Friction between solids is responsible for many phenomena such as earthquakes, wear or crack propagation1, 2, 3, 4. Unlike macroscopic objects, which only touch locally owing to their surface roughness, spatially extended contacts form between atomically flat surfaces. They are described by the Frenkel–Kontorova model, which considers a monolayer of interacting particles on a periodic substrate potential5, 6, 7, 8. In addition to the well-known stick–slip motion, such models also predict the formation of kinks and antikinks9, 10, 11, 12, which greatly reduce the friction between the monolayer and the substrate. Here, we report the direct observation of kinks and antikinks in a two-dimensional colloidal crystal that is driven across different types of ordered substrate. We show that the frictional properties only depend on the number and density of such excitations, which propagate through the monolayer along the direction of the applied force. In addition, we also observe kinks on quasicrystalline surfaces, which demonstrates that they are not limited to periodic substrates but occur under more general conditions.
Figures at a glance
Figure 1: Colloidal monolayers driven on optical interference patterns. 
a, Sketch of a colloidal monolayer driven with force F across an energy landscape created by interference of laser beams. The potential strength and length scales of these potentials can be adjusted by the laser intensity and the angle under which the laser beams intersect. b, Mean colloidal velocity v of a crystalline monolayer with lattice constant a=5.7 μm versus F for commensurate (a=s=5.7 μm, green), incommensurate (s=5.2 μm, red; s=4.8 μm, blue) and quasiperiodic (magenta) substrates. The dashed line corresponds to free sliding on a flat substrate. Inset: v for larger F where v~F. c–e, Trajectories for commensurate conditions and F=0 fN (c), 49 fN (d) and 82 fN (e). Scale bar, 30 μm.
Figure 2: Particle velocity and lattice deformation. 
a–c, Snapshots of particle velocities for commensurate conditions (a=s=5.7 μm) and F=0 fN (a), 49 fN (b) and 82 fN (c). Fast and slow particles are marked in dark and light blue depending on whether their velocities are above or below 70% of the maximum particle velocity. d–f, Voronoi tessellation with colour-coded areas of the Voronoi cells: light (large) to dark green (small). g–l, Corresponding plots for incommensurate conditions a>s=5.2 μm and driving forces 0 fN (g,j), 19 fN (h,k) and 82 fN (i,l). The laser intensity is identical to that in Fig. 1b. Scale bar, 30 μm.
Figure 3: Kink propagation through a colloidal monolayer. 
a, Propagating compression zone (dark green) on a commensurate substrate for F=40 fN. The time interval between the snapshots is 13 s. b, x component of particle trajectories marked in a (orange dots). Each particle is displaced by one lattice site (dashed lines) to the right during passage of the compression zone. c, Sketch of a kink in a particle chain on a one-dimensional substrate potential. A kink forms when two particles in the same potential well lead to a local compression in the particle chain. The mobility of kinks is larger than that of a single particle because the energy barrier required for kink motion is smaller than the substrate amplitude. Therefore, mass transport through kinks provides an effective mechanism for the motion of the chain in the direction of F. d, Sketch of an antikink, which corresponds to a local expansion in the particle chain. Antikinks move in the direction opposite to that of F.
Figure 4: Localized kinks on quasiperiodic substrates. 
a, Particle trajectories on a quasiperiodic substrate for F=46 fN (applied to the right), which is close to the depinning transition. Scale bar, 30 μm. b, Magnification of particle trajectories close to a highly symmetric motive (flower) of the substrate potential. The trajectories are colour coded and change from red to yellow to green as time proceeds. c, Angular coordinates of the particle trajectories shown in b, which suggest a correlated kink-like particle motion.
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