Spontaneous Twirls and Structural Frustration in Moiré Materials

Structural twirls form spontaneously in the domain wall networks of some moiré materials. We show that in heterobilayers, neighboring twirl chiralities tend to antialign, forming staggered patterns that are well described by antiferromagnetic lattice ϕ^{4} theories. In moiré systems with triangular domains, this leads to frustration in the chirality configuration of the twirls and to hysteresis with respect to variation of the average twist angle and possibly other control parameters. We expect that in typical materials, the ordering temperature of twirls is about 10^{3}  K, and that thermal fluctuations in individual twirl chiralities freeze below room temperature.