Topological transport of magnetic colloids on non-periodic patterns

本项目旨在了解和控制非周期性磁性图案上方磁性胶体颗粒的传输。我们有丰富的经验研究周期性模式的运输。在那里，胶体颗粒位于周期性图案上方，并由外部磁场驱动。外部磁场在空间上是均匀的，其方向随时间变化。我们执行场的方向的闭合循环，使得方向在一个循环完成后返回到初始值。环绕特定方向的环在拓扑上是非平凡的，并诱导胶体粒子的传输。一旦环返回到其初始位置，粒子就被图案的一个单位单元传输。运输是拓扑保护的，因为它只依赖于一组拓扑不变量：围绕特殊方向的环的缠绕数。由于拓扑保护，传输对扰动是鲁棒的。这允许我们例如沿着沿着不同方向同时运输不同颗粒（例如不同长度的胶体棒）的集合。然而，由于图案的周期性，我们无法控制图案上方粒子的相对位置。也就是说，两个相同的颗粒沿沿着相同的方向传输，而与它们在图案上方的位置无关。在这个理论和实验相结合的方案中，我们将研究非周期性模式中的输运。我们将创建图案，其中晶格向量的局部对称性、方向和大小取决于空间坐标。通过这样做，我们将能够根据粒子在图案上方的位置来控制传输的方向和速度。我们将设计图案和调制回路，它们可以根据图案上方粒子的位置，沿沿着不同的轨迹传输相同的粒子。我们还将能够将胶体颗粒从最初未知的位置运输到图案上方的明确位置。从这样的位置，将有可能在胶体颗粒上诱导任意复杂的轨迹。传输的复杂性将被编码在模式和调制环路中。例如，我们将设计带有隐形区域的图案，粒子将在其轨迹中自动避开这些区域。这种隐形区域可以用作芯片实验室设备中的结构元件。

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.