Topological transport of magnetic colloids on non-periodic patterns

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This project aims at understanding and controlling the transport of magnetic colloidal particles above non-periodic magnetic patterns. We have ample experience studying transport in periodic patterns. There, the colloidal particles are located above the periodic pattern and are driven by an external magnetic field. The external magnetic field is uniform in space and its orientation changes in time. We perform closed loops of the orientation of the field, such that the orientation returns to the initial value after completion of one loop. Loops that wind around special orientations are topologically nontrivial and induce transport of the colloidal particles. Once the loop returns to its initial position, the particle has been transported by one unit cell of the pattern. The transport is topologically protected since it depends only on a set of topological invariants: the winding numbers of the loop around the special orientations. Due to the topological protection, the transport is robust against perturbations. This allow us to e.g. transport simultaneously a collection of different particles (e.g. colloidal rods of different lengths) along different directions. However, due to the periodicity of the pattern, we have no control over the relative position of the particles above the pattern. That is, two identical particles are transported along the same direction independently of their position above the pattern. In this combined theoretical and experimental proposal, we will study transport in non-periodic patterns. We will create patterns in which the local symmetry, the orientation, and the size of the lattice vectors depend on the space coordinates. By doing so, we will be able to control the direction and the speed of the transport as a function of the position of the particle above the pattern. We will design patterns and modulation loops that can transport identical particles along different trajectories, depending on the position of the particles above the pattern. We will also be able to transport colloidal particles from an initially unknown position to a well defined location above the pattern. From such location it will be possible to induce an arbitrarily complex trajectory on the colloidal particle. The complexity of the transport will be encoded in both the pattern and the modulation loop. For example, we will design patterns with cloaked regions that the particles will automatically avoid during their trajectories. Such cloaked regions could be used as structural elements in lab-on-a-chip devices.