Realizing colloidal artificial ice on arrays of optical traps

Droplet tilings in precessive fields: hysteresis, elastic defects, and annealing

Two-component Marangoni contracted droplets can be arranged into arbitrary two-dimensional tiling patterns where they display rich dynamics due to vapor-mediated long-range interactions. Recent work has characterized the centered hexagonal honeycomb lattice, showing it to be a highly frustrated system with many metastable states and relaxation occurring over multiple timescales [Molina et al., Proc. Natl. Acad. Sci. U. S. A., 2021, 118, e2020014118]. Here, we study this system under the influence of a rotating gravitational field. High amplitudes are able to completely disrupt droplet-droplet interactions, making it possible to identify a transition between field-dominated and interaction-dominated regimes. The system displays complex hysteresis behavior, the details of which are connected to the emergence of linear mesoscale structures. These mesoscale features display an elasticity that is governed by the balance between gravity and long-range vapor-mediated attractions. We find that disorder plays an important role in determining the dynamics of these features. Finally, we demonstrate annealing the system by progressively reducing the field amplitude, a process that reduces configurational energy compared to a rapid quench. The ability to manipulate vapor-mediated interactions in deliberately designed droplet tilings provides a novel platform for table-top explorations of multi-body interactions.

Modelling nanomagnet vertex dynamics through Coulomb charges

We investigate the magnetization dynamics in nanomagnet vertices often found in artificial spin ices. Our analysis involves creating a simplified model that depicts edge magnetization using magnetic charges. We utilize the model to explore the energy landscape, its associated curvatures, and the fundamental modes. Our study uncovers specific magnonic regimes and transitions between magnetization states, marked by zero-modes, which can be understood within the framework of Landau theory. To verify our model, we compare it with micromagnetic simulations, demonstrating a noteworthy agreement.

Depletion-driven antiferromagnetic, paramagnetic, and ferromagnetic behavior in quasi-two-dimensional buckled colloidal solids

We investigate quasi-two-dimensional buckled colloidal monolayers on a triangular lattice with tunable depletion interactions. Without depletion attraction, the experimental system provides a colloidal analog of the well-known geometrically frustrated Ising antiferromagnet [Y. Han et al., Nature 456, 898-903 (2008)]. In this contribution, we show that the added depletion attraction can influence both the magnitude and sign of an Ising spin coupling constant. As a result, the nearest-neighbor Ising "spin" interactions can be made to vary from antiferromagnetic to para- and ferromagnetic. Using a simple theory, we compute an effective Ising nearest-neighbor coupling constant, and we show how competition between entropic effects permits for the modification of the coupling constant. We then experimentally demonstrate depletion-induced modification of the coupling constant, including its sign, and other behaviors. Depletion interactions are induced by rod-like surfactant micelles that change length with temperature and thus offer means for tuning the depletion attraction in situ. Buckled colloidal suspensions exhibit a crossover from an Ising antiferromagnetic to paramagnetic phase as a function of increasing depletion attraction. Additional dynamical experiments reveal structural arrest in various regimes of the coupling-constant, driven by different mechanisms. In total, this work introduces novel colloidal matter with "magnetic" features and complex dynamics rarely observed in traditional spin systems.

Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems

A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.

Topological Boundary Constraints in Artificial Colloidal Ice

The effect of boundaries and how these can be used to influence the bulk behavior in geometrically frustrated systems are both long-standing puzzles, often relegated to a secondary role. Here, we use numerical simulations and "proof of concept" experiments to demonstrate that boundaries can be engineered to control the bulk behavior in a colloidal artificial ice. We show that an antiferromagnetic frontier forces the system to rapidly reach the ground state (GS), as opposed to the commonly implemented open or periodic boundary conditions. We also show that strategically placing defects at the corners generates novel bistable states, or topological strings, which result from competing GS regions in the bulk. Our results could be generalized to other frustrated micro- and nanostructures where boundary conditions may be engineered with lithographic techniques.

