Lattice symmetries and the topologically protected transport of colloidal particles

Abstract

The topologically protected transport of colloidal particles on top of periodic magnetic patterns is studied experimentally, theoretically, and with computer simulations. To uncover the interplay between topology and symmetry we use patterns of all possible two dimensional magnetic point group symmetries with equal lengths lattice vectors. Transport of colloids is achieved by modulating the potential with external, homogeneous but time dependent magnetic fields. The modulation loops can be classified into topologically distinct classes. All loops falling into the same class cause motion in the same direction, making the transport robust against internal and external perturbations. We show that the lattice symmetry has a profound influence on the transport modes, the accessibility of transport networks, and the individual transport directions of paramagnetic and diamagnetic colloidal particles. We show how the transport of colloidal particles above a two fold symmetric stripe pattern changes from universal adiabatic transport at large elevations via a topologically protected ratchet motion at intermediate elevations toward a non-transport regime at low elevations. Transport above four-fold symmetric patterns is closely related to the two-fold symmetric case. The three-fold symmetric case however consists of a whole family of patterns that continuously vary with a phase variable. We show how this family can be divided into two topologically distinct classes supporting different transport modes and being protected by proper and improper six fold symmetries. We discuss and experimentally demonstrate the topological transition between both classes. All three-fold symmetric patterns support independent transport directions of paramagnetic and diamagnetic particles. The similarities and the differences in the lattice symmetry protected transport of classical over-damped colloidal particles versus the topologically protected transport in quantum mechanical systems are emphasized.

Leveraging collective effects in externally driven colloidal suspensions: experiments and simulations

“…Patterned magnetic substrates, while limited in their reconfigurability, are a promising system for microfludic transport, as they allow for particle transport at quite high velocities [35]. Recent work with these substrates has demonstrated that, due underlying to lattice symmetries, certain transport paths are topologically protected [38,39]. This system has also been used to create a landscape with quenched disorder by permanently placing large obstacles at random positions on the substrate, and then studying their interaction with translating magnetic particles [40].…”

Hard topological versus soft geometrical magnetic particle transport

“…where H ext (t) is the external field at time t and H p (x A ) is the magnetic field created by the pattern at position of the particle x A in action space A, see Refs. [22,23]. The particles interact via the purely repulsive Weeks-Chandler-Andersen potential where r is the distance between the particles, fix our unit and energy, and σ is the effective particle length that we fix to σ/a = 0.2 which is the same as in the experiments (transport of single spheres).…”

Preferential weakening of rotational magnetic anisotropy by keV-He ion bombardment in polycrystalline exchange bias layer systems

“…Its possible use in creating magnetic logic elements has similarly been proven [14] as its potential to create engineered domain patterns by ion beam writing or when combined with lithographical techniques [1,4,[15][16][17]. The latter patterns have shown to be useful for magnetic particle transport by moving domain walls [18], by changing potential energy landscapes associated with the stray fields above the engineered domains [19,20] or by topological transport [21].…”