice structure in a rotating triple-well trap potential and its pinning shows very interesting features. We show the existence and pinning of a new type of hidden vortices whose phase profile is similar to that of the visible vortices.