Skyrmion Spin Ice in Liquid Crystals

We propose the first skyrmion spin ice, realized via confined, interacting liquid crystal skyrmions. Skyrmions in a chiral nematic liquid crystal behave as quasiparticles that can be dynamically confined, bound, and created or annihilated individually with ease and precision. We show that these quasiparticles can be employed to realize binary variables that interact to form ice-rule states. Because of their unique versatility, liquid crystal skyrmions can open entirely novel avenues in the field of frustrated systems. More broadly, our findings also demonstrate the viability of liquid crystal skyrmions as elementary degrees of freedom in the design of collective complex behaviors.

Modal Frustration and Periodicity Breaking in Artificial Spin Ice

Here, an artificial spin ice lattice is introduced that exhibits unique Ising and non-Ising behavior under specific field switching protocols because of the inclusion of coupled nanomagnets into the unit cell. In the Ising regime, a magnetic switching mechanism that generates a uni- or bimodal distribution of states dependent on the alignment of the field is demonstrated with respect to the lattice unit cell. In addition, a method for generating a plethora of randomly distributed energy states across the lattice, consisting of Ising and Landau states, is investigated through magnetic force microscopy and micromagnetic modeling. It is demonstrated that the dispersed energy distribution across the lattice is a result of the intrinsic design and can be finely tuned through control of the incident angle of a critical field. The present manuscript explores a complex frustrated environment beyond the 16-vertex Ising model for the development of novel logic-based technologies.

Topology Restricts Quasidegeneracy in Sheared Square Colloidal Ice

Recovery of ground-state degeneracy in two-dimensional square ice is a significant challenge in the field of geometric frustration with far-reaching fundamental implications, such as realization of vertex models and understanding the effect of dimensionality reduction. We combine experiments, theory, and numerical simulations to demonstrate that sheared square colloidal ice partially recovers the ground-state degeneracy for a wide range of field strengths and lattice shear angles. Our method could inspire engineering a novel class of frustrated microstructures and nanostructures based on sheared magnetic lattices in a wide range of soft- and condensed-matter systems.

Ice rule fragility via topological charge transfer in artificial colloidal ice

Artificial particle ices are model systems of constrained, interacting particles. They have been introduced theoretically to study ice-manifolds emergent from frustration, along with domain wall and grain boundary dynamics, doping, pinning-depinning, controlled transport of topological defects, avalanches, and memory effects. Recently such particle-based ices have been experimentally realized with vortices in nano-patterned superconductors or gravitationally trapped colloids. Here we demonstrate that, although these ices are generally considered equivalent to magnetic spin ices, they can access a novel spectrum of phenomenologies that are inaccessible to the latter. With experiments, theory and simulations we demonstrate that in mixed coordination geometries, entropy-driven negative monopoles spontaneously appear at a density determined by the vertex-mixture ratio. Unlike its spin-based analogue, the colloidal system displays a "fragile ice" manifold, where local energetics oppose the ice rule, which is instead enforced through conservation of the global topological charge. The fragile colloidal ice, stabilized by topology, can be spontaneously broken by topological charge transfer.

Switchable geometric frustration in an artificial-spin-ice-superconductor heterosystem

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical applications in microelectronics¹, such as data storage, memory and logic². However, it is difficult to achieve very high degeneracy, especially in a two-dimensional system^3,4. Here, we showcase in situ controllable geometric frustration with high degeneracy in a two-dimensional flux-quantum system. We create this in a superconducting thin film placed underneath a reconfigurable artificial-spin-ice structure⁵. The tunable magnetic charges in the artificial-spin-ice strongly interact with the flux quanta in the superconductor, enabling switching between frustrated and crystallized flux quanta states. The different states have measurable effects on the superconducting critical current profile, which can be reconfigured by precise selection of the spin-ice magnetic state through the application of an external magnetic field. We demonstrate the applicability of these effects by realizing a reprogrammable flux quanta diode. The tailoring of the energy landscape of interacting 'particles' using artificial-spin-ices provides a new paradigm for the design of geometric frustration, which could illuminate a path to control new functionalities in other material systems, such as magnetic skyrmions⁶, electrons and holes in two-dimensional materials^7,8, and topological insulators⁹, as well as colloids in soft materials^10-13.

