Fig. 1: Topological structures and 3D network colloidal assembly in a 1D splay-bend cusp-like nematic moiré pattern.

A Schematic of the system with a patterned top substrate (pink) rotated by an angle \(\Psi\) and an identically patterned, fixed bottom substrate (dark green). Short rods represent surface-preferred nematic orientations, and the geometric periodicity of the pattern is \(L\). B Mapping from the geometric cosinsoidal pattern to the nematic surface pattern. Top and side views of the simulated defect structures at \(\Psi={12}^{\circ}\) when \(H/L=0.3\) (C), \(H/L=0.7\) (D) and \(H/L=0.9\) (E) (colored by angle \(\beta\)). In (E), the 1st group of disclinations is near the top surface, and the 2nd group defect is generated close to the bottom surface. F Defect state diagram in terms of \(H/L\) and \(\Psi\), blue dotted line for \({\Psi=12}^{\circ}\) and red dotted line for \(H/L=0.43\) (Fig. 2E, F). G Periodic, helical topological structure of the C-state (colored by angle \(\beta\)). H Topological structure of the S-state and W-state (colored by angle \(\alpha\)). I–K Corresponding POM images for the S-, C-, and W-states at \(\Psi\, \approx \,{12}^{\circ}\) showing good agreement with the simulation. Using confocal microscopy to scan the cell from top to bottom, we observe L disclination lines (the first group) close to the top substrate and M the disclination lines (the second group) appearing near the bottom substrate. N, O Two 3D rotation views of the sample to visualize the two groups at the same time. \({z}_{c}\) is the spacing between the two groups in the scanning process, \({z}_{c}=40{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\). N When the two groups of disclinations are visualized from the cell top at the same time, the bright lines are the first group disclination lines, close to the top substrate. O Viewing the sample from the cell bottom. Both groups of lines are shown due to the scattering effect, and the second group of lines close to the bottom substrate is in gray because of lower contrast. P 3D colloidal assembly in the W-state. Scale bar: 50 μm.