Coexisting orbits and chaotic dynamics of a confined self-propelled particle.

We investigate theoretically the dynamics of a confined active swimmer with velocity and orientation axis coupled to each other via a self-alignment torque. For an isotropic harmonic potential, this system is known to exhibit two distinct dynamical phases: a climbing one, where the particle is oriented radially and undergoes angular Brownian motion, and a circularly orbiting phase. Here we show that for nonradially symmetric confinement an assortment of complex phenomena emerge. For an elliptic harmonic potential the orbiting phase splits into several periodic orbits with a diversity of shapes: ovals, lemniscates, and generalized lemniscates with multiple lobes. These orbits can coexist in the parameter space and decay into one another induced by noise. For anharmonic confining potentials, we report transitions from periodic to chaotic dynamics, as one changes the intensity of the self-alignment torque and noise-induced complex orbits. These results demonstrate that the combination of the shape of the trapping potential and self-alignment torque can induce a rich variety of nontrivial dynamical states of a confined active particle.

Mesoscale Phase Separation of Skyrmion-Vortex Matter in Chiral-Magnet-Superconductor Heterostructures.

We investigate theoretically the equilibrium configurations of many magnetic skyrmions interacting with many superconducting vortices in a superconductor-chiral-magnet bilayer. We show that miscible mixtures of vortices and skyrmions in this system break down at a particular wave number for sufficiently strong coupling, giving place to remarkably diverse mesoscale patterns: gel, stripes, clusters, intercalated stripes, and composite gel-cluster structures. We also demonstrate that, by appropriate choice of parameters, one can thermally tune between the homogeneous and density-modulated phases.

Conformal Vortex Crystals.

We investigate theoretically globally nonuniform configurations of quantized-flux vortices in clean superconductors trapped by an external force field that induces a nonuniform vortex density profile. Using an extensive series of numerical simulations, we demonstrate that, for suitable choices of the force field, and bellow a certain transition temperature, the vortex system self-organizes into highly inhomogeneous conformal crystals in a way as to minimize the total energy. These nonuniform structures are topologically ordered and can be mathematically mapped into a triangular Abrikosov lattice via a conformal transformation. Above the crystallization temperature, the conformal vortex crystal becomes unstable and gives place to a nonuniform polycrystalline structure. We propose a simple method to engineer the potential energy profile necessary for the observation of conformal crystals of vortices, which can also be applied to other 2D particle systems, and suggest possible experiments in which conformal or quasi-conformal vortex crystals could be observed in bulk superconductors and in thin films.