Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review

Power-law intermittency in the gradient-induced self-propulsion of colloidal swimmers

Active colloidal microswimmers serve as archetypical active fluid systems, and as models for biological swimmers. Here, by studying in detail their velocity traces, we find robust power-law intermittency with system-dependent exponential cut off. We model the intermittent motion by an interplay of the field gradient-dependent active force, which depends on a fluid gradient and is reduced when the swimmer moves, and the locally fluctuating hydrodynamic drag, that is set by the wetting properties of the substrate. The model closely describes the velocity distributions of two disparate swimmer systems: AC field activated and catalytic swimmers. The generality is highlighted by the collapse of all data in a single master curve, suggesting the applicability to further systems, both synthetic and biological.

Peak effect and dynamics of stripe- and pattern-forming systems on a periodic one-dimensional substrate

We examine the ordering, pinning, and dynamics of two-dimensional pattern-forming systems interacting with a periodic one-dimensional substrate. In the absence of the substrate, particles with competing long-range repulsion and short-range attraction form anisotropic crystal, stripe, and bubble states. When the system is tuned across the stripe transition in the presence of a substrate, we find that there is a peak effect in the critical depinning force when the stripes align and become commensurate with the substrate. Under an applied drive, the anisotropic crystal and stripe states can exhibit soliton depinning and plastic flow. When the stripes depin plastically, they dynamically reorder into a moving stripe state that is perpendicular to the substrate trough direction. We also find that when the substrate spacing is smaller than the widths of the bubbles or stripes, the system forms pinned stripe states that are perpendicular to the substrate trough direction. The system exhibits multiple reentrant pinning effects as a function of increasing attraction, with the anisotropic crystal and large bubble states experiencing weak pinning but the stripe and smaller bubble states showing stronger pinning. We map out the different dynamic phases as a function of filling, the strength of the attractive interaction term, the substrate strength, and the drive, and demonstrate that the different phases produce identifiable features in the transport curves and particle orderings.

Experimental observation of current-driven antiskyrmion sliding in stripe domains

Magnetic skyrmions are promising as next-generation information units. Their antiparticle-the antiskyrmion-has also been discovered in chiral magnets. Here we experimentally demonstrate antiskyrmion sliding in response to a pulsed electric current at room temperature without the requirement of an external magnetic field. This is realized by embedding antiskyrmions in helical stripe domains, which naturally provide one-dimensional straight tracks along which antiskyrmion sliding can be easily launched with low current density and without transverse deflection from the antiskyrmion Hall effect. The higher mobility of the antiskyrmions in the background of helical stripes in contrast to the typical ferromagnetic state is a result of intrinsic material parameters and elastic energy of the stripe domain, thereby smearing out the random pinning potential, as supported by micromagnetic simulations. The demonstration and comprehensive understanding of antiskyrmion movement along naturally straight tracks offers a new perspective for (anti)skyrmion application in spintronics.

Solvable model of driven matter with pinning

We present a simple model of driven matter in a 1D medium with pinning impurities, applicable to magnetic domains walls, confined colloids, and other systems. We find rich dynamics, including hysteresis, reentrance, quasiperiodicity, and two distinct routes to chaos. In contrast to other minimal models of driven matter, the model is solvable: we derive the full phase diagram for small N, and for large N, we derive expressions for order parameters and several bifurcation curves. The model is also realistic. Its collective states match those seen in the experiments of magnetic domain walls.

Reversible, irreversible, and mixed regimes for periodically driven disks in random obstacle arrays

We examine an assembly of repulsive disks interacting with a random obstacle array under a periodic drive and find a transition from reversible to irreversible dynamics as a function of drive amplitude or disk density. At low densities and drives, the system rapidly forms a reversible state where the disks return to their exact positions at the end of each cycle. In contrast, at high amplitudes or high densities, the system enters an irreversible state where the disks exhibit normal diffusion. Between these two regimes, there can be an intermediate irreversible state where most of the system is reversible, but localized irreversible regions are present that are prevented from spreading through the system due to a screening effect from the obstacles. We also find states that we term "combinatorial reversible states" in which the disks return to their original positions after multiple driving cycles. In these states, individual disks exchange positions but form the same configurations during the subcycles of the larger reversible cycle.

Tuning the stability of a model quasicrystal and its approximants with a periodic substrate

Quasicrystals and their periodic approximants are complex crystalline phases. They have now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates, the type of complex phase was found to change depending on thermodynamic conditions and the type of substrate used. Here, we investigate the effect of a substrate on the relative thermodynamic stability of a two-dimensional model quasicrystal and its approximants. Our simulation model is particles interacting via the Lennard-Jones-Gauss potential. Our numerical methods are molecular dynamics simulations and free energy calculations that take into account phason flips explicitly. For substrates interacting weakly with the particles, we observe an incommensurate-commensurate transition, in which a continuous series of quasicrystal approximants locks into a small number of approximants. Interestingly, we observe that the 3/2 approximant exhibits phason mode fluctuations in thermodynamic equilibrium. Such fluctuations are reminiscent of random tiling and a phenomenon usually associated only with quasiperiodic order. For stronger substrates, we find an enhancement of the stability of the dodecagonal quasicrystal and variants of square lattices. We explain all observed phenomena by the interplay of the model system with the substrate. Our results demonstrate that designing novel complex periodic and quasiperiodic structures by choice of suitable substrates is a promising strategy.