Unexpected Phenomenology in Particle-Based Ice Absent in Magnetic Spin Ice

While particle-based ices are often considered essentially equivalent to magnet-based spin ices, the two differ essentially in frustration and energetics. We show that at equilibrium particle-based ices correspond exactly to spin ices coupled to a background field. In trivial geometries, such a field has no effect, and the two systems are indeed thermodynamically equivalent. In other cases, however, the field controls a richer phenomenology, absent in magnetic ices, and still largely unexplored: ice rule fragility, topological charge transfer, radial polarization, decimation induced disorder, and glassiness.

Attraction Controls the Entropy of Fluctuations in Isosceles Triangular Networks

We study two-dimensional triangular-network models, which have degenerate ground states composed of straight or randomly-zigzagging stripes and thus sub-extensive residual entropy. We show that attraction is responsible for the inversion of the stable phase by changing the entropy of fluctuations around the ground-state configurations. By using a real-space shell-expansion method, we compute the exact expression of the entropy for harmonic interactions, while for repulsive harmonic interactions we obtain the entropy arising from a limited subset of the system by numerical integration. We compare these results with a three-dimensional triangular-network model, which shows the same attraction-mediated selection mechanism of the stable phase, and conclude that this effect is general with respect to the dimensionality of the system.

Inner Phases of Colloidal Hexagonal Spin Ice

Using numerical simulations that mimic recent experiments on hexagonal colloidal ice, we show that colloidal hexagonal artificial spin ice exhibits an inner phase within its ice state that has not been observed previously. Under increasing colloid-colloid repulsion, the initially paramagnetic system crosses into a disordered ice regime, then forms a topologically charge ordered state with disordered colloids, and finally reaches a threefold degenerate, ordered ferromagnetic state. This is reminiscent of, yet distinct from, the inner phases of the magnetic kagome spin ice analog. The difference in the inner phases of the two systems is explained by their difference in energetics and frustration.

Attraction Controls the Inversion of Order by Disorder in Buckled Colloidal Monolayers

We show how including attraction in interparticle interactions reverses the effect of fluctuations in ordering of a prototypical artificial frustrated system. Buckled colloidal monolayers exhibit the same ground state as the Ising antiferromagnet on a deformable triangular lattice, but it is unclear if ordering in the two systems is driven by the same geometric mechanism. By a real-space expansion we find that, for buckled colloids, bent stripes constitute the stable phase, whereas in the Ising antiferromagnet straight stripes are favored. For generic pair potentials we show that attraction governs this selection mechanism, in a manner that is linked to local packing considerations. This supports the geometric origin of entropy in jammed sphere packings and provides a tool for designing self-assembled colloidal structures.

Dynamic Control of Topological Defects in Artificial Colloidal Ice

We demonstrate the use of an external field to stabilize and control defect lines connecting topological monopoles in spin ice. For definiteness we perform Brownian dynamics simulations with realistic units mimicking experimentally realized artificial colloidal spin ice systems, and show how defect lines can grow, shrink or move under the action of direct and alternating fields. Asymmetric alternating biasing forces can cause the defect line to ratchet in either direction, making it possible to precisely position the line at a desired location. Such manipulation could be employed to achieve mobile information storage in these metamaterials.

