Fig. 1

Skyrmions and schooling. a Underwater photograph of fish schooling. b Zoomed-out grayscale polarizing optical micrograph of a school of skyrmions. The scale bar in the bottom left is 100 µm. c Photograph of the skyrmion school shown in b, visible with the unaided eye as the cloudy region within the sample. The scale bar is 1 in. d Schematic of a sample with voltage application across the LC by using transparent electrodes on the inner surfaces of the confining substrates. The dark region within the schematic represents the moving skyrmion school shown in b, c. e, f Low-magnification experimental polarizing micrographs of a region within the school at U = 0 V (e) and U = 3.5 V (f). The scale bar in the bottom left of e is 100 µm. g Numerically simulated n(r) of an individual skyrmion at U = 0 shown by arrows colored according to points on the two-sphere, as shown in the right-side inset. h, i Computer-simulated polarizing micrograph (h) closely matches its experimental counterpart (i). Numerically simulated n(r) of skyrmions at U = 3.5 V (j) and U = 4.0 V (k), with corresponding computer-simulated (l) and experimental (m) polarizing micrographs at U = 4.0 V. Bottom-left insets in g, j, k are smoothly colored representations of n(r). The scale bars in i and m are 10 µm. Directions of E, skyrmion motion velocity direction v_s, U, T_U, double arrows denoting polarizer orientations and time t are marked throughout. Numerical simulations are based on material parameters of LC mixture of nematic MLC-6609 and right-handed chiral additive CB-15 (see Methods) and d ≈ p ≈ 10 µm