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mo[Formula: see text]Ge[Formula: see text] film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

A Quenched Disorder in the Quantum-Critical Superconductor CeCoIn5

Emergent inhomogeneous electronic phases in metallic quantum systems are crucial for understanding high-Tc superconductivity and other novel quantum states. In particular, spin droplets introduced by nonmagnetic dopants in quantum-critical superconductors (QCSs) can lead to a novel magnetic state in superconducting phases. However, the role of disorders caused by nonmagnetic dopants in quantum-critical regimes and their precise relation with superconductivity remain unclear. Here, the systematic evolution of a strong correlation between superconductive intertwined electronic phases and antiferromagnetism in Cd-doped CeCoIn5 is presented by measuring current-voltage characteristics under an external pressure. In the low-pressure coexisting regime where antiferromagnetic (AFM) and superconducting (SC) orders coexist, the critical current (Ic ) is gradually suppressed by the increasing magnetic field, as in conventional type-II superconductors. At pressures higher than the critical pressure where the AFM order disappears, Ic remarkably shows a sudden spike near the irreversible magnetic field. In addition, at high pressures far from the critical pressure point, the peak effect is not suppressed, but remains robust over the whole superconducting region. These results indicate that magnetic islands are protected around dopant sites despite being suppressed by the increasingly correlated effects under pressure, providing a new perspective on the role of quenched disorders in QCSs.

Nonlinear-cost random walk: Exact statistics of the distance covered for fixed budget

We consider the nonlinear-cost random-walk model in discrete time introduced in Phys. Rev. Lett. 130, 237102 (2023)10.1103/PhysRevLett.130.237102, where a fee is charged for each jump of the walker. The nonlinear cost function is such that slow or short jumps incur a flat fee, while for fast or long jumps the cost is proportional to the distance covered. In this paper we compute analytically the average and variance of the distance covered in n steps when the total budget C is fixed, as well as the statistics of the number of long or short jumps in a trajectory of length n, for the exponential jump distribution. These observables exhibit a very rich and nonmonotonic scaling behavior as a function of the variable C/n, which is traced back to the makeup of a typical trajectory in terms of long or short jumps, and the resulting entropy thereof. As a by-product, we compute the asymptotic behavior of ratios of Kummer hypergeometric functions when both the first and last arguments are large. All our analytical results are corroborated by numerical simulations.

Characterizing different motility-induced regimes in active matter with machine learning and noise

We examine motility-induced phase separation (MIPS) in two-dimensional run-and-tumble disk systems using both machine learning and noise fluctuation analysis. Our measures suggest that within the MIPS state there are several distinct regimes as a function of density and run time, so that systems with MIPS transitions exhibit an active fluid, an active crystal, and a critical regime. The different regimes can be detected by combining an order parameter extracted from principal component analysis with a cluster stability measurement. The principal component-derived order parameter is maximized in the critical regime, remains low in the active fluid, and has an intermediate value in the active crystal regime. We demonstrate that machine learning can better capture dynamical properties of the MIPS regimes compared to more standard structural measures such as the maximum cluster size. The different regimes can also be characterized via changes in the noise power of the fluctuations in the average speed. In the critical regime, the noise power passes through a maximum and has a broad spectrum with a 1/f^{1.6} signature, similar to the noise observed near depinning transitions or for solids undergoing plastic deformation.

Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes

Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. We design a pattern featuring a topological defect that functions as an attractor or a repeller of microparticles, as well as a pattern that directs microparticles along a prescribed complex trajectory. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently. Our findings pave the way for new avenues in transport control and dynamic self-assembly in colloidal science.

Swarmalators on a ring with uncorrelated pinning

We present a case study of swarmalators (mobile oscillators) that move on a 1D ring and are subject to pinning. Previous work considered the special case where the pinning in space and the pinning in the phase dimension were correlated. Here, we study the general case where the space and phase pinning are uncorrelated, both being chosen uniformly at random. This induces several new effects, such as pinned async, mixed states, and a first-order phase transition. These phenomena may be found in real world swarmalators, such as systems of vinegar eels, Janus matchsticks, electrorotated Quincke rollers, or Japanese tree frogs.

