Fig. 5: 2D pattern defect structure characterization.

A Schematic of the system with the patterned top substrate in pink and the bottom substrate in dark green. The inset is a schematic of the 2D pattern. B The mapping from the dot-screen pattern to the \(\pm 1\) defect lattice pattern (left) and the superposed 2D geometric square gratings formed at \(\Psi={5}^{\circ}\). C Superposed 2D geometric moiré pattern at \(\Psi\, \approx \,{36.8}^{\circ}\). D Simulated defect structure in the nematic moiré at \(\Psi={5}^{\circ}\). E, F Experimental bright field snapshots corresponding to two boxed regions in the dashed box in (B, D). G Superposed period \(T/L\) from geometric moiré pattern theory, simulation, and experiment. H Superposed tilting angle \(\omega\) from geometric moiré pattern theory, simulation, and experiment. Yellow is for the \(\Psi \le {21}^{\circ }\) regime with \(({{{{\mathrm{1,0}}}}},-{{{{\mathrm{1,0}}}}})\) as the dominating moiré, and blue is for the \(\Psi \in [{34}^{\circ },{40}^{\circ }]\) regime with dominating moiré \(\left({{{{\mathrm{1,2}}}}},-2,-1\right)\), with a singular point (infinitely large period) at \(\Psi={\tan }^{-1}(3/4).\) For the other angle ranges, \(\Psi \in [{21}^{\circ },{34}^{\circ }]\) and \(\Psi\, > \,{34}^{\circ }\), no dominating moiré is observed (using green). I Nematic moiré in simulation for \(\Psi \, \approx \,{36.8}^{\circ}\). Its period and tilting angle are \(\widetilde{T}\) and \(\widetilde{\omega }.\) J Experimental coloured POM snapshots (top) and bright field image (bottom) of a periodic defect structure at \(\Psi\, \approx \,{36.8}^{\circ}\) corresponding to the boxed region in (C). K Fast rotation simulation snapshots at \(\Psi={15}^{\circ}\) (left) and \(\Psi={180}^{\circ}\) (right) with the simulation time ratio being \({\tau }_{{{{{{\rm{s}}}}}}}\)/\({\tau }_{{{{{{\rm{cell}}}}}}}=35.4\) (“Methods”). Scale bar: \(50{{{{{\rm{\mu }}}}}}{{{{{\rm{m}}}}}}\). Source data are provided as a Source Data file.