Orientational ordering, buckling, and dynamic transitions for vortices interacting with a periodic quasi-one-dimensional substrate

Abstract

We examine the statics and dynamics of vortices in the presence of a periodic quasi-one dimensional substrate, focusing on the limit where the vortex lattice constant is smaller than the substrate lattice period. As a function of the substrate strength and filling factor, within the pinned state we observe a series of order-disorder transitions associated with buckling phenomena in which the number of vortex rows that fit between neighboring substrate maxima increases. These transitions coincide with steps in the depinning threshold, jumps in the density of topological defects, and changes in the structure factor. At the buckling transition the vortices are disordered, while between the buckling transitions the vortices form a variety of crystalline and partially ordered states. In the weak substrate limit, the buckling transitions are absent and the vortices form an ordered hexagonal lattice that undergoes changes in its orientation with respect to the substrate as a function of vortex density. At intermediate substrate strength, certain ordered states appear that are correlated with peaks in the depinning force. Under an applied drive the system exhibits a rich variety of distinct dynamical phases, including plastic flow, a density-modulated moving crystal, and moving floating solid phases. We also find a dynamic smectic-to-smectic transition in which the smectic ordering changes from being aligned with the substrate to being aligned with the external drive. The different dynamical phases can be characterized using velocity histograms and the structure factor. We discuss how these results are related to recent experiments on vortex ordering in thin films with periodic thickness modulations. Our results should also be relevant for other types of systems such as ions, colloids, or Wigner crystals interacting with periodic quasi-one-dimensional substrates.

Structures and diffusion of two-dimensional dusty plasmas on one-dimensional periodic substrates

“…There are a variety of two-dimensional (2D) systems that can be effectively described as a collection of particles interacting with a periodic one-dimensional (1D) substrate. Specific examples of such systems include charged colloids on optical trap arrays [1][2][3][4][5], magnetic particles on patterned surfaces [6,7], vortices in type-II superconductors with 1D periodic pinning arrays [8][9][10][11][12][13], vortices in Bose-Einstein condensates on 1D optical arrays [14], and the ordering of molecules and atoms on anisotropic surfaces [15,16]. In these systems, a variety of distinct commensurate-incommensurate transitions occur along with multiple ordering or disordering transitions as functions of the substrate strength or the ratio of the number of particles to the number of substrate minima, known as the filling factor.…”

Thickness-modulated tungsten–carbon superconducting nanostructures grown by focused ion beam induced deposition for vortex pinning up to high magnetic fields

“…Given the broad range of magnetic field and temperature where matching effects have been observed in these W–C films, this material could be interesting to probe dynamical effects of the vortex lattice with one-dimensional pinning potentials. This was recently studied theoretically and showed a rich phase diagram [52]. These W–C films are also convenient for fundamental studies regarding the nature of the vortex-glass to vortex-liquid transition under one-dimensional pinning potential given that previous studies in flat W–C films without artificial pinning have shown good scaling behavior [18].…”

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

“…In experiments with laser beams, researchers have successfully prepared substrates with different geometries like quasi-crystalline substrates, 20 2D periodic substrates 21 and quasiperiodic substrates. 22,23 Studies with such substrates reveal a variety of phenomena like a commensurate–incommensurate phase transition, 24–27 pinning-depinning transitions. 28–31 There are a wide variety of particle-like systems coupled with the underlying substrate exhibit depinning transition with the external driving forces.…”