Dynamic phases and combing effects for elongated particles moving over quenched disorder

We consider a two-dimensional system of elongated particles driven over a landscape containing randomly placed pinning sites. For varied pinning site density, external drive magnitude, and particle elongation, we find a wide variety of dynamic phases, including random structures, stripe or combed phases with nematic order, and clogged states. The different regimes can be identified by examining nematic ordering, cluster size, number of pinned particles, and transverse diffusion. In some regimes we find that the pinning can enhance the particle alignment, producing a nonmonotonic signature in the nematic ordering with a maximum at a particular combination of pinning density and drive. The optimal nematic occurs when a sufficient number of particles can be pinned, generating a local shear and leading to what we call a combing effect. At high drives, the combing effect is reduced when the number of pinned particles decreases. For stronger pinning, the particles form a heterogeneous clustered or clogged state that depins into a fluctuating state with high diffusion.

Overcrowding induces fast colloidal solitons in a slowly rotating potential landscape

Collective particle transport across periodic energy landscapes is ubiquitously present in many condensed matter systems spanning from vortices in high-temperature superconductors, frictional atomic sliding, driven skyrmions to biological and active matter. Here we report the emergence of fast solitons propagating against a rotating optical landscape. These experimentally observed solitons are stable cluster waves that originate from a coordinated particle exchange process which occurs when the number of trapped microparticles exceeds the number of potential wells. The size and speed of individual solitons rapidly increase with the particle diameter as predicted by theory and confirmed by numerical simulations. We show that when several solitons coexist, an effective repulsive interaction can stabilize their propagation along the periodic potential. Our experiments demonstrate a generic mechanism for cluster-mediated transport with potential applications to condensed matter systems on different length scales.

Cost of Diffusion: Nonlinearity and Giant Fluctuations

We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The model-inspired by the way taxi meters work-exhibits a very rich behavior. The cost for trajectories of equal length and equal duration exhibits giant fluctuations at a critical value of the scaled distance traveled. Furthermore, the full distribution of the cost until the target is reached exhibits an interesting "freezing" transition in the large-deviation regime. All the analytical results are corroborated by numerical simulations. Our results also apply to elastic systems near the depinning transition, when driven by a random force.

Nematically Templated Vortex Lattices in Superconducting FeSe

New pathways to controlling the morphology of superconducting vortex lattices─and their subsequent dynamics─are required to guide and scale vortex world-lines into a computing platform. We have found that the nematic twin boundaries align superconducting vortices in the adjacent terraces due to the incommensurate potential between vortices surrounding twin boundaries and those trapped within them. With the varying density and morphology of twin boundaries, the vortex lattice assumes several distinct structural phases, including square, regular, and irregular one-dimensional lattices. Through concomitant analysis of vortex lattice models, we have inferred the characteristic energetics of the twin boundary potential and furthermore predicted the existence of geometric size effects as a function of increasing confinement by the twin boundaries. These findings extend the ideas of directed control over vortex lattices to intrinsic topological defects and their self-organized networks, which have direct implications for the future design and control of strain-based topological quantum computing architectures.

Active Brownian particles in random and porous environments

The transport of active particles may occur in complex environments, in which it emerges from the interplay between the mobility of the active components and the quenched disorder of the environment. Here, we explore the structural and dynamical properties of active Brownian particles (ABPs) in random environments composed of fixed obstacles in three dimensions. We consider different arrangements of the obstacles. In particular, we consider two particular situations corresponding to experimentally realizable settings. First, we model pinning particles in (non-overlapping) random positions and, second, in a percolating gel structure and provide an extensive characterization of the structure and dynamics of ABPs in these complex environments. We find that the confinement increases the heterogeneity of the dynamics, with new populations of absorbed and localized particles appearing close to the obstacles. This heterogeneity has a profound impact on the motility induced phase separation exhibited by the particles at high activity, ranging from nucleation and growth in random disorder to a complex phase separation in porous environments.

Current-Induced Reversible Split of Elliptically Distorted Skyrmions in Geometrically Confined Fe3 Sn2 Nanotrack

Skyrmions are swirling spin textures with topological characters promising for future spintronic applications. Skyrmionic devices typically rely on the electrical manipulation of skyrmions with a circular shape. However, manipulating elliptically distorted skyrmions can lead to numerous exotic magneto-electrical functions distinct from those of conventional circular skyrmions, significantly broadening the capability to design innovative spintronic devices. Despite the promising potential, its experimental realization so far remains elusive. In this study, the current-driven dynamics of the elliptically distorted skyrmions in geometrically confined magnet Fe3 Sn2 is experimentally explored. This study finds that the elliptical skyrmions can reversibly split into smaller-sized circular skyrmions at a current density of 3.8 × 1010 A m-2 with the current injected along their minor axis. Combined experiments with micromagnetic simulations reveal that this dynamic behavior originates from a delicate interplay of the spin-transfer torque, geometrical confinement, and pinning effect, and strongly depends on the ratio of the major axis to the minor axis of the elliptical skyrmions. The results indicate that the morphology is a new degree of freedom for manipulating the current-driven dynamics of skyrmions, providing a compelling route for the future development of spintronic devices.