Emergent inequality and self-organized social classes in a network of power and frustration

We propose a simple agent-based model on a network to conceptualize the allocation of limited wealth among more abundant expectations at the interplay of power, frustration, and initiative. Concepts imported from the statistical physics of frustrated systems in and out of equilibrium allow us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from or lose wealth to anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. This picture is however dramatically ameliorated when hard constraints are imposed over agents in the form of a limiting network of transactions. There, an out of equilibrium dynamics of the networks, based on a competition between power and frustration in the decision-making of agents, leads to network coevolution. The ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of equality. It also leads, for proper values of social initiative, to the emergence of three self-organized social classes, lower, middle, and upper class. Their dynamics, which appears mostly controlled by the middle class, drives a cyclical regime of dramatic social changes.

Defect Dynamics in Artificial Colloidal Ice: Real-Time Observation, Manipulation, and Logic Gate

We study the defect dynamics in a colloidal spin ice system realized by filling a square lattice of topographic double well islands with repulsively interacting magnetic colloids. We focus on the contraction of defects in the ground state, and contraction or expansion in a metastable biased state. Combining real-time experiments with simulations, we prove that these defects behave like emergent topological monopoles obeying a Coulomb law with an additional line tension. We further show how to realize a completely resettable "nor" gate, which provides guidelines for fabrication of nanoscale logic devices based on the motion of topological magnetic monopoles.

Engineering of frustration in colloidal artificial ices realized on microfeatured grooved lattices

Artificial spin ice systems, namely lattices of interacting single domain ferromagnetic islands, have been used to date as microscopic models of frustration induced by lattice topology, allowing for the direct visualization of spin arrangements and textures. However, the engineering of frustrated ice states in which individual spins can be manipulated in situ and the real-time observation of their collective dynamics remain both challenging tasks. Inspired by recent theoretical advances, here we realize a colloidal version of an artificial spin ice system using interacting polarizable particles confined to lattices of bistable gravitational traps. We show quantitatively that ice-selection rules emerge in this frustrated soft matter system by tuning the strength of the pair interactions between the microscopic units. Via independent control of particle positioning and dipolar coupling, we introduce monopole-like defects and strings and use loops with defined chirality as an elementary unit to store binary information.

Visualizing the dynamics of electron spins in frustrated systems is a challenging task, which may require an alternative way at the microscale. Here, the authors realize an artificial system composed of interacting colloidal particles to mimick frustrated spins, which is potentially helpful in information storage.

Freezing and thawing of artificial ice by thermal switching of geometric frustration in magnetic flux lattices

The problem of an ensemble of repulsive particles on a potential-energy landscape is common to many physical systems and has been studied in multiple artificial playgrounds. However, the latter usually involve fixed energy landscapes, thereby impeding in situ investigations of the particles' collective response to controlled changes in the landscape geometry. Here, we experimentally realize a system in which the geometry of the potential-energy landscape can be switched using temperature as the control knob. This realization is based on a high-temperature superconductor in which we engineer a nanoscale spatial modulation of the superconducting condensate. Depending on the temperature, the flux quanta induced by an applied magnetic field see either a geometrically frustrated energy landscape that favours an ice-like flux ordering, or an unfrustrated landscape that yields a periodic flux distribution. This effect is reflected in a dramatic change in the superconductor's magneto-transport. The thermal switching of the energy landscape geometry opens new opportunities for the study of ordering and reorganization in repulsive particle manifolds.

Thermal fluctuations in artificial spin ice

Artificial spin ice systems have been proposed as a playground for the study of monopole-like magnetic excitations, similar to those observed in pyrochlore spin ice materials. Currents of magnetic monopole excitations have been observed, demonstrating the possibility for the realization of magnetic-charge-based circuitry. Artificial spin ice systems that support thermal fluctuations can serve as an ideal setting for observing dynamical effects such as monopole propagation and as a potential medium for magnetricity investigations. Here, we report on the transition from a frozen to a dynamic state in artificial spin ice with a square lattice. Magnetic imaging is used to determine the magnetic state of the islands in thermal equilibrium. The temperature-induced onset of magnetic fluctuations and excitation populations are shown to depend on the lattice spacing and related interaction strength between islands. The excitations are described by Boltzmann distributions with their factors in the frozen state relating to the blocking temperatures of the array. Our results provide insight into the design of thermal artificial spin ice arrays where the magnetic charge density and response to external fields can be studied in thermal equilibrium.

