Fig. 5
From: Schools of skyrmions with electrically tunable elastic interactions

Schools of skyrmions with internal clusters and chains. a, b Polarizing micrographs show schooling of skyrmions with clusters at U = 3.5 V (a) and chains at U = 4.0 V (b), where f = 50 Hz. The scale bar in a is 100 µm. c, d Normalized skyrmion count distributions ρ⊥(rcc) and ρ||(rcc) for directions perpendicular and parallel to the motion directions for clusters (c) and chains (d) shown in a, b, respectively. e Log–log plots of ΔN versus <N> for clusters (red) and chains (blue); linear fits with slope α values and a black dashed line with α = 0.5 (for reference) are displayed. f, g Computer-simulated moving cluster of seven quasi-hexagonally assembled skyrmions at U = 3.5 V displayed using arrows colored according to the color scheme in Fig. 1g. (f) and corresponding smoothly colored representation of n(r) (g). h Simulated and i experimental polarizing optical micrographs of a similar moving cluster. j, k Simulated moving linear chain of five skyrmions at U = 4.0 V (j) with corresponding smoothly colored n(r) representation (k). l Simulated and m experimental polarizing micrographs of the moving chain. Scale bars in i, m are 10 µm. Upon turning voltage off and on again while minimizing n(r), the clusters in f, j shift laterally within the computational volume by about ~0.5p. n Experimental normalized distributions for inter-skyrmion distance in chains during motion versus U for f = 50, 75, and 100 Hz. Polarizer orientations (double arrows), vs and E, are labeled throughout. The LC is the nematic ZLI-2806 doped with the chiral additive CB-15