Depinning dynamics of confined colloidal dispersions under oscillatory shear

Strongly confined colloidal dispersions under shear can exhibit a variety of dynamical phenomena, including depinning transitions and complex structural changes. Here, we investigate the behavior of such systems under pure oscillatory shearing with shear rate γ[over ̇](t)=γ[over ̇]_{0}cos(ωt), as it is a common scenario in rheological experiments. The colloids' depinning behavior is assessed from a particle level based on trajectories, obtained from overdamped Brownian dynamics simulations. The numerical approach is complemented by an analytic one based on an effective single-particle model in the limits of weak and strong driving. Investigating a broad spectrum of shear rate amplitudes γ[over ̇]_{0} and frequencies ω, we observe complete pinning as well as temporary depinning behavior. We discover that temporary depinning occurs for shear rate amplitudes above a frequency-dependent critical amplitude γ[over ̇]_{0}^{crit}(ω), for which we attain an approximate functional expression. For a range of frequencies, approaching γ[over ̇]_{0}^{crit}(ω) is accompanied by a strongly increasing settling time. Above γ[over ̇]_{0}^{crit}(ω), we further observe a variety of dynamical structures, whose stability exhibits an intriguing (γ[over ̇]_{0},ω) dependence. This might enable new perspectives for potential control schemes.

Pattern formation and flocking for particles near the jamming transition on resource gradient substrates

We numerically examine a bidisperse system of active and passive particles coupled to a resource substrate. The active particles deplete the resource at a fixed rate and move toward regions with higher resources, while all of the particles interact sterically with each other. We show that at high densities, this system exhibits a rich variety of pattern-forming phases along with directed motion or flocking as a function of the relative rates of resource absorption and consumption as well as the active to passive particle ratio. These include partial phase separation into rivers of active particles flowing through passive clusters, strongly phase separated states where the active particles induce crystallization of the passive particles, mixed jammed states, and fluctuating mixed fluid phases. For higher resource recovery rates, we demonstrate that the active particles can undergo motility-induced phase separation, while at high densities, there can be a coherent flock containing only active particles or a solid mixture of active and passive particles. The directed flocking motion typically shows a transient in which the flow switches among different directions before settling into one direction, and there is a critical density below which flocking does not occur. We map out the different phases as function of system density, resource absorption and recovery rates, and the ratio of active to passive particles.

Magnetic-Field-Assisted Diffusion Motion of Magnetic Skyrmions

Studies of the diffusion dynamics of magnetic skyrmions have generated widespread interest in both fundamental physics and spintronics applications. Here we report the magnetic-field-assisted diffusion motion of skyrmions in a microstructured chiral FeGe magnet. We demonstrate the enhancement of diffusion motion of magnetic skyrmions that is manipulated and driven by an oscillatory magnetic field. Further, the directed diffusion of skyrmions is observed when an in-plane field was introduced to break the symmetry of the system. Finally, we demonstrate the application of a magnetic field can induce an arrangements transition of skyrmions assemble in microstructure, that is, from a stiff hexagonal lattice to a weak interactional isotropic state. By using a step-ascended magnetic field we finished the observation of a particle-like diffusive motion for magnetic skyrmions that transport from high-concentration regions to low-concentration regions and the diffusion flux is proportional to the concentration gradient followed Fick's law.

Ordered Bose Glass of Vortices in Superconducting YBa2Cu3O7-δ Thin Films with a Periodic Pin Lattice Created by Focused Helium Ion Irradiation

The defect-rich morphology of YBa₂Cu₃O_7-δ (YBCO) thin films leads to a glass-like arrangement of Abrikosov vortices which causes the resistance to disappear in vanishing current densities. This vortex glass consists of entangled vortex lines and is identified by a characteristic scaling of the voltage-current isotherms. Randomly distributed columnar defects stratify the vortex lines and lead to a Bose glass. Here, we report on the observation of an ordered Bose glass in a YBCO thin film with a hexagonal array of columnar defects with 30 nm spacings. The periodic pinning landscape was engineered by a focused beam of 30 keV He⁺ ions in a helium-ion microscope.

Colloidal transport in twisted lattices of optical tweezers

We simulate the transport of colloidal particles driven by a static and homogeneous drift force, and subject to the optical potential created by two lattices of optical tweezers. The lattices of optical tweezers are parallel to each other, shifted, and rotated by a twist angle. Due to a negative interference between the potential of the two lattices, flat channels appear in the total optical potential. At specific twist angles, known as magic angles, the flat channels percolate the entire system and the colloidal particles can then be transported using a weak external drift force. We characterize the transport in both square and hexagonal lattices of twisted optical tweezers.

