When particles are driven across crystalline surfaces, their trajectories do not necessarily follow the applied force but become locked to the substrate lattice directions. Such directional locking, being relevant for bottom-up nanodevice assembly1,2 and particle sorting3,4,5,6, has been intensively studied for isolated or single particles3,4,5,6,7,8,9,10,11. Here we experimentally study the motion of extended colloidal clusters sliding over a periodically corrugated surface. We observe that both their orientational and centre-of-mass motions become locked into directions not coinciding with the substrate symmetry but determined by the geometrical moiré superstructure formed by the cluster and substrate lattices. In general, such moiré superstructures are not strictly periodic, which leads to competing locking directions depending on cluster size. Remarkably, we uncover a dependence of directional locking on the higher Fourier components of the surface corrugation profile, which can be tuned on atomic surfaces via the external load12,13. This allows for an unprecedented control of cluster steering relevant for nanomanipulations on surfaces.
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The data that support the findings of this study are available from the corresponding author upon request.
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We thank E. Tosatti for stimulating discussions, C. Lozano for helpful discussions and suggestions, P. Graus for assisting in the characterization of topographical substrates, and N. Narinder for sharing his polyacrylamide–water solution at the beginning of the research. X.C. acknowledges funding from the Alexander von Humboldt Foundation. E.P. and A.V. acknowledge the financial support of the ERC grant no. 320796, MODPHYSFRICT.
The authors declare no competing interests.
Journal peer review information: Nature Physics thanks Pietro Tierno and the other anonymous reviewer(s) for their contribution to the peer review of this work.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Figs. 1–9 and Table 1.
Orientational and directional locking of variously sized and shaped clusters on top of a b = 5.80 µm periodic substrate. The resulting directional locking and orientation angles are θd = θo = 19.1°. In all cases, the driving force points from the left to the right of the screen. Video acceleration: 40 × real time.
Orientational and directional locking of a cluster of 86 particles at F = 62.9 fN and varied φF on top of a b = 5.80 µm substrate. The driving force always pushes horizontally left to right, and its orientation φF was changed by rotating the substrate (indicated by arrows) along the axis perpendicular to the field of view. Video acceleration: 40 × real time.
Orientational and directional locking of a cluster of 46 particles at F = 71.6 fN and various φF on top of a b = 5.80 µm substrate. The driving force always pushes horizontally left to right, and its orientation φF was changed by rotating the substrate (indicated by arrows) along the axis perpendicular to the field of view. Video acceleration: 40 × real time.
The colour-coded video for the cluster in Fig. 2a, with the same colour coding as in Fig. 2b. Stick–slip behaviour is observed and superstructures of blue particles (close to substrate minima) appear periodically when the cluster is in directional locking. Note that, after a slip motion, one nearest neighbour of each blue particle becomes a new blue particle. Video acceleration: 8 × real time.
Orientational and directional locking of variously sized and shaped experimental clusters on top of a b = 5.40 µm substrate. Observe two competing locking directions θd = 13.9° and θd = 0°, corresponding to orientations θo = 13.9° and θo = 30°, respectively. In all cases, the driving force pushes left to right. Video acceleration: 40 × real time.
A cluster sliding on a b = 5.40 µm substrate changes its orientation from θo = 13.9° to θo = 30.0° and direction of motion from θd = 13.9° to θd = 0°; namely, it changes from the (n1, n2, m1, m2) = (3, 0, 3, 1) superstructure to the (n1, n2, m1, m2) = (1, 1, 2, 0) superstructure. Video acceleration: 40 × real time.
Illustration of experimental procedure on formation and growth of clusters. After tilting a freshly made sample, small clusters form and start to slide across the substrate and thereby grow larger by absorbing particles on their way. Video acceleration: 800 × real time.
Orientational and directional locking of a cluster on a b = 6.20 µm substrate with θd = 13.9° and θo = 33.2°. The driving force goes from the left to the right of the screen. Video acceleration: 40 × real time.