Physics in ordered and disordered colloidal matter composed of poly(N-isopropylacrylamide) microgel particles

This review collects and describes experiments that employ colloidal suspensions to probe physics in ordered and disordered solids and related complex fluids. The unifying feature of this body of work is its clever usage of poly(N-isopropylacrylamide) (PNIPAM) microgel particles. These temperature-sensitive colloidal particles provide experimenters with a 'knob' for in situ control of particle size, particle interaction and particle packing fraction that, in turn, influence the structural and dynamical behavior of the complex fluids and solids. A brief summary of PNIPAM particle synthesis and properties is given, followed by a synopsis of current activity in the field. The latter discussion describes a variety of soft matter investigations including those that explore formation and melting of crystals and clusters, and those that probe structure, rearrangement and rheology of disordered (jammed/glassy) and partially ordered matter. The review, therefore, provides a snapshot of a broad range of physics phenomenology which benefits from the unique properties of responsive microgel particles.

Dynamic regimes for driven colloidal particles on a periodic substrate at commensurate and incommensurate fillings

We numerically examine colloidal particles driven over a muffin tin substrate. Previous studies of this model identified a variety of commensurate and incommensurate static phases in which topological defects can form domain walls, ordered stripes, superlattices, or disordered patchy regimes as a function of the filling fraction. Here, we show that the addition of an external drive to these static phases can produce distinct dynamical responses. At incommensurate fillings the flow occurs in the form of localized pulses or solitons correlated with topological defect structures. Transitions between different modes of motion can occur as a function of increasing drive. We measure the average particle velocity for specific ranges of external drive and show that changes in the velocity response correlate with changes in the topological defect arrangements. We also demonstrate that in the different dynamic phases, the particles have distinct trajectories and velocity distributions. Dynamic transitions between ordered and disordered flows exhibit hysteresis, while in strongly disordered regimes there is no hysteresis and the velocity-force curves are smooth. When stripe patterns are present, transport can occur at an angle to the driving direction.

Degeneracy and criticality from emergent frustration in artificial spin ice

Although initially introduced to mimic the spin-ice pyrochlores, no artificial spin ice has yet exhibited the expected degenerate ice phase with critical correlations similar to the celebrated Coulomb phase in the pyrochlore lattice. Here we study a novel artificial spin ice based on a vertex-frustrated rather than pairwise frustrated geometry and show that it exhibits a quasicritical ice phase of extensive residual entropy and, significantly, algebraic correlations. Interesting in its own regard as a novel realization of frustration in a vertex system, our lattice opens new pathways to study defects in a critical manifold and to design degeneracy in artificial magnetic nanoarrays, a task so far elusive.

Artificial ferroic systems: novel functionality from structure, interactions and dynamics