Superlubric-pinned transition of a two-dimensional solid dusty plasma under a periodic triangular substrate

The superlubric-pinned transition in the depinning dynamics of a two-dimensional (2D) solid dusty plasma modulated by 2D triangular periodic substrates is investigated using Langevin dynamical simulations. When the lattice structure of the 2D solid dusty plasma perfectly matches the triangular substrate, two distinctive pinned and moving ordered states are observed as the external uniform driving force gradually increases from zero. When there is a mismatch between the lattice structure and the triangular substrate, however, on shallow substrates, it is discovered that all of the particles can slide freely on the substrate even when the applied driving force is tiny. This is a typical example of superlubricity, which is caused by the competition between the substrate-particle and particle-particle interactions. If the substrate depth increases further, as the driving force increases from zero, there are three dynamical states consisting of the pinned state, the disordered plastic flow state, and the moving ordered state. In an underdense system, where there are fewer particles than potential well minima, it is found that the occurrence of the three different dynamical states is controlled by the depth of the substrate, which is quantitatively characterized using the average mobility.

Directional locking in a two-dimensional Yukawa solid modulated by a two-dimensional periodic substrate

Directional depinning dynamics of a two-dimensional (2D) dusty plasma solid modulated by a 2D square periodic substrate are investigated using Langevin dynamical simulations. We observe prominent directional locking effects when the direction of the external driving force is varied relative to the underlying square substrate. These locking steps appear when the direction of the driving force is close to the symmetry direction of the substrate, corresponding to the different dynamical flow patterns and the structures. In the conditions between the adjacent locking steps, moving ordered states are observed. Although the discontinuous transitions often occur between the locking steps and the nonlocking portion, the continuous transitions are also found around the locking step associated with the disordered plastic flow close to its termini. Our results show that directional locking also occurs for underdamped systems, which could be tested experimentally in dusty plasmas modulated by 2D substrates.

Skyrmion pinning energetics in thin film systems

A key issue for skyrmion dynamics and devices are pinning effects present in real systems. While posing a challenge for the realization of conventional skyrmionics devices, exploiting pinning effects can enable non-conventional computing approaches if the details of the pinning in real samples are quantified and understood. We demonstrate that using thermal skyrmion dynamics, we can characterize the pinning of a sample and we ascertain the spatially resolved energy landscape. To understand the mechanism of the pinning, we probe the strong skyrmion size and shape dependence of the pinning. Magnetic microscopy imaging demonstrates that in contrast to findings in previous investigations, for large skyrmions the pinning originates at the skyrmion boundary and not at its core. The boundary pinning is strongly influenced by the very complex pinning energy landscape that goes beyond the conventional effective rigid quasi-particle description. This gives rise to complex skyrmion shape distortions and allows for dynamic switching of pinning sites and flexible tuning of the pinning.

Skyrmions, topological spin textures, can be pinned by defects present in the material that hosts them, influencing their motion. Here, Gruber et al show that the skyrmions are pinned at their boundary where the finite size of the skyrmions governs their pinning, and they demonstrate that certain pinning sites can switched on and off in-situ.

Reversible to Irreversible Transitions for Cyclically Driven Particles on Periodic Obstacle Arrays

We examine the collective dynamics of disks moving through a square array of obstacles under cyclic square wave driving. Below a critical density we find that system organizes into a reversible state in which the disks return to the same positions at the end of every drive cycle. Above this density, the dynamics are irreversible and the disks do not return to the same positions after each cycle. The critical density depends strongly on the angle θ between the driving direction and a symmetry axis of the obstacle array, with the highest critical densities appearing at commensurate angles such as θ=0{degree sign} and θ=45{degree sign} and the lowest critical densities falling at θ=arctan(0.618), the inverse of the golden ratio, where the flow is the most frustrated. As the density increases, the number of cycles required to reach a reversible state grows as a power law with an exponent near ν=1.36, similar to what is found in periodically driven colloidal and superconducting vortex systems.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the interaction between a pair of liquid crystalline (LC) particles. The underlying substrate potential with which the GB particles interact varies sinusoidally in one direction only. At a given temperature and density of the GB system, we varied the substrate's periodicity (a_s) but fixed the substrate strength. We observed that with a small value of a_s, an underlying substrate helps to stabilize a disordered LC nematic phase to a 2D solid phase. However, for an intermediate range of a_s, the system melts and transitions to a modulate-smectic. Finally, with a further increase in a_s, the system undergoes a structural depinning transition and returns to an LC nematic phase like a free system with no substrate. We argue that a three-way interplay of the energies arising from orientation-dependent particle-particle and particle-substrate interaction makes it possible for the system to undergo substrate-periodicity-dependent multiple phase transitions in the GB LC system.

Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

We study the critical dynamics of vortices associated with dynamic disordering near the depinning transitions driven by dc force (dc current I) and vortex density (magnetic field B). Independent of the driving parameters, I and B, we observe the critical behavior of the depinning transitions, not only on the moving side, but also on the pinned side of the transition, which is the first convincing verification of the theoretical prediction. Relaxation times, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (I)$$\end{document}τ(I) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (B)$$\end{document}τ(B), to reach either the moving or pinned state, plotted against I and B, respectively, exhibit a power-law divergence at the depinning thresholds. The critical exponents of both transitions are, within errors, identical to each other, which are in agreement with the values expected for an absorbing phase transition in the two-dimensional directed-percolation universality class. With an increase in B under constant I, the depinning transition at low B is replaced by the repinning transition at high B in the peak-effect regime. We find a trend that the critical exponents in the peak-effect regime are slightly smaller than those in the low-B regime and the theoretical one, which is attributed to the slight difference in the depinning mechanism in the peak-effect regime.

