Symmetry locking and commensurate vortex domain formation in periodic pinning arrays

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

We review the depinning and nonequilibrium phases of collectively interacting particle systems driven over random or periodic substrates. This type of system is relevant to vortices in type-II superconductors, sliding charge density waves, electron crystals, colloids, stripe and pattern forming systems, and skyrmions, and could also have connections to jamming, glassy behaviors, and active matter. These systems are also ideal for exploring the broader issues of characterizing transient and steady state nonequilibrium flow phases as well as nonequilibrium phase transitions between distinct dynamical phases, analogous to phase transitions between different equilibrium states. We discuss the differences between elastic and plastic depinning on random substrates and the different types of nonequilibrium phases which are associated with specific features in the velocity-force curves, fluctuation spectra, scaling relations, and local or global particle ordering. We describe how these quantities can change depending on the dimension, anisotropy, disorder strength, and the presence of hysteresis. Within the moving phase we discuss how there can be a transition from a liquid-like state to dynamically ordered moving crystal, smectic, or nematic states. Systems with periodic or quasiperiodic substrates can have multiple nonequilibrium second or first order transitions in the moving state between chaotic and coherent phases, and can exhibit hysteresis. We also discuss systems with competing repulsive and attractive interactions, which undergo dynamical transitions into stripes and other complex morphologies when driven over random substrates. Throughout this work we highlight open issues and future directions such as absorbing phase transitions, nonequilibrium work relations, inertia, the role of non-dissipative dynamics such as Magnus effects, and how these results could be extended to the broader issues of plasticity in crystals, amorphous solids, and jamming phenomena.

Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors

It was recently proposed to use the stray magnetic fields of superconducting vortex lattices to trap ultracold atoms for building quantum emulators. This calls for new methods for engineering and manipulating of the vortex states. One of the possible routes utilizes type-1.5 superconducting layered systems with multi-scale inter-vortex interactions. In order to explore the possible vortex states that can be engineered, we present two phase diagrams of phenomenological vortex matter models with multi-scale inter-vortex interactions featuring several attractive and repulsive length scales. The phase diagrams exhibit a plethora of phases, including conventional 2D lattice phases, five stripe phases, dimer, trimer, and tetramer phases, void phases, and stable low-temperature disordered phases. The transitions between these states can be controlled by the value of an applied external field.

A radio-frequency coil for the microwave characterization of vortex dynamics in thin film superconductors

A radio-frequency coil for the experimental investigation of the magnetic properties of thin superconducting films under microwave fields at different values of temperature and dc magnetic field has been developed. The system has been used for low-temperature microwave frequency-dependent magnetization measurements in a Pb thin film with an engineered periodical antidot array. The characteristic frequencies and the electric and magnetic fields of the resonant system formed by a multi-turn coil with a sample loaded in its core are estimated using the helical approach. A good agreement of the calculated values with those recorded in swept-frequency spectra is obtained. The relation between the characteristics of the resonant structure and the frequency-driven magnetic response of the sample at different nominal microwave powers documents the capability and sensitivity of the layout.

Strongly enhanced pinning of magnetic vortices in type-II superconductors by conformal crystal arrays

Conformal crystals are nonuniform structures created by a conformal transformation of regular two-dimensional lattices. We show that gradient-driven vortices interacting with a conformal pinning array exhibit substantially stronger pinning effects over a much larger range of field than found for random or periodic pinning arrangements. The pinning enhancement is partially due to matching of the critical flux gradient with the pinning gradient, but the preservation of local ordering in the conformally transformed hexagonal lattice and the arching arrangement of the pinning also play crucial roles. Our results can be generalized to a wide class of gradient-driven interacting particle systems such as colloids on optical trap arrays.