Lithographic processing and film growth technologies are continuing to advance, so that it is now possible to create patterned ferroic materials consisting of arrays of sub-1 μm elements with high definition. Some of the most fascinating behaviour of these arrays can be realised by exploiting interactions between the individual elements to create new functionality. The properties of these artificial ferroic systems differ strikingly from those of their constituent components, with novel emergent behaviour arising from the collective dynamics of the interacting elements, which are arranged in specific designs and can be activated by applying magnetic or electric fields. We first focus on artificial spin systems consisting of arrays of dipolar-coupled nanomagnets and, in particular, review the field of artificial spin ice, which demonstrates a wide range of fascinating phenomena arising from the frustration inherent in particular arrangements of nanomagnets, including emergent magnetic monopoles, domains of ordered macrospins, and novel avalanche behaviour. We outline how demagnetisation protocols have been employed as an effective thermal anneal in an attempt to reach the ground state, comment on phenomena that arise in thermally activated systems and discuss strategies for selectively generating specific configurations using applied magnetic fields. We then move on from slow field and temperature driven dynamics to high frequency phenomena, discussing spinwave excitations in the context of magnonic crystals constructed from arrays of patterned magnetic elements. At high frequencies, these arrays are studied in terms of potential applications including magnetic logic, linear and non-linear microwave optics, and fast, efficient switching, and we consider the possibility to create tunable magnonic crystals with artificial spin ice. Finally, we discuss how functional ferroic composites can be incorporated to realise magnetoelectric effects. Specifically, we discuss artificial multiferroics (or multiferroic composites), which hold promise for new applications that involve electric field control of magnetism, or electric and magnetic field responsive devices for high frequency integrated circuit design in microwave and terahertz signal processing. We close with comments on how enhanced functionality can be realised through engineering of nanostructures with interacting ferroic components, creating opportunities for novel spin electronic devices that, for example, make use of the transport of magnetic charges, thermally activated elements, and reprogrammable nanomagnet systems.

Realization of artificial ice systems for magnetic vortices in a superconducting MoGe thin film with patterned nanostructures

We report an anomalous matching effect in MoGe thin films containing pairs of circular holes arranged in such a way that four of those pairs meet at each vertex point of a square lattice. A remarkably pronounced fractional matching was observed in the magnetic field dependences of both the resistance and the critical current. At the half matching field the critical current can be even higher than that at zero field. This has never been observed before for vortices in superconductors with pinning arrays. Numerical simulations within the nonlinear Ginzburg-Landau theory reveal a square vortex ice configuration in the ground state at the half matching field and demonstrate similar characteristic features in the field dependence of the critical current, confirming the experimental realization of an artificial ice system for vortices for the first time.

Frustrated colloidal ordering and fully packed loops in arrays of optical traps

We propose that a system of colloidal particles interacting with a honeycomb array of optical traps that each contain three wells can be used to realize a fully packed loop model. One of the phases in this system can be mapped to Baxter's three-coloring problem, offering an easily accessible physical realization of this problem. As a function of temperature and interaction strength, we find a series of phases, including long range ordered loop or stripe states, stripes with sliding symmetries, random packed loop states, and disordered states in which the loops break apart. Our geometry could be constructed using ion trap arrays, BEC vortices in optical traps, or magnetic vortices in nanostructured superconductors.

Hysteresis and return-point memory in colloidal artificial spin ice systems

Using computer simulations, we investigate hysteresis loops and return-point memory for artificial square and kagome spin ice systems by cycling an applied bias force and comparing microscopic effective spin configurations throughout the hysteresis cycle. Return-point memory loss is caused by motion of individual defects in kagome ice or of grain boundaries in square ice. In successive cycles, return-point memory is recovered rapidly in kagome ice. Memory is recovered more gradually in square ice due to the extended nature of the grain boundaries. Increasing the amount of quenched disorder increases the defect density but also enhances the return-point memory since the defects become trapped more easily.

Orbital ice: an exact Coulomb phase on the diamond lattice

We demonstrate the existence of an orbital Coulomb phase as the exact ground state of a p-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that the orbital ice model exhibits an emergent geometrical frustration by mapping the degenerate quantum orbital ground states to the spin-ice states obeying the 2-in-2-out constraints on the pyrochlore lattice. We also discuss possible realization of the orbital ice model in optical lattices with p-band fermionic cold atoms.

Diversity enabling equilibration: disorder and the ground state in artificial spin ice

We report a novel approach to the question of whether and how the ground state can be achieved in square artificial spin ices where frustration is incomplete. We identify two sources of randomness that affect the approach to ground state: quenched disorder in the island response to fields and randomness in the sequence of driving fields. Numerical simulations show that quenched disorder can lead to final states with lower energy, and randomness in the sequence of driving fields always lowers the final energy attained by the system. We use a network picture to understand these two effects: disorder in island responses creates new dynamical pathways, and a random sequence of driving fields allows more pathways to be followed.

