Topologically protected colloidal transport above a square magnetic   lattice
  We theoretically study the motion of magnetic colloidal particles above a magnetic pattern and compare the predictions with Brownian dynamics simulations. The pattern consists of alternating square domains of positive and negative magnetization. The colloidal motion is driven by periodic modulation loops of an external magnetic field. There exist loops that induce topologically protected colloidal transport between two different unit cells of the pattern. The transport is very robust against internal and external perturbations. Theory and simulations are in perfect agreement. 
Daniel de las Heras, Johannes Loehr, Michael Loenne, and Thomas M.   Fischer
cond-mat.soft