Phonon spectra of a two-dimensional solid dusty plasma modified by two-dimensional periodic substrates

Phonon spectra of a two-dimensional (2D) solid dusty plasma modulated by 2D square and triangular periodic substrates are investigated using Langevin dynamical simulations. The commensurability ratio, i.e., the ratio of the number of particles to the number of potential well minima, is set to 1 or 2. The resulting phonon spectra show that propagation of waves is always suppressed due to the confinement of particles by the applied 2D periodic substrates. For a commensurability ratio of 1, the spectra indicate that all particles mainly oscillate at one specific frequency, corresponding to the harmonic oscillation frequency of one single particle inside one potential well. At a commensurability ratio of 2, the substrate allows two particles to sit inside the bottom of each potential well, and the resulting longitudinal and transverse spectra exhibit four branches in total. We find that the two moderate branches come from the harmonic oscillations of one single particle and two combined particles in the potential well. The other two branches correspond to the relative motion of the two-body structure in each potential well in the radial and azimuthal directions. The difference in the spectra between the square and triangular substrates is attributed to the anisotropy of the substrates and the resulting alignment directions of the two-body structure in each potential well.

The dynamics of chemically propelled dimer motor on a pinning substrate

The dynamics of self-propelled micro-motors, in a thin fluid film containing an attractive substrate, is investigated by means of a particle-based simulation. A chemically powered sphere dimer, consisting of a...

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

Critical behavior of density-driven and shear-driven reversible-irreversible transitions in cyclically sheared vortices

Random assemblies of particles subjected to cyclic shear undergo a reversible–irreversible transition (RIT) with increasing a shear amplitude d or particle density n, while the latter type of RIT has not been verified experimentally. Here, we measure the time-dependent velocity of cyclically sheared vortices and observe the critical behavior of RIT driven by vortex density B as well as d. At the critical point of each RIT, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B_{\mathrm {c}}$$\end{document}Bc and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc, the relaxation time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}τ to reach the steady state shows a power-law divergence. The critical exponent for B-driven RIT is in agreement with that for d-driven RIT and both types of RIT fall into the same universality class as the absorbing transition in the two-dimensional directed-percolation universality class. As d is decreased to the average intervortex spacing in the reversible regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) shows a significant drop, indicating a transition or crossover from a loop-reversible state with vortex-vortex collisions to a collisionless point-reversible state. In either regime, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau (d)$$\end{document}τ(d) exhibits a power-law divergence at the same \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{\mathrm {c}}$$\end{document}dc with nearly the same exponent.

Kink propagation and solute partitioning in an atomic monolayer on a substrate

When a monolayer of Lennard-Jones atoms is driven by an external force over an atomically spaced lattice, the atoms do not move in the direction of the force. By considering monolayers containing a solvent and two different solutes, we show that the different atomic species follow distinct directions and so partition from one another and from the solvent. The strength of the driving force is chosen so that at any instant, most atoms are stationary while only a small fraction propagates as solitary waves. In this regime, the mean velocity of the layer is due to the nonzero contribution from merely a few atoms. We also present a simple theory, based on the probability that an atom in the monolayer will hop from one equilibrium location to the next, that explains the distinct directions of atomic migration.

Microdynamic Study of Spin-Lattice Coupling Effects on Skyrmion Transport

Skyrmion transport fundamentally determines the speed, energy consumption, and functionality of skyrmion-based spintronic devices, attracting considerable attention. Recent experimental studies found there is a migration barrier for the thermal activated transport of a skyrmion, which is speculated to be induced by the pinning effects of crystalline defects. In this Letter, we propose an alternative source of migration barrier for skyrmion transport, i.e., a local lattice distortion field due to spin-lattice coupling, which can lead to the same Arrhenius diffusion behavior in defect-free skyrmion materials. By performing spin-lattice dynamics simulations, we study the microdynamic insight into the influence of local lattice distortion field, which refreshes the mechanistic understanding on skyrmion transport.

Clogging, dynamics, and reentrant fluid for active matter on periodic substrates

We examine the collective states of run-and-tumble active matter disks driven over a periodic obstacle array. When the drive is applied along a symmetry direction of the array, we find a clog-free uniform liquid state for low activity, while at higher activity, the density becomes increasingly heterogeneous and an active clogged state emerges in which the mobility is strongly reduced. For driving along nonsymmetry or incommensurate directions, there are two different clogging behaviors consisting of a drive-dependent clogged state in the low activity thermal limit and a drive-independent clogged state at high activity. These regimes are separated by a uniform flowing liquid at intermediate activity. There is a critical activity level above which the thermal clogged state does not occur, as well as an optimal activity level that maximizes the disk mobility. Thermal clogged states are dependent on the driving direction while active clogged states are not. In the low activity regime, diluting the obstacles produces a monotonic increase in the mobility; however, for large activities, the mobility is more robust against obstacle dilution. We also examine the velocity-force curves for driving along nonsymmetry directions and find that they are linear when the activity is low or intermediate but become nonlinear at high activity and show behavior similar to that found for the plastic depinning of solids. At higher drives, the active clustering is lost. For low activity, we also find a reentrant fluid phase, where the system transitions from a high mobility fluid at low drives to a clogged state at higher drives and then back into another fluid phase at very high drives. We map the regions in which the thermally clogged, partially clogged, active uniform fluid, clustered fluid, active clogged, and directionally locked states occur as a function of disk density, drift force, and activity.