A colloidal model system with tunable disorder: solid-fluid transition and discontinuities in the limit of zero disorder

We study a colloidal model system where disorder can be continuously tuned from no disorder--corresponding to a system that can crystallize--to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.

Positive and negative drag, dynamic phases, and commensurability in coupled one-dimensional channels of particles with Yukawa interactions

We introduce a simple model consisting of two or three coupled one-dimensional channels of particles with Yukawa interactions. For the two-channel system, when an external drive is applied only to the top or primary channel, we find a transition from locked flow, where particles in both channels move together, to decoupled flow, where the particles in the secondary or undriven channel move at a slower velocity than the particles in the primary or driven channel. Pronounced commensurability effects in the decoupling transition occur when the ratio of the number of particles in the top and bottom channels is varied, and the coupling of the two channels is enhanced when this ratio is an integer or a rational fraction. Near the commensurate fillings, we find additional features in the velocity-force curves caused by the slipping of individual vacancies or incommensurations in the secondary channels. For three coupled channels, when only the top channel is driven we find a remarkably rich variety of distinct dynamic phases, including multiple decoupling and recoupling transitions. These transitions produce pronounced signatures in the velocity response of each channel. We also find regimes where a negative drag effect can be induced in one of the nondriven channels. The particles in this channel move in the opposite direction from the particles in the driven channel due to the mixing of the two different periodic frequencies produced by the discrete motion of the particles in the two other channels. In the two-channel system, we also demonstrate a ratchet effect for the particles in the secondary channel when an asymmetric drive is applied to the primary channel. This ratchet effect is similar to that observed in superconducting vortex systems when there is a coupling between two different species of vortices.

Dynamics of colloids in a narrow channel driven by a nonuniform force

Using Brownian dynamics simulations, we investigate the dynamics of colloids confined in two-dimensional narrow channels driven by a nonuniform force Fdr(y) . We considered linear-gradient, parabolic, and deltalike driving-force profiles. This driving force induces melting of the colloidal solid (i.e., shear-induced melting), and the colloidal motion experiences a transition from elastic to plastic regime with increasing Fdr. For intermediate Fdr (i.e., in the transition region) the response of the system, i.e., the distribution of the velocities of the colloidal chains upsiloni(y) , in general does not coincide with the profile of the driving force Fdr(y), and depends on the magnitude of Fdr, the width of the channel, and the density of colloids. For example, we show that the onset of plasticity is first observed near the boundaries while the motion in the central region is elastic. This is explained by: (i) (in)commensurability between the chains due to the larger density of colloids near the boundaries, and (ii) the gradient in Fdr. Our study provides a deeper understanding of the dynamics of colloids in channels and could be accessed in experiments on colloids (or in dusty plasma) with, e.g., asymmetric channels or in the presence of a gradient potential field.

Creating artificial ice states using vortices in nanostructured superconductors

We demonstrate that it is possible to realize vortex ice states that are analogous to square and kagome ice. With numerical simulations, we show that the system can be brought into a state that obeys either global or local ice rules by applying an external current according to an annealing protocol. We explore the breakdown of the ice rules due to disorder in the nanostructure array and show that in square ice, topological defects appear along grain boundaries, while in kagome ice, individual defects appear. We argue that the vortex system offers significant advantages over other artificial ice systems.

Stripes, zigzags, and slow dynamics in buckled hard spheres

We study the analogy between buckled colloidal monolayers and the triangular-lattice Ising antiferromagnet. We calculate free-volume-induced Ising interactions, show how lattice deformations favor zigzag stripes that partially remove the Ising model ground-state degeneracy, and identify the martensitic mechanism prohibiting perfect stripes. Slowly inflating the spheres yields jamming as well as logarithmically slow relaxation reminiscent of the glassy dynamics observed experimentally.