Wire network behavior in superconducting Nb films with diluted triangular arrays of holes

We present results of transport measurements on superconducting Nb films with diluted triangular arrays (honeycomb and kagomé) of holes. The patterned films have large disk-shaped interstitial regions even when the edge-to-edge separations between nearest neighboring holes are comparable to the coherence length. Changes in the field interval of two consecutive minima in the field dependent resistance R(H) curves are observed. In the low field region, fine structures in the R(H) and T(c)(H) curves are identified in both arrays. Comparison of experimental data with calculation results reveals that these structures observed in honeycomb and kagomé hole arrays resemble those in wire networks with triangular and T(3) symmetries, respectively. The findings suggest that even in these specified periodic hole arrays with very large interstitial regions, the low field fine structures are determined by the connectivity of the nanostructures.

Effect of half-quantum vortices on magnetoresistance of perforated superconducting films

Recent cantilever magnetometry measurements of annular micron-size samples of Sr2RuO4 have revealed evidence for the existence of half-quantum vortices (HQVs) in this material [J. Jang et al., Science 331, 186 (2011)]. We propose to look for HQVs in transport measurements and calculate magnetoresistance of a perforated superconducting film close to the transition temperature in the presence of HQVs. We analyze the dependence of magnetoresistance on the thermodynamic stability of HQVs which, according to Jang et al., can be varied by the application of an in-plane magnetic field and point out features which may help to identify them.

Formation of stripelike flux patterns obtained by freezing kinematic vortices in a superconducting Pb film

We demonstrate experimentally and theoretically that the dissipative state of superconducting samples with a periodic array of holes at high current densities consists of flux rivers resulting from a short-range attractive interaction between vortices. This dynamically induced vortex-vortex attraction results from the migration of quasiparticles out of the vortex core (kinematic vortices). We have directly visualized the formation of vortex chains by scanning Hall probe microscopy after freezing the dynamic state by a field cooling procedure at a constant bias current. Similar experiments carried out in a sample without holes show no hint of flux river formation. We shed light on this nonequilibrium phenomena modeled by time-dependent Ginzburg-Landau simulations.

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.

Spontaneous transverse response and amplified switching in superconductors with honeycomb pinning arrays

Using numerical simulations, we show that a novel spontaneous transverse response can appear when a longitudinal drive is applied to type-II superconductors with honeycomb pinning arrays in a magnetic field near certain filling fractions. This response is generated by dynamical symmetry breaking that occurs at fields away from commensurability. We find a coherent strongly amplified transverse switching effect when an additional transverse ac drive is applied. The transverse ac drive can also be used to control switching in the longitudinal velocity response. We discuss how these effects could be used to create new types of devices such as current effect transistors.

Point-defect dynamics in two-dimensional colloidal crystals

We study the topological configurations and dynamics of individual point defect vacancies and interstitials in a two-dimensional crystal of colloids interacting via a repulsive Yukawa potential. Our Brownian dynamics simulations show that the diffusion mechanism for vacancy defects occurs in two phases. The defect can glide along the crystal lattice directions, and it can rotate during an excited topological transition configuration to assume a different direction for the next period of gliding. The results for the vacancy defects are in good agreement with recent experiments. For interstitial point defects, which were not studied in the experiments, we find several of the same modes of motion as in the vacancy defect case along with two additional diffusion pathways. The interstitial defects are more mobile than the vacancy defects due to the more two-dimensional nature of the diffusion of the interstitial defects.

Observation of vortex pinning in Bose-Einstein condensates

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.

Vortex-antivortex nucleation in magnetically nanotextured superconductors: magnetic-field-driven and thermal scenarios

Within the Ginzburg-Landau formalism, we predict two novel mechanisms of vortex-antivortex nucleation in a magnetically nanostructured superconductor. Although counterintuitive, nucleation of vortex-antivortex pairs can be activated in a superconducting (SC) film covered by arrays of submicron ferromagnets (FMs) when exposed to an external homogeneous magnetic field. In another scenario, we predict the thermal induction of vortex-antivortex configurations in SC-FM samples. This phenomenon leads to a new type of Little-Parks oscillations of the FM magnetization-temperature phase boundary of the SC film.