Reconfigurable Josephson Phase Shifter

Phase shifter is one of the key elements of quantum electronics. In order to facilitate operation and avoid decoherence, it has to be reconfigurable, persistent, and nondissipative. In this work, we demonstrate prototypes of such devices in which a Josephson phase shift is generated by coreless superconducting vortices. The smallness of the vortex allows a broad-range tunability by nanoscale manipulation of vortices in a micron-size array of vortex traps. We show that a phase shift in a device containing just a few vortex traps can be reconfigured between a large number of quantized states in a broad [-3π, +3π] range.

Universality classes of the domain-wall creep motion driven by spin-transfer torques

With the stochastic Landau-Lifshitz-Gilbert equation, we numerically simulate the creep motion of a magnetic domain wall driven by the adiabatic and nonadiabatic spin-transfer torques induced by the electric current. The creep exponent μ and the roughness exponent ζ are accurately determined from the scaling behaviors. The creep motions driven by the adiabatic and nonadiabatic spin-transfer torques belong to different universality classes. The scaling relation between μ and ζ based on certain simplified assumptions is valid for the nonadiabatic spin-transfer torque, while invalid for the adiabatic one. Our results are compatible with the experimental ones, but go beyond the existing theoretical prediction. Our investigation reveals that the disorder-induced pinning effect on the domain-wall rotation alters the universality class of the creep motion.

Directional locking and the influence of obstacle density on skyrmion dynamics in triangular and honeycomb arrays

We numerically examine the dynamics of a single skyrmion driven over triangular and honeycomb obstacle arrays at zero temperature. The skyrmion Hall angleθ_sk, defined as the angle between the applied external drive and the direction of the skyrmion motion, increases in quantized steps or continuously as a function of the applied drive. For the obstacle arrays studied in this work, the skyrmion exhibits two main directional locking angles ofθ_sk= -30° and -60°. We show that these directions are privileged due to the obstacle landscape symmetry, and coincide with channels along which the skyrmion may move with few or no obstacle collisions. Here we investigate how changes in the obstacle density can modify the skyrmion Hall angles and cause some dynamic phases to appear or grow while other phases vanish. This interesting behavior can be used to guide skyrmions along designated trajectories via regions with different obstacle densities. For fixed obstacle densities, we investigate the evolution of the lockedθ_sk= -30° and -60° phases as a function of the Magnus force, and discuss possibilities for switching between these phases using topological selection.

Dynamical time scales of friction dynamics in active microrheology of a model glass

Owing to the local/heterogeneous structures in supercooled liquids, after several decades of research, it is now clear that supercooled liquids are structurally different from their conventional liquid counterparts. Accordingly, an approach based on a local probe should provide a better understanding about the local mechanical properties as well as heterogeneous structures. Recently, the superiority of active microrheology over global rheology has been demonstrated [Yu et al., Sci. Adv., 2020, 6, 8766]. Here, we elaborate this new avenue of research and provide more evidence for such superiority. We report on the results of an extensive molecular dynamics simulation of active microrheology of a model glass. We identify several time scales in time series of friction, and detect a transition in dynamical behavior of friction. We discuss the possible relation to structural heterogeneities-a subject of considerable interest in glass physics.

Directional clogging and phase separation for disk flow through periodic and diluted obstacle arrays

We model collective disk flow though a square array of obstacles as the flow direction is changed relative to the symmetry directions of the array. At lower disk densities there is no clogging for any driving direction, but as the disk density increases, the average disk velocity decreases and develops a drive angle dependence. For certain driving angles, the flow is reduced or drops to zero when the system forms a heterogeneous clogged state consisting of high density clogged regions coexisting with empty regions. The clogged states are fragile and can be unclogged by changing the driving angle. For large obstacle sizes, we find a uniform clogged state that is distinct from the collective clogging regime. Within the clogged phases, depinning transitions can occur as a function of increasing driving force, with intermittent motion appearing just above the depinning threshold. The clogging is robust against the random removal or dilution of the obstacle sites, and the disks are able to form system-spanning clogged clusters even under increasing dilution. If the dilution becomes too large, however, the clogging behavior is lost.

