We use particle-based simulations to examine the static and driven collective phases of skyrmions interacting with random quenched disorder. We show that non-dissipative effects due to the Magnus term reduce the depinning threshold and strongly affect the skyrmion motion and the nature of the dynamic phases. The quenched disorder causes the Hall angle to become drive-dependent in the moving skyrmion phase, while different flow regimes produce distinct signatures in the transport curves. For weak disorder, the skyrmions form a pinned crystal and depin elastically, while for strong disorder the system forms a pinned amorphous state that depins plastically. At high drives the skyrmions can dynamically reorder into a moving crystal, with the onset of reordering determined by the strength of the Magnus term.

We examine the dynamics of a skyrmion moving over a two-dimensional periodic substrate utilizing simulations of a particle-based skyrmion model. We specifically examine the role of the non-dissipative Magnus term on the driven motion and the resulting skyrmion velocity-force curves. In the overdamped limit, there is a depinning transition into a sliding state in which the skyrmion moves in the same direction as the external drive. When there is a finite Magnus component in the equation of motion, a skyrmion in the absence of a substrate moves at an angle with respect to the direction of the external driving force. When a periodic substrate is added, the direction of motion or Hall angle of the skyrmion is dependent on the amplitude of the external drive, only approaching the substrate-free limit for higher drives. Due to the underlying symmetry of the substrate the direction of skyrmion motion does not change continuously as a function of drive, but rather forms a series of discrete steps corresponding to integer or rational ratios of the velocity components perpendicular ( V ⊥ ) and parallel ( V || ) to the external drive direction: V ⊥ / V || = n/m, where n and m are integers. The skyrmion passes through a series of directional locking phases in which the motion is locked to certain symmetry directions of the substrate for fixed intervals of the drive amplitude. Within a given directionally locked phase, the Hall angle remains constant and the skyrmion moves in an orderly fashion through the sample. Signatures of the transitions into and out of these locked phases take the form of pronounced cusps in the skyrmion velocity versus force curves, as well as regions of negative differential mobility in which the net skyrmion velocity decreases with increasing external driving force. The number of steps in the transport curve increases when the relative strength of the Magnus term is increased. We also observe an overshoot phenomena in the directional locking, where the skyrmion motion can lock to a Hall angle greater than the clean limit value and then jump back to the lower value at higher drives. The skyrmion-substrate interactions can also produce a skyrmion acceleration effect in which, due to the non-dissipative dynamics, the skyrmion velocity exceeds the value expected to be produced by the external drive. We find that these effects are robust for different types of periodic substrates. Using a simple model for a skyrmion interacting with a single pinning site, we can capture the behavior of the change in the Hall angle with increasing external drive. When the skyrmion moves through the pinning site, its trajectory exhibits a side step phenomenon since the Magnus term induces a curvature in the skyrmion orbit. As the drive increases, this curvature is reduced and the side step effect is also reduced. Increasing the strength of the Magnus term reduces the range of impact parameters over which the skyrmion can be captured by a pinning site, which is one of the reasons that strong Magnus force effects reduce the...

We numerically examine run-and-tumble active matter particles in Casimir geometries composed of two finite parallel walls. We find that there is an attractive force between the two walls of a magnitude that increases with increasing run length. The attraction exhibits an unusual exponential dependence on the wall separation, and it arises due to a depletion of swimmers in the region between the walls by a combination of the motion of the particles along the walls and a geometric shadowing effect. This attraction is robust as long as the wall separation is comparable to or smaller than the swimmer run length, and is only slightly reduced by the inclusion of steric interactions between swimmers. We also examine other geometries and find regimes in which there is a crossover from attraction to repulsion between the walls as a function of wall separation and run length.PACS numbers: 64.75. Xc,47.63.Gd,87.18.Hf The Casimir geometry consists of two finite parallel plates placed at a fixed distance from each other that experience an attraction due to the confinement of fluctuations in the media between the plates [1]. In the original Casimir effect calculation, electromagnetic vacuum fluctuations produce an attractive force between two metal places in a vacuum. Much later, Casimir forces were experimentally measured [2], and they have recently been studied in a variety of systems in order to understand how to control their magnitude [3] or polarity [4]. Confined classical fluctuations can produce the so-called critical Casimir effect [5][6][7], as first proposed by Fisher and de Gennes near critical demixing in bulk mixtures. The critical Casimir effect has been directly measured [8] and studied in various colloidal systems where it can produce colloidal aggregation [8,9]. Casimir type effects have also been studied in granular media, where attractive forces arise between objects or plates placed in vibrated or flowing sand [10]. Critical Casimir effects have also been proposed to occur near percolation thresholds [11] and in biological systems such as near fluctuating cellular membranes [12]. The ability to enhance or control such forces can lead to a wide variety of applications in self-assembly, particle transport, and the creation of novel devices.Strong fluctuations appear in active matter or selfdriven particle systems [13] such as swimming bacteria undergoing run-and-tumble dynamics [14,15]. Recently a number of non-biological active matter systems have been realized experimentally, including artificial swimmers [16], self-driven colloids [17][18][19], or light-activated colloidal particles performing a directed random walk [18][19][20]. Studies of interacting particles undergoing runand-tumble or active Brownian motion show a phase separation phenomenon at large run length or high density in which the particles form dense regions separated by a dilute active gas [20][21][22][23]. Monodisperse active particles, such as self-propelled disks, can form intermittent dense patches with crystalline order, termed "l...

Conformal crystals are non-uniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of the sixfold ordering in the conformally transformed hexagonal lattice plays a crucial role. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.PACS numbers: 74.25. Wx,74.25.Uv One of the most important problems for applications of type-II superconductors is how to create high critical currents or strong vortex pinning over a wide range of applied magnetic fields 1 . For over sixty years, it has been understood that the ground state vortex structure is a hexagonal lattice 2 , so many methods have been developed to increase the critical current using uniform pinning arrays that incorporate periodicity to match the vortex structure 3-13 . The pinning is enhanced at commensurate fields when the number of vortices equals an integer multiple of the number of pinning sites, but away from these specific matching fields, the enhancement of the critical current is lost 14 . Efforts to enhance the pinning at incommensurate fields have included the use of quasicrystalline substrates 15 or diluted periodic arrays [16][17][18][19][20] , where studies show that new types of non-integer commensurate states can arise in addition to the integer matching configurations. Hyperbolic tessellation arrays were also recently considered 21 .Part of the problem is the fact that under an applied current, the vortex structure does not remain uniform but instead develops a Bean-like flux gradient 22 : the vortex density is highest at the edges of the sample when the magnetic field is increased, and highest in the center of the sample when the magnetic field is removed and only trapped flux remains inside the sample. As a consequence, uniform pinning arrays generally have a portion of the pinning sites that are not fully occupied, suggesting that a more optimal pinning arrangement should include some type of density gradient to match the critical flux gradient. Here we show that a novel type of pinning structure, created using a conformal transformation of a uniform hexagonal lattice, produces a much higher critical current over a much wider range of magnetic fields than any pinning geometry considered up until now. Conformal crystals not only have a density gradient, but also preserve aspects of the hexagonal ordering naturally adopted by the vortex lattice. The pinning enhancement we find is substantial and will be very important for a wide range of superconductor applications and flux control. Our results can also be important for stabilizing novel self-assembled structures created using de...