Active matter commensuration and frustration effects on periodic substrates

We show that self-driven particles coupled to a periodic obstacle array exhibit active matter commensuration effects that are absent in the Brownian limit. As the obstacle size is varied for sufficiently large activity, a series of commensuration effects appear in which the motility induced phase separation produces commensurate crystalline states, while for other obstacle sizes we find frustrated or amorphous states. The commensuration effects are associated with peaks in the amount of sixfold ordering and the maximum cluster size. When a drift force is added to the system, the mobility contains peaks and dips similar to those found in transport studies for commensuration effects in superconducting vortices and colloidal particles.

Continuous and discontinuous transitions in the depinning of two-dimensional dusty plasmas on a one-dimensional periodic substrate

Langevin dynamical simulations are performed to study the depinning dynamics of two-dimensional dusty plasmas on a one-dimensional periodic substrate. From the diagnostics of the sixfold coordinated particles P_{6} and the collective drift velocity V_{x}, three different states appear, which are the pinning, disordered plastic flow, and moving ordered states. It is found that the depth of the substrate is able to modulate the properties of the depinning phase transition, based on the results of P_{6} and V_{x}, as well as the observation of hysteresis of V_{x} while increasing and decreasing the driving force monotonically. When the depth of the substrate is shallow, there are two continuous phase transitions. When the potential well depth slightly increases, the phase transition from the pinned to the disordered plastic flow states is continuous; however, the phase transition from the disordered plastic flow to the moving ordered states is discontinuous. When the substrate is even deeper, the phase transition from the pinned to the disordered plastic flow states changes to discontinuous. When the depth of the substrate further increases, as the driving force increases, the pinned state changes to the moving ordered state directly, so that the disordered plastic flow state disappears completely.

Vortex Dynamics in a Compact Kardar-Parisi-Zhang System

We study the dynamics of vortices in a two-dimensional, nonequilibrium system, described by the compact Kardar-Parisi-Zhang equation, after a sudden quench across the critical region. Our exact numerical solution of the phase-ordering kinetics shows that the unique interplay between nonequilibrium and the variable degree of spatial anisotropy leads to different critical regimes. We provide an analytical expression for the vortex evolution, based on scaling arguments, which is in agreement with the numerical results, and confirms the form of the interaction potential between vortices in this system.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Directional locking effects for active matter particles coupled to a periodic substrate

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

Propagating bands of plastic deformation in a metal alloy as critical avalanches

The plastic deformation of metal alloys localizes in the Portevin-Le Chatelier effect in bands of different types, including propagating, or type "A" bands, usually characterized by their width and a typical propagation velocity. This plastic instability arises from collective dynamics of dislocations interacting with mobile solute atoms, but the resulting sensitivity to the strain rate lacks fundamental understanding. Here, we show, by using high-resolution imaging in tensile deformation experiments of an aluminum alloy, that the band velocities exhibit large fluctuations. Each band produces a velocity signal reminiscent of crackling noise bursts observed in numerous driven avalanching systems from propagating cracks in fracture to the Barkhausen effect in ferromagnets. The statistical features of these velocity bursts including their average shapes and size distributions obey predictions of a simple mean-field model of critical avalanche dynamics. Our results thus reveal a previously unknown paradigm of criticality in the localization of deformation.

Structural lubricity in soft and hard matter systems

Over the recent decades there has been tremendous progress in understanding and controlling friction between surfaces in relative motion. However the complex nature of the involved processes has forced most of this work to be of rather empirical nature. Two very distinctive physical systems, hard two-dimensional layered materials and soft microscopic systems, such as optically or topographically trapped colloids, have recently opened novel rationally designed lines of research in the field of tribology, leading to a number of new discoveries. Here, we provide an overview of these emerging directions of research, and discuss how the interplay between hard and soft matter promotes our understanding of frictional phenomena.

Structural lubricity is one of the most interesting concepts in modern tribology, which promises to achieve ultra-low friction over a wide range of length-scales. Here the authors highlight novel research lines in this area achievable by combining theoretical and experimental efforts on hard two-dimensional materials and soft colloidal and cold ion systems.

Dynamics and clogging of colloidal monolayers magnetically driven through a heterogeneous landscape

We combine experiments and numerical simulations to investigate the emergence of clogging in a system of interacting paramagnetic colloidal particles driven against a disordered landscape of larger obstacles. We consider a single aperture in a landscape of immobile silica particles which are irreversibly attached to the substrate. We use an external rotating magnetic field to generate a traveling wave potential which drives the magnetic particles against these obstacles at a constant and frequency tunable speed. Experimentally we find that the particles display an intermittent dynamics with power law distributions at high frequencies. We reproduce these results by using numerical simulations and show that clogging in our system arises at large frequency, when the particles desynchronize with the moving landscape. Further, we use the model to explore the hidden role of flexibility in the obstacle displacements and the effect of hydrodynamic interactions between the particles. We also consider numerically the situation of a straight wall and investigate the range of parameters where clogging emerges in such case. Our work provides a soft matter test-bed system to investigate the effect of clogging